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Blackjack Strategy Puzzle

Shouldn’t You Hit?

by Arnold Snyder
(From Blackjack Forum Volume XXI #2, Summer 2001)
© Blackjack Forum 2001

Four blackjack players, all of them professional gamblers, were sitting at a quarter table in a Vegas Strip casino. I stopped to watch the game because the bets on the table were unusual. Two players had bet the table minimum — $25; one player had bet the max — $2000; and the other player had a $200 bet on the hand. Often, if I see a pro playing, I can tell whether the count is positive or negative by looking at his bet size. Here I was looking at four pros, and I didn’t have a clue. It was a typical six-deck Strip game with all the good rules – including DAS and surrender.

I knew each of the four players, but to my knowledge, none of them knew each other. I suspected that they had each independently chosen this table, unaware that the other players at the table were also pros. Pros don’t generally like to sit down with other pros because their bets tend to mimic each other’s as the count rises and falls. One thing I do know about those who have been playing professionally for any length of time, however, is that their strategies, on the surface, are not easy to analyze. That, in fact, is what has kept those with staying power in the game.

As it happened, the round I stopped to watch was one of the most unusual rounds of blackjack I would ever witness. Every one of the four players was dealt a pair of 4s! I won’t waste any time estimating the odds against four players at the same table being dealt identical pairs. As it turned out, that was not the most unusual occurrence in this round. What truly boggled my mind was the way each player played his hand. The dealer had a deuce up. Here’s what happened:

The first player doubled down.

The second player split the pair.

The third player stood.

And the fourth player surrendered!

As any neophyte basic strategy player knows, the correct way to play a pair of 4s versus a deuce is to treat the hand as a hard eight, and hit. Yet, not only did no player hit his hand as expected, but every player played the hand differently from every other player!

I wandered away from the pit scratching my head. Over the next few days, I contacted each of the four players to find out why each had bet and played his respective identical hand so inexplicably.

As I suspected, none of the four did know any of the others. As soon as I mentioned that I had witnessed this bizarre round with four pairs of 4s, each player immediately recalled the round, and commented on the absurd plays the others at the table had made; but every one defended his own weird play.

Here are their explanations…

The first player, who had the $2K table limit bet, said: “I was tracking the shuffle and I was in a monster slug of high cards. That’s why I had the big bet out. When all those 4s hit the felt, I was stunned, because it meant the remainder of the slug was even richer in high cards. Generally, when you’ve got a pair of 4s against any dealer low card in a DAS game, splitting the 4s supersedes doubling down on the eight total. But not with 4s against a deuce. With Hi-Lo, you can double down hard eight versus 2 at a true of +13, but you need +15 to split the 4s. Using the NRS formula, I estimated this slug was now up around +13 to +14, but not quite high enough to split, so I doubled down. I played the hand correctly.”

The second player, who had a $200 bet on the hand, said: “I was counting, and the count was up, so I had a mid-size bet out. This was a rookie dealer and to my amazement, she flashed her hole card! It’s pretty unusual to get a hole card on a shoe game, but she was very clumsy with the cards and caught the edge of her hole card on her upcard when she was doing the turn over. She probably trained at home and had some uncle in the pit who had juiced her into the job. With four of us sitting there with a pair of 4s, imagine how shocked I was to see she had a 4 in the hole! What are the odds? But essentially, I wasn’t playing my pair of 4s against a deuce; I was facing a hard 6. With any plus count, the best play is to split your 4s against a 6 in a DAS game. So I split. I played the hand correctly.”

The third player, with a $25 table minimum bet, said: “The fact is, I was looking for a good cheap camouflage play when I got those 4s. I had beaten that joint out of a lot of money in my last few sessions, so I was in there to slow play it, lay some cover, and feel them out for heat. The count was up, but I had a small bet out because I had lost a number of hands in a row; I didn’t want to raise my bet after losses. A hard eight against a deuce only has a negative expectation of about -2% if you play it correctly and hit. The dealer’s got about a 35% probability of busting when he shows a deuce. But I’m side-counting the 7s, 8s, and 9s, and I know that the shoe is virtually depleted of all of these cards! I know his bust probability is actually much higher than 35%. With a normal distribution of these cards, standing would cost me 65% of $25, or about $16. But with the positive count, and very few 7s, 8s, and 9s left in the shoe, I figure his bust probability is closer to 50%. Since my bet’s only $25 on the hand, I figure it’s maybe costing me twelve bucks for making what looks like the stupidest play on earth, standing on an eight total against a deuce! Did you see the boss smirking when I made that play? Of course, I acted like it was an accident, and I misread my hand as a twelve, but that idiot play bought me a lot of time in that joint. I played the hand correctly.”

The fourth player, who had also bet $25, said: “I wasn’t playing a count game. I was sequencing the aces. I had the table to myself for the previous shoe, then those jerks showed up. I was going to leave, but figured I’d play out this last shoe on the off chance I could catch one of my aces, despite having these other players crowding the game. The last hit card that was dealt to the jerk who split his fours was the third key card I was looking for to indicate an ace was coming. The first two keys were 4s. Since my sequence cards tend to be spaced about seven cards apart with this shuffle, it appeared at that point that I’d never get the ace myself. With two players and the dealer left to play out their hands, then three players in front of me on the next round, I had no hope. Then, the imbecile to my right stands! He uses no cards! It occurs to me that if I use no cards, I’ve got an excellent chance of steering that ace to myself on the next round, provided the dealer uses only one card, maybe two, for his own hand. So I surrendered. The dealer only busts about 35% of the time with a deuce up, so standing would cost me -65%. Surrender, at -50%, has a higher EV than standing. I was basically paying $12.50 for the ace on the next round, when I intended to spread to two hands of table max. That’s a small price to pay for an ace. I played the hand correctly.”

Anyway, the dealer hit to a 7-card 21, wiping out all bets except for the guy who had surrendered (though assuring the surrenderer that he would not get the ace he was hoping for on the next round).

Blackjack, alas, is always a game of probabilities. Virtually nothing is ever certain. Because of this, there may be numerous “correct” ways to play a hand or bet on a round. The betting and playing strategies of a traditional card counter, a shuffle tracker, a hole card player, and an ace sequencer, sitting at the same table, will make little sense to each other. Yet, all of them are playing with an advantage, and playing correctly, given the information that each is using.

The two players who made the most inane looking plays — standing and surrendering — both had a pretty good idea what these plays cost, in dollars, based on the percentage of time the dealer will bust with a deuce up, or the depletion of 7s, 8s, and 9s, or the potential value of an approaching ace.

What is the moral of this story?

Simply this: Those players who continue to play blackjack at a professional level are often invisible to the casinos because their blackjack strategies are invisible even to each other. They are looking for opportunities that don’t show up in the Blackjack Survey Voice analysis. Everybody in the pit knows what a card counter’s blackjack strategy looks like these days. If you’re going to make it now, you won’t look like a counter. Your blackjack play would make perfect sense, but it would leave Arnold Snyder himself scratching his head in bewilderment. ♠

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Non-Random Shuffle Discoveries

Shoehenge: Probing the Mysteries of the Non-Random Shuffle

by Arnold Snyder
(Blackjack Forum Vol. X #4, December 1990)
© Blackjack Forum 1990

[Arnold Snyder is the author of The Blackjack Shuffle Tracker’s Cookbook: How Players Win (and Why They Lose) With Shuffle-Tracking.]

Many times over the years I have had to eat my own words. So many times, in fact, that my words have become an essential part of my diet.

How often have I insisted in print and otherwise that any non-random shuffle that you are likely to find at a casino blackjack table makes no difference whatsoever to your expectation as a player?

Hold the phone…

Whoops!

What I meant was…

That is to say…

You see, this computer freak named Imming comes out of nowhere with this program that mimics human shuffles. And you start playing with it and testing it and gaining confidence in its results, because all of the results seem to support what you already know and already believe.

The thing is, there are hundreds of serious players out there who now own this software, and they’re all running tests that just a year ago would have been impossible for any average player to run because software like this wasn’t available at any price. So, it’s inevitable that letters start coming in from players who are using this software asking why they’re getting such and such weird results when they set up certain weird conditions. Most of these results can be explained pretty easily. And then one day, hmmm… What have we here?

Hmmm…

Set the table, baby.

It’s word eating time again.

Recap of Earlier Research on Non-Random Shuffles

If you haven’t read the feature article in the March ’90 issue of Blackjack Forum (Vol. X #1), “Ruffled by the Shuffle,” I would suggest you read that article as background material for this one. In that article, I not only reviewed numerous previous computer studies on non-random shuffles — by Stanford Wong, Dr John Gwynn, Mason Malmuth, and Percy Diaconis, I published a lot of data I had personally obtained using John Imming’s Real World Casino software.

A brief recap of the results indicate:

  1. That the play of the hands without any shuffling puts the cards into an order that favors the players.
  2. Multiple players at the table diminish this no-shuffle advantage.
  3. Even the slightest shuffling eliminates the player advantage completely, making the results no different from those obtained with a completely random shuffle.
  4. Card counting systems work just as well with the random and non-random shuffles.
  5. Winning and losing “streaks” are not predictable by looking at previous wins/losses, regardless of whether or not the shuffle is random or non-random.
  6. Even if new decks are brought into play every 50 shuffles, with all shuffles being grossly inadequate – far sloppier than you could ever hope to find in a casino – the player results show no significant difference from what you would expect with a completely random shuffle.

My readers, however, cynical, mistrustful bunch that you are, still were not satisfied.

One reader wrote: “It is interesting to see that it doesn’t take much of a shuffle to return the players’ expectation to normal. But what happens immediately after new decks are brought into play? We often see short runs of cards m sequence by suit, indicating that the initial shuffle was poor. Although your simulations show that the players’ expectations average out to about normal when new decks are brought in every 50 shuffles, is a player’s expectation normal on the first round after fresh decks are put into play?”

The Effect of New-Deck Order on Blackjack Basic Strategy Players

This was an interesting question which had not previously been answered. The first simulation I set up to discover the effect of cards in new deck order on basic strategy players. I set up an 8-deck shoe in new deck order, put seven players at the table, all using basic strategy, and played through six of the eight decks with Atlantic City rules. No shuffle was done, not even a cut. I just played through that one shoe in new deck order.

The house lost at the rate of 28%, 6 of the 7 players won. First base won at the rate of 67%. There’s nothing all that exciting about this weird result. Obviously, we’ll never find a casino that will offer this game.

Next, I tried the same game with one difference — a random cut was performed prior to the deal. Now the house lost at the rate of only 15%. But 5 of the 7 players won, first base taking top gain again with a 38% win rate. Interesting, but of no practical value.

Next, I performed a “wash” on the decks which consisted of cards being picked up in clumps of up to 8 cards in sequence. This is the “gross wash” in version 3.0 of Imming’s RWC Universal Blackjack Engine. Then, with no other shuffling, the cards were dealt. With this wash, 35 out of every 36 cards dealt are in new-deck sequences, running up or down; the length of the sequences varies from 2 to 8 cards. At the end of every shoe, I started again with fresh decks. I ran 10 million hands for each player.

With a single player at the table, the effect of the sequences again worked to the basic strategy player’s advantage. Instead of losing at the rate of 0.5%, the player won at the rate of 1%.

Seating Position and Non-Random Shuffles

With three players at the table, however, it became obvious that seating position is everything when the cards are in sequential order. The first base player’s expectation was still 1.5% above his normal basic strategy expectation. The third base player’s expectation, however, was 1.2% below his random basic strategy expectation. The player in the middle seat, was about a quarter percent below normal.

Running simulations for various numbers of players at the table, the trend was obvious: the first base side of the table wins; the third base side loses. With a full table, seven players, the first three players at the table all do notably better than they would expect from basic strategy. The player sitting dead center, seat 4, is only about 0.1% over his basic expectation. The players in seats 5, 6, and 7 do not do so well. Seat 5 does about 0.4% worse than he’d expect with a random shuffle. Seat 6 does 1.9% worse. And seat 7, third base, loses at a rate 4.5% worse than his random shuffle expectation.

Although we’ll never find a casino that will deal unshuffled cards, these tests provide us with some insight into the ways sequences affect players. Even when changing penetration levels and the number of decks in play, as well as the number of players at the table, cards in new-deck sequences are advantageous for the first base players and disadvantageous for third base.

Card Counting and Non-Random Shuffles

I then tested a theory of the non-random shuffle system proponents—that card counting wouldn’t work if the cards were in sequences. With seven players at the table, and no shuffling—just that one gross wash—card counting was actually much stronger than when the cards are in random order.

With a random shuffle, betting one unit on advantageous hands only, the player’s average gain over his basic strategy expectation is about 1.3%. With just a gross wash, however, this same betting strategy raised the counter’s expectation by 2.2%! Again, the lion’s share of the profits went to the first base side of the table. Third base still loses, though at a slower rate.

Is it possible for players to make money by seeking out poorly shuffled new decks and sitting at first base?

Probably not.

Remember, these results are all for playing new-deck sequences with decks that haven’t been shuffled at all, but simply “rearranged” in sequential clumps of varying length. All casino dealers, in fact, shuffle.

However, these results do indicate that sequential cards have a notable effect that varies by seating position. We’ve all seen short sequences of unshuffled cards come out immediately after new decks have been brought into play. Certainly, not 35 out of 36 cards, as in this simulation test, but the fact remains that sequences have measurable effects. The question is: How much of the sequential effect will be retained through a sloppy shuffle, and how many shuffles does it take until the game returns to normal?

As soon as I put in two very gross riffles, even on the first round after the shuffle, the first base player’s advantage completely disappeared. The third base player, who had been losing at a rate 4.5% worse with a gross wash than his expectation with a random shuffle, was still losing after two gross riffles, but only at a rate of 1.4% worse. But 1.4% is a significant amount!

Does this mean that the third base side of the table should be avoided immediately after new decks are introduced?

Possibly. The gross wash and two gross riffles I used in this simulation were, to be sure, still far more gross than anything you’d expect to find in a real casino. A “wash” that retains 35 out of 36 cards in new-deck sequences would be highly unusual.

And Imming’s “gross riffle” interleaves cards equally in one, two, three and four card clumps. Empirical studies of professional dealers show that pros almost never riffle a four-card clump, and rarely a three-card clump. The new-deck sequences we see after fresh decks have been brought into play are more likely caused by “lopsided” picks which leave a relatively small proportion of the cards unriffled.

When I tested a more thorough shuffle, however, which was poor but not impossible, all seven players at the table lost more on the first hand after the shuffle than they would expect to lose with a completely random shuffle. With a finer wash, and two “fine riffles,” first base did best again, but lost at a rate of about 0.2% below his random basic strategy expectation. Third base did worst, losing at a rate of 0.6% below his random expectation.

One interesting discovery was that when a card counting strategy was used, the discrepancies between the first-base and third-base win rates disappeared. Although basic strategy players who play through all hands do notably worse on the third base side of the table, card counters (who leave the table when their advantage disappears) all win at approximately the same rate regardless of seating position. This indicates that the third base disadvantage occurs at negative counts. For some reason, the negative counts do not affect the first base side of the table in the same negative way.

It must also be noted that on the first round after a poor shuffle on fresh decks, as described above, even the card courters’ win rates were all about 0.3% below what their expectation would be with a completely random shuffle. Counting still beats the game, but at a slower rate.

Eddie Olsen’s Phase II System for Non-Random Shuffles with “Card Clumping”

This raises the question: is it possible that a different basic strategy might be advisable if the player knows that a significant portion of the cards are in new-deck sequences? I know of one such strategy that has been published. In July of 1987, Eddie Olsen (inventor of the TARGET system), in his Blackjack Confidential newsletter, published a new basic strategy he called “Phase II,” specifically designed for games with like-card clumping, and especially for poor washes and insufficient shuffles on new decks.

Then in July of 1988, he published a revised version of the Phase II strategy based on more extensive empirical data. Olsen suggests in his revised Phase II article that the player can test the Phase II strategy by dealing and playing through an unshuffled 4-deck shoe and comparing the results to the standard basic strategy results. (Olsen did not, incidentally, mention that seating position might affect the player or the strategy.)

I tried a somewhat different test. I played through six decks in new deck order with no shuffle, first with basic strategy, then with Phase II. With basic, the player won at a rate of 44.7%. With Phase II, the player’s win rate went up to 52.6% – a gain of almost 8% just by altering the basic strategy!

But, had Olsen discovered a real strategy that could milk the new deck sequences caused by an inadequate shuffle? No casino, in fact, would deal a game off the top of new decks with no shuffling whatsoever. I wanted to see what would happen in the 8-deck game, 75% dealt, A C. rules, with 7 players at the table, when the cards were in sequences, but grossly washed.

I used Imming’s gross wash again which leaves 35 out of 36 cards in new-deck sequences, with no other shuffling. Unfortunately, even this minimal reordering of the cards invalidated Olson’s Phase II strategy. These are the results, after 140 million hands for each simulation (20 million for each individual player), showing the overall house advantage, and each player’s advantage by seating position:

 House:P1P2P3P4P5P6P7
Basic:+1.1+0.4+0.5+0.1-0.4-0.9-2.4-5.0
Ph II:+2.3-1.3-0.8-1.1-1.6-2.2-3.4-5.1

Phase II, unfortunately, killed the advantage on the first base side of the table. Varying the number of players at the table, and using various sloppy shuffles, all of the Phase II results I obtained indicate that this strategy would be ill-advised when cards are clumped in new deck sequences (unless no shuffling at all is done).

Olsen states that his strategy was devised by analyzing the results of some 468,000 hands played in the A C casinos over a six-year period. I would guess this is why his strategy fails. Although 468,000 hands may seem like a lot to any one player, it is statistically insignificant for purposes of devising a playing strategy.

Olsen, for instance, in his Phase II strategy, changed 26 of the basic strategy pair split decisions. According to Julian Braun’s simulation studies (How to Play Winning Blackjack, p.82), some of these pair split decisions will occur only 38 times per 100,000 hands. So, in an observation of 468,000 hands, we’d expect to see these hands only about 178 times each.

Many of the individual hit/stand decisions would not be observed more than a couple thousand times each. In devising a strategy via simulation, it is often necessary to play out more than a million hands for each individual decision. Basing your decisions on the results of a few hundred or a few thousand hands is futile. The standard deviation for such a statistically small sample is too great to yield a valid strategy.

Change Blackjack Basic Strategy for the Shuffle?

This, however, does not mean that some changes to basic strategy might not be in order if extreme new deck sequences were observed.

The problem is that the more out of sequence the cards are, the less applicable your new “sequential” basic strategy will be. Also, and most importantly, your basic strategy would assuredly vary by seating position. To be honest, if I saw a large proportion of cards coming out in new deck sequences, my strategy would be simple: sit at first base!

It is also probably impossible to come up with a universal strategy for use against all poor shuffles in a casino environment. If I program the computer to use two “fine” riffles, following a finer wash of the fresh cards, then stack each deck one on top of the other with no attempt to intermix the cards, the house advantage on the first round after the shuffle goes up by about 0.4%.

If I use two washes, one “gross” the other “fine,” followed by one “fine riffle,” the house advantage right after the shuffle is the same as with a completely random shuffle, though the advantage for specific players at the table varies. First base, again, does best, with an expectation of about 0.3% better than with basic strategy. (There’s something about that first base seat that sequential order favors.)

Small differences in the poor shuffles can cause significant differences to the various players. Any casino that purposely shuffled fresh decks poorly, possibly believing that sequential cards hurt the players, could risk being taken to the cleaners by high rollers on the first base side of the table.

Based on the data I’ve obtained thus far using the Real World Casino software, I would personally avoid sitting on the third base side of the table immediately after fresh decks were introduced if I felt the shuffle were inadequate. For me, this is a big change in my opinion, but the fact is it takes a fairly thorough shuffle to completely eliminate the third base disadvantage.

I don’t know whether or not any of the non-random theorists have ever pointed out the first-base/third-base effects of sequential cards. If not, then they have missed the most striking effects of a poor shuffle on fresh decks. This first-base/third-base dichotomy is present with virtually every poor shuffle on fresh decks I’ve tested.

I’ve also learned that if a very poor shuffle is continued through a shoe, it can take a number of shuffles to completely eliminate the non-random effects. Players should realize, however, that these effects are, at most, measured in tenths of a percent. In his Phase II article, Eddie Olsen estimates that the Atlantic City “zone” and “stutter” shuffles put the basic strategy player at about a 15% disadvantage to the house. Highly unlikely, in my opinion.

Version 3.0 of Imming’s Universal Blackjack Engine, which I used in these tests, allows only one type of standard multi-deck shuffle, the old “center cut, riffle and stack.” The new version 4.0, which will be available by the time this issue of Blackjack Forum goes to press, will allow user-programmable shuffles, including “zone” and “stutter” variations.

From the tests I’ve run thus far, however, my initial conclusions are:

  1. Totally unshuffled fresh decks strongly favor the players, not the house.
  2. As the new-deck sequences are broken down, the player advantage swings to a small house advantage, especially over the third base side of the table. The first base side of the table retains an advantage over the house if new-deck sequences are still present.
  3. If the fresh deck shuffle is thorough enough to break up virtually all of the fresh deck sequences, a small advantage, measurable in tenths of a percent, swings to the house over all players at the table.
  4. Depending on how poor the shuffle is, this house advantage may continue through a number of successive shoes before the random basic strategy expectation returns.

It seems unlikely to me that any type of shuffle, “stutter” or otherwise, could create a strong house advantage (15%?), though I will assuredly test the A C. style stutter shuffle when I get the new version 4.0 of this software (as I’m sure hundreds of other players will!)

Contrary to what the non-random shuffle theorists have also reported, card counting does work, even when the sequential effects of a poor shuffle on fresh decks are present. Card counters who play only when the count is in their favor need not worry about entering games at any betting position after fresh decks have been introduced, though the advantage from counting may be lowered a few tenths of a percent.

Thanks to John Imming’s efforts, and his phenomenal Real World Casino software, for the first time average players can test systems that they previously had to accept on faith. And so-called experts like me sometimes have to eat our own words. ♠

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Super Sevens

Super Sevens Snafu

by Arnold Snyder
(Blackjack Forum Vol. XII #2, June 1992)
© Blackjack Forum 1992

There’s a new side-bet popping up at blackjack tables called Super Sevens. You’ll find it at the new Foxwoods Casino in Connecticut, and on various cruise ships. You’ll also find it at Caesars, in both Las Vegas and Stateline. The option was invented last year by Caesars Tahoe pit boss Ken Perrie — the same man who brought us the over/under rule. Like the over/under, the Super Sevens option may be offered at any otherwise normal blackjack game — except that the option requires that at least three decks be in play. A $1 dollar side-bet prior to the deal offers various payouts for different combinations of player hands containing one, two, or three sevens, depending on whether the sevens are suited or unsuited. The maximum payout is $5,000 for three suited sevens.

I have not previously revealed that I had a hand in the initial mathematical analysis of this option. The fact is, I was hired by Ken Perrie last summer to analyze this rule, and all of the possibilities and probabilities which could affect the house expectations. I suspect Ken hired me for this job because I was the guy who first published a counting system for attacking his over/under option.

In any case, Ken explained to me the basics of the Super Sevens rule over the phone, and asked me to look at the payout schedule that he had devised, as well as his mathematical analysis of the expectations. I knew from the get-go that this option offered little to card counters. Even if the effects of removal proved to be high – and I suspected they would – with a maximum bet of $1, no card counter could ever get enough action on the bet to expect anything but a minute return on his investment.

I told Ken I would do an analysis of the rule for my standard $75 per hour. Using a pocket calculator, I quickly analyzed his payout schedule. My results differed from his, so I called my math genius in residence (in residence in San Jose, that is) – Sam Case.

I explained the option to Sam, and asked him if he could do a quick spreadsheet analysis. He called me back within an hour. His computer analysis agreed with my calculator analysis. So, I called Ken and told him what we’d come up with. I agreed to play with various payout schedules until I could find one that offered an off-the-top house advantage in the neighborhood of what Ken was looking for, 10% to 11%.

Using Sam’s spreadsheet, I ran through dozens of variations of payout schedules, and called Ken back a couple days later with the front runners. By this time I had found many payout schedules which would give the house its 10% edge off the top, retaining the maximum payout of $5,000 for three suited sevens, but which would also be more attractive to card counters. I accomplished this by lowering the high-end payouts, raising the low-end payouts, and allowing a max bet of more than $1.

I argued with Ken about the wisdom of his $1 max bet. “The fact is, Ken,” I said, “with a $1 max bet, you may be stifling the opportunities for card counters, but you’re also severely limiting the potential gain for the house. Ten percent of a buck is only a dime. By allowing bigger bets, and providing smaller payouts at the high end, you’ll increase the action considerably.” (Hey, guys, I tried…) He wouldn’t buy it. He just didn’t want any possibility of card counters taking any significant profits from the option. He picked the payout schedule that he liked best of those I’d drawn up, and I agreed to supply him with computer printouts of the spreadsheet analysis, as well as a typed report describing the analysis, including estimates of potential house profits based on the estimated hourly action per table. He also requested that I include in my report an explanation of why card counters could not win any significant amount of money from the Super Sevens bet.

I soon sent him the complete report, along with my estimated total time spent on the project of thirteen hours and twenty minutes, plus my bill for $1,000. I was saddened that I had been unable to convince him to make the bet more attractive to counters, but what the hay, at least one card counter was going to make a cool grand on the option without ever placing the bet!

A week later, Ken called me. He had shown my analysis to one of the bean counters at Caesars, and the guy told him I’d made a mistake – that I had neglected to account for the $1 which the player automatically lost any time he was not dealt an initial seven. I told Ken I’d look at the spreadsheet and get back to him, but that I was sure the analysis was accurate, as I had checked and double-checked my work.

Unfortunately, I should have triple-checked it. All of the probabilities did total to 1.0 on the bottom line, indicating that all possible dealing sequences had been accounted for, but, as Ken had stated, I had placed a “0,” instead of a “-1,” in the payout column for a player who is dealt an initial non-seven. How embarrassing. . .

I called Ken back and apologized for the error. Then I redid the analyses, adjusting the payouts, and revised my written report accordingly. Naturally, I didn’t charge Ken for these hours. I was just thankful that he had not already begun his marketing efforts. He could have sued me for a bundle if my error were not discovered until after numerous casinos were employing the option, and losing their shirts. So much for my lucrative consulting business. . . Shortly after I sent him my new report, he sent me a check for $1,000, never mentioning my potentially costly error. What a gentleman. . .

Some months later, I got an invitation from Ken to attend a combination golf tournament/party he was sponsoring to celebrate the success of his gaming company. These events were taking place in Las Vegas on the same weekend as the World Gaming Congress, which I was already planning to attend.

I didn’t get into Vegas early enough to participate in the golf match, but I did make it to the party, which was being held in the VIP Room of the Olympic Gardens. The Olympic Gardens, to put it bluntly, is a strip joint. More specifically, it’s a table dance club, i.e., a strip joint where the dancers meander through the crowd to perform close-up “table dances” for tipping customers. Of course, it’s all just innocent fun.

At the buffet table, Ken introduced me to his business partner, an L.A. dentist. In the course of my conversation with this gentleman, I learned that my embarrassing mistake in analyzing the Super Sevens option had proven very costly to Ken.

“That error cost us a bundle,” said the entrepreneurial dentist. “Right after Ken got your initial payout analysis, he had the typesetting done on our marketing brochures, and had them printed. Full color. It wasn’t cheap. They all had to be trashed and redone.”

Why hadn’t Ken mentioned this to me? I felt terrible. My first thought was that I should return my consulting fee to him. Why hadn’t he said something before? As I was looking for him, one of the table dancers started tugging at my arm.

“Let’s go,” she said. “I’m going to dance for you.”

I begged off with a “maybe later.” I had to find Ken.

“Sorry,” she said. “You can’t get out of it. It’s already been paid for.” As she talked, she was dragging me by the shirt sleeve to a vacant chair against the far wall. “Now just sit still,” she instructed me, “and no touching.”

“Who paid for it?” I demanded, dumbfounded.

“He did,” she said, pointing to a face in the gathering crowd.

There stood Ken Perrie, with a grin on his face from ear to ear.

“Thanks, Ken!” I yelled, as the dancer pulled her top off.

“My pleasure, Arnold,” he called to me.

Some godawful heavy metal noise started screeching in my ear from a speaker over my head. I was trying to get Ken’s attention, to tell him I was sorry, that I would give him his money back. He was only a few feet away from me, but I could only catch glimpses of him through the writhing flesh in front of my nose. I tried craning my neck, only to have the dancer bop me one on the head.

“Now, sit still!” she warned me. “Be a good boy!”

At this point it dawned on me that the Great Snyder was surrounded by guffawing casino execs, as a gorgeous young dancer in a g-string was climbing all over his bod. What am I doing here? I’m a religious leader of this community! What if my wife finds out? What if the Griffin Agency is here taking pictures? Maybe they’ll use one of these shots in their next book of undesirables! Already, I could see the caption: “Snyder, Arnold; Alias: The Bishop; Shown here exhibiting his unique ‘front-loading’ style.”

So, this is how Mr. Perrie gets back at a man of the cloth for a simple little mistake in math that anyone could have made! He places me in a compromising position, publicly embarrasses me, ruins my reputation, and attempts to destroy my marriage, while making me a laughing stock in the casino world.

After the dance, nursing my shame at the bar, some guy I didn’t know came up to me and said, “That looked like fun. How much did she charge you?”

“I didn’t pay for it,” I said grumpily. “A buddy of mine set me up.”

“Oh,” he said. “Do you know how much it cost him?”

“A thousand bucks,” I said. “Plus, about twenty for the dancer.” ♠

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The “Senior’s System”

Card Counting for Players with Weak Vision

by Arnold Snyder
[From Card Player, September 1994]
© 1994 Arnold Snyder

Question from a Reader:  I do not have very good eyesight. I love playing blackjack, but as you might imagine, card counting is not easy for me. I have no trouble distinguishing aces, kings, queens, jacks, or 2s, 3s, 4s, 5s or 6s on the table, but I have great difficulty distinguishing 7s, 8s, 9s and 10s from each other when they are across the table from me. So, after learning to use the high low count at home, I found I could not use it in a casino environment.

Finally, I developed my own card counting system, which I call the “Senior’s System,” for people whose eyes aren’t what they used to be. The easiest version counts jacks, queens and kings as -1, and 4s, 5s and 6s as +1. Sort of like a simplified Hi-Opt I. The more advanced version, which I use, counts jacks, queens, kings and aces as -1, and 3s, 4s, 5s, and 6s as +1. That’s my seniors’ version of the high low count.

I’ve been doing pretty well with this method of playing, but I’m wondering how good it really is. I use the standard high low strategy variations. What do you think?

Answer:  This is one of the most original (and best!) methods of card counting I’ve seen for anyone with who has vision problems. The “advanced ” method is better. It has a betting correlation of about 90%, compared to the high low’s 97%; and a playing efficiency of about 43%, compared to the high low’s 51%. So, this “Senior’s System” retains about 90% of the power of the complete high low count. That’s very impressive.

In the past, a number of blackjack players with poor vision have told me that the only system they could use was the Uston Ace-Five count, from Ken’s book, Million Dollar Blackjack (SRS, 1981), which is very inferior to the method you’ve developed. Uston’s Ace-Five Count has virtually no playing efficiency and is simply played with basic strategy. Aces count as -1, and fives count as +1. The betting correlation is about 53%, which is impressive only because the system is so simple. The 90% betting correlation you’ve attained, however, despite your bad eyes, is quite an accomplishment.

I also suspect that most of the strategy indices you are using from the high low iwill work pretty well with your simplified version of the high low count. The only computer software on the market that I know of that will devise strategy indices, and allow you to assign a 0 value to the “pip” tens and a +1 value to the “paints,” is John Imming’s Universal Blackjack Engine. If you have this software, or you know someone who does, you could devise strategy indices especifically for the Senior’s Count. If you do not have this software, my advice is to continue using the standard high low indices, as most of these are going to be pretty accurate for the Senior’s Count, and the few changes will be on more or less borderline decisions.

Played accurately, I would consider your Senior’s Count to be every bit a professional level system. Congratulations on developing a powerful method of card counting that can be used by the visually impaired!

The simpler version of your Senior’s Count, which ignores the aces and 3s, has a slightly higher playing efficiency (about 56%) than the advanced version, (and this is even higher than the high low’s 51%), but a considerably lower betting correlation, only about 80%. If you have no trouble distinguishing aces and threes, then the advanced version is definitely worth the effort. But even this simplified Senior’s Count is a vast improvement over Uston’s Ace-Five Count when it comes to total system power. Hi-Opt I indices from Lance Humble and Carl Cooper’s 1981 book, The World’s Greatest Blackjack Book (Doubleday), should work just fine if you do not have the software to devise the count specific indices.

Another excellent variation of your method would be to keep the simpler version of the Senior’s Count, using the Hi-Opt I indices for playing your hands, along with a side count of the aces for betting accuracy.

Somewhat off the subject, one of the most amusing stories I’ve heard about card counters’ efforts at camouflage was from a counter who claimed he wore wraparound sunglasses and carried a cane and represented himself at the table as being totally blind! His wife would accompany him, her job being to tell him his hand total and the dealer’s upcard. In fact, he had perfect vision and had no trouble seeing every card on the table. He claimed this act allowed him to use a very large betting spread while taking his time whenever it was needed to recall strategy indices, figure out insurance, etc. Whatever works!  ♠

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Are Side Counts Worth the Trouble?

Can Side Counting Make You a Super Card Counter?

by Arnold Snyder
(From Blackjack Forum Volume IV #3, September 1984)
© Blackjack Forum 1984

I’ve spent the past four years advising blackjack players to streamline their card counting strategies.

In 1980, in The Blackjack Formula, I showed that the most important factor in a card counter’s win rate is penetration. Since then, computer tests and mathematical analyses have shown time and again that the most important factors affecting the card counter’s win rate are indeed the blackjack game conditions — shuffle-point, the number of decks in play, hands per hour, etc.

Given like conditions, the more complex systems, such as those with side-counts, rarely significantly outperform the simpler systems. This is especially true in multi-deck games, where side-counts have even less value. My angle on beating the tables has been to exploit those games that are the easiest to beat, rather than struggle to get an edge in a tough game.

Most card counters, because they are not full-time professional gamblers, do not have enough time to dedicate to the memorization and practice required for the more difficult card counting systems. Yet, casual players who can recognize which games are more exploitable, can do quite well as blackjack players if they can accurately apply a simple count strategy.

One of the major simplifications a player can employ, with little effect on his win rate, is to quit attempting to side-count aces. Many card-counting systems provide ace adjustment advice, but maintaining two separate counts, and then utilizing this information with precision, is not an easy task for most players. In multi-deck games, a side-count of aces will rarely increase a card counter’s win rate by more than 1/20 of 1%. Even in a deeply dealt single-deck game, a side-count of aces is not worth more than 1/5 of 1% to a counter’s win rate.

Players who follow some sort of Kelly betting scheme, however, will find that any percentage increase in win rate will be worth more, in dollars and cents, than is immediately apparent. A Kelly betting scheme is loosely one in which the player attempts to bet a proportion of his bankroll equal to his percentage expectation. For instance, a player with a 2% advantage would bet roughly 2% of his bankroll (actually, slightly less, to account for the increased fluctuation from double downs and pair splits).

Side Counts and Kelly Betting

Let’s look at a simple example of the effect of Kelly betting on the value of a side count.. Forget for the moment that the game is blackjack, and ignore the intricacies of the game. Assume that two players, each with a $1000 bankroll, are betting in a game where one player has an advantage of 1% over the house; the other player, due to a superior strategy, has an advantage of 2% over the house.

If both of these players placed equal sized bets, then the player with the 2% advantage would expect to win twice as much money as the player with the 1% advantage. If both players were using a Kelly-type betting scheme, however, the player with the 2% advantage would expect to win 4 times the expectation of the player with the 1% advantage.

Here’s why: With a Kelly betting scheme, the player with the 1% advantage would bet 1% of his bankroll, or $10. His expectation on this bet would be 1% of $10, or 10в. The player with the 2% advantage, however, would make a bet of $20 (2% of his bankroll). His expectation on his bet would be 2% of $20, or 40в. So, with twice the advantage, he’d expect 4 times the return in $.

Simply side-counting aces would not double anyone’s advantage, so you couldn’t expect to quadruple your return. But the same effect as illustrated above would occur, albeit less dramatically, with smaller increases in advantage.

For instance, if one player had a 1.5% advantage, and another had a 1.7% advantage, you might quickly estimate that the player with the greater advantage would expect to win $17 for every $15 expected by the player with the lesser advantage. But this would only be true if both players were betting equal amounts of money. Using a Kelly method of bet sizing, the player with the 1.7% advantage would expect to win more than $19 for every $15 won by the player with the 1.5% advantage.

Mathematicians have been arguing for some years now about the long run effect of Kelly betting. Far be it from me to proclaim that in the long run doubling your advantage would quadruple your dollar expectation. But on any one given bet this is so.

Since a Kelly bettor sizes his bets according to the size of his bankroll, he will also find that a small increase in win rate could have a significant long run effect on his dollar return. One tenth of a percent may look like nothing on paper, but when you consider it might be the difference between a 1% win rate and a 1.1% win rate, it’s actually a rate of return 10% higher. When you’re thinking seriously about how many hundreds of hours it might take you to double a bankroll, small differences like this look much more significant.

When a Side Count May Be Worth the Trouble

So, the first players I might advise to side-count aces would be those who are serious players who play primarily in single-deck games, who have the talent to side-count easily and accurately. This does not mean I’d advise most serious players to side-count aces. Most of the blackjack pros I’ve asked about this do not side-count aces. They feel their time at the tables is more profitably spent maintaining a friendlier camouflage than would be possible for them with a multi-parameter counting system.

There are also many serious players who do not employ any type of Kelly betting scheme. There are nickel chip players who have been playing with nickels for years, who may profit up to a few thousand dollars per year at the blackjack tables. They play frequently and are talented counters dedicated to winning.

But these players don’t think in terms of “bankroll.” If they win $500 in a week, they do not increase the size of their bets the following week. And if they lose $500, they do not decrease their bets. Winnings are simply treated as income, and losses are absorbed.

These players, though serious about winning at the game, are not trying to get rich or become high stakes pros. They generally hold jobs and play blackjack for enjoyment. There are also high stakes players who pay no attention to the Kelly criterion. They are often junketeers who always play at a certain level to maintain their comp ratings. Though they may be excellent and consistently winning card counters, they have little use for Kelly betting.

Most of the card counters I know who have really made a fortune playing blackjack have used some form of Kelly betting. But this isn’t for everyone. Some players will side-count aces regardless of how small the dollar return might be, simply to play more accurately for the sake of playing more accurately. This type of player enjoys the challenge of playing a mathematically precise game more than any other aspect of card counting, including profit potential.

One such player said to me: “I like counting cards and I do it well. I’m not going to eliminate my ace count just because it’s only worth two dollars per week. Neither am I going to throw two dollars out the window every week, just because it’s only two dollars.”

For those players who want to count aces, for whatever reason, I will present the best ace-counting methods I know.

The Best Ace Side Counts

In Blackjack Forum II #3, I reviewed a book by C. Ionescu Tulcea titled A Book on Casino Blackjack (1982). In my review, I mentioned that although Tulcea’s counting systems were presented impractically for non-mathematicians, I liked his method of side-counting aces. What he proposed was to keep the ace count as a balanced count, balancing the aces vs. specified low cards, then adjusting the primary running count by adding the two counts together.

Tulcea advises using this method with my Zen Count (which he calls the “Main Count”). I would never advise side-counting aces with the Zen Count, which already has a high betting correlation.

The simplest count system that would lend itself well to this approach is the Hi-Opt I count: Tens = -1; 3s, 4s, 5s, and 6s = +1. For your ace side-count, you would count aces as -1, and deuces as +1.

 Hi-Opt IAce Count
A:0-1
2:0+1
3:+10
4:+10
5:+10
6:+10
7:00
8:00
9:00
X:-10

For example, your count starts at 0/0. The first “0” is your Hi-Opt I running count; the second “0” your ace-deuce running count. Let’s say the first hand uses 2 tens, a 7, a 5 and an 8. Your running count is now -1/0. The second hand uses 2 tens, a 5, a 2, and a 9. Your running count now becomes -2/+1. In order to make an ace-adjustment, you would simply add together the two running counts. -2 + 1 = -1 (your ace-adjusted running count).

This ace-adjusted running count, in fact, is exactly what your running count would be if you were keeping the Hi-Lo Count only. The ace-deuce count does not measure the proportion of aces left in the remaining deck(s); it measures only the proportion of aces to deuces. But by adding the ace-deuce count to your primary count (Hi-Opt I), you would raise your betting correlation from .88 to .97, as high as you could hope to raise it with a perfect side-count of the proportion of aces to the remaining deck(s).

To use this count in play, you would use the Hi-Opt I count alone for all insurance and playing strategy decisions, except doubling down on hard 9 and 10 and splitting 10’s. You would use your ace adjusted count for all betting decisions, doubling down on hard 9 and 10, and splitting tens. The reason you would use the ace-adjusted count for these few doubling and splitting decisions is that the Hi-Lo Count has a slightly higher playing strategy correlation than the Hi-Opt I Count for these decisions.

Your true count adjustment should be made after your ace adjustment. If you play in single-deck games, you could use Armand Seri’s Optimal Running Count strategy tables (see Blackjack Forum III #4), and eliminate the necessity of true counting entirely.

The most cumbersome thing about keeping a double-parameter count like this, is that you could become confused with the slash (/) separating your two counts in your head, especially when one count is positive and the other negative, with one count going up while the other is going down, etc.

One method of eliminating some of this confusion is to remove the +/- sign from your ace-deuce count. Start your count at 0/50. Your Hi-Opt I Count would still go back and forth between positive and negative, but the ace-deuce count would always be a positive number. In single-deck games, it would only run from 46 to 54, and even in multi-deck games, it would rarely go below 40 or above 60 (possible, but highly unlikely). You would adjust your count by adding or subtracting the number above or below 50 to your primary (Hi-Opt 1) count. Example: -2/47 = -5 (ace adjusted running count).

My Side Count Method

One method I taught myself for keeping a double-parameter count some years back was to keep the secondary count with letters, instead of numbers. I started my secondary count at the letter “M,” and added or subtracted letters instead of numbers. A running count of -1P would adjust to a running count of +2, since “P” is 3 letters higher than “M.” This method totally eliminates the number confusion of maintaining two separate numbers in your head. It does require that you train yourself to count with letters. This is not difficult but takes practice.

First, learn to recite the alphabet backwards as quickly as forwards. Second learn to count letters by twos and threes, backwards and forwards quickly and effortlessly.

For example, you should be able to recite an “even” alphabet and an “odd” alphabet, these being: ACEGIKMOQSUWY; and BDFHJLNPRTVXZ. You must be able to recite these fragmented alphabets with the same ease with which you could count 2, 4, 6, 8, 10, 12, etc., or 1, 3, 5, 7, 9, etc.

Most people can count by 2s and 3s automatically, backwards and forwards, with numbers. Try it with letters, however, and most people are incapable, simply because they’ve never had any need to practice this. It’s easy if you make an effort to learn it. The third step to counting with letters is learning to associate each letter with a specific number:I = -4
J = -3
K = -2
L = -I
M = 0
N = I
0 = 2
P = 3
Q = 4

This is simply the memorization of a chart, which will allow you to make your ace-adjustment quickly and accurately.

What I like most about side counting aces with a balanced running count, rather than by comparing the number of remaining aces to an estimated number of quarter decks, is that it reduces the degree of error inherent in the approximation method. But is it worth it to make an accurate ace adjustment to a level one count, such as Hi-Opt?

You might consider the fact that a higher level count system such as Hi-Opt II or the Zen Count would perform as well with no ace side count as Hi-Opt I with an ace side count. It seems to me that it would be easier for most players to learn and use Hi-Opt II than to learn and use Hi-Opt I with an accurate side count of aces.

Some counters disagree with this and have told me so. Apparently, multi-level counting, i.e., assigning point values higher than + or -1, is more difficult for some players than multi-parameter counting, i.e., keeping more than one tally of numbers. We all have different capabilities when it comes to math, so you have to consider your own talents when choosing a system.

But what if you are capable of using a multi-level counting system, and maintaining a secondary count. Okay, blackjack fiends, this is how to ace-adjust the Hi-Opt II Count system. Your primary count is Hi-Opt II: 10s = -2; 2s, 3s, 6s and 7s = +1; 4s and 5s = +2. Your secondary count is: Aces = -2; 3s and 6s = + 1.

 Hi-Opt IAce Count
A:0-2
2:+10
3:+1+1
4:+20
5:+20
6:+1+1
7:+10
8:00
9:00
X:-20

The difficulty here is that not only are you maintaining two level two running counts, but that the 3s and 6s are counted as + I in both counts. The nice thing about this counting system is that when you make your ace-adjustment, which is done exactly as with the Hi-Opt I Count, by adding your two running counts together, your ace-adjusted Hi-Opt II Count becomes Revere’s Level II Point Count, with a betting correlation of .99. This is as accurate a counting system as is possible with only two parameters.

Adding Additional Side Counts

If you want to play more accurately than this, you’ll have to add more parameters. The major problem with adding parameters even if you are capable of keeping many separate tallies in your head is in utilizing the information properly for strategy decisions. Optimally, all of your separate counts would be cross-referenced, and you would have to memorize myriad strategy charts to accurately make your decisions.

Probably the most ambitious multi-parameter counting system readily available is the complete Hi-Opt I system with multi-parameter charts developed by Peter Griffin. To use this system you would keep Hi-Opt I as a primary count with 5 separate side-counts of the aces, deuces, 7s, 8s and 9s.

At the 1981 Conference on Gambling and Risk-Taking, Dr. John Gwynn, Jr. and Jeffrey Tsai presented computer simulation results which showed that, considering the difficulty of using this approach in the 4-deck game, the gains from employing this count system are not significantly greater than those of the Hi-Opt I with no side-counts.

More recently, Dr. Gwynn has run some single-deck simulations of this system. In single-deck games, especially when deeply dealt, the complete Hi-Opt I system does significantly outperform the simple Hi-Opt 1. The complete Hi-Opt I performs a few tenths of a percent poorer than “perfect” computer play, a variation of which Gwynn also tested. The results of these simulations will be in a paper Gwynn will present at the Sixth Gambling Conference in Atlantic City in December of this year. (See his abstract for this paper elsewhere in this issue).

Some time back, I developed a counting system, which I humbly dubbed “Snyder’s Folly,” based on a combination of numbers, subtle body postures, and code words, which allowed me to keep perfect track of the exact number of every denomination of card remaining in a single-deck. I practiced with it for awhile, got pretty quick at counting down a deck, then gave a demonstration to Sam Case. He dealt about half a dozen hands to me, which I played out, then he asked me what my count was.

“It’s 5 duckboy 3,” I answered.

“What does that mean to you?” he asked.

“It means there are seven l0s remaining, one ace, no twos, one 3, two 4s, no 5s, three 6s, no 7s, no 8s and one 9.”

Sam spread out the cards, put them in order, and, as I expected, my count was 100% accurate. “That’s incredible,” he said. “Do it again.”

We ran through a few more decks with him dealing, and at various points he would ask me for my deck analysis, which always proved accurate. Then the inevitable happened. He dealt himself an ace up and asked me if I wanted to take insurance. Five seconds later, with no response from me, he said, “What’s wrong? You can’t take this long to decide on the insurance bet.”

“Well,” I explained, “I know you’ve got eleven tens, three aces, four deuces, one 3, four 4s, two 5s, two 6s, two 7s, one 8, and three 9s remaining. I know this because my count is 9 Farley 3 and I’m sitting with my weight on my right cheek. But I can’t make my insurance decision till I tally up all these damn numbers and figure out the ten ratio.”

Sam laughed. “Your incredible new counting system sucks, Snyder. If you can’t even make an insurance decision, how do you make your other strategy decisions?”

“Well,” I admitted. “I can’t use this count for strategy decisions. It’s too complicated. I have to play basic strategy when I keep this count.” Sam laughed harder. “What the hell good is this counting system? Can’t you even devise a set of strategy tables for it?”

“I could come up with a great set of strategy table for it using Griffin’s book,” I explained. “But it would take me too long to make my decisions at the tables. And it would also be too much to memorize.”

“Then what good is Snyder’s Folly?” Sam asked. “It’s a waste of time. You’re side counting for no reason. You’re not using the count data!”

“It’s good for one thing,” I confessed. “Impressing other card counters. You know I’m not in this game for the money, Sam. I just enjoy being a big shot. Wait’ll I demonstrate this count to Stanford Wong, or Ken Uston, or Peter Griffin . . . Why, they’ll go nuts over it!”

“Just pray you don’t have to make an insurance decision,” Sam said. ♠

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Costa Rican Rummy

Can You Beat Costa Rican Rummy with Card Counting?

by Arnold Snyder
(First published in Card Player, December 1993)
© 1993 Arnold Snyder

Question from a Player:  I will be vacationing in Costa Rica again this year. They have casinos there, but blackjack is illegal. Instead, they have their own variation of blackjack, which they call “rummy” — not in any way related to the card game of rummy as played in the U.S.

“Rummy” in Costa Rica is exactly like blackjack, dealt by a house dealer, except that they have a slew of weird rules and bonuses. The game is dealt from a 4-deck shoe, and they deal pretty deeply — I’d say about 3 decks dealt.

Costa Rican Rummy Rules

The one bad rule is that blackjacks pay even money. But, listen to the good rules:

*Dealer stands on soft 17.

*Unlimited resplits of pairs, including aces.

*Double down on any two cards.

*Double after splits allowed.

*Early surrender vs. both ten and ace!

*Three 7s pays 5-to-1.

*Any other 3 of a kind pays 3-to-1.

*Take insurance on a dealer ten up! (And if the dealer has an ace in the hole, the insurance pays 10-to-1!)

*Three card straight flushes pay 3-to-1!

Have you ever heard of a set of rules like this before? I’ve been an amateur card counter for many years. I use the old John Archer ten-count. Can you tell me what kind of an advantage I can get in this Costa Rican rummy game, and also do I take insurance vs. ten up at the same count that I use for insurance with an ace up? Thanks!

Costa Rican Rummy—the Killer Rule

Answer:  Frankly, I doubt that you can get much of an advantage in this game. Because of the deep shuffle point, you may be able to get an edge if you use a very large spread, but it won’t be much of an edge. I admit that I have not done any detailed analysis of this unique game, because I believe it’s a waste of time.

That “one bad rule” — blackjacks pay even money — is a killer, worth about 2.3% to the house. Even with all of the other great rules and bonuses, the house still probably has close to a 1% advantage over you off the top of the deck. That’s tough to beat with card counting at this level of penetration.

Regarding the option to take insurance when the dealer has a ten-valued card up — don’t do it. This is a sucker bet. That 10-to-1 payoff is just too low. You would need about 12-to-1 to make it a break even proposition.

Also, your card counting system will provide no help in determining when to place this bet. You would want to be counting aces vs. non-aces in order to know when to place this bet, but with such a poor payoff, you’d be wasting your time if you kept the side count. If they ever offer the option with a 12-to-1 payoff, then it might be worth it to count the aces. The house would still have the advantage off the top, but you would see occasional profitable insurance opportunities. At 10-to-1, don’t hold your breath.

Despite the vast array of bonus payouts, altogether they are not worth very much. All of those 3-card hands are pretty rare. It’s more likely that the house makes more money by offering these bonuses than the players make by collecting on them. Some players will be tempted to violate basic strategy in order to try for the bonus payouts, such as occasionally hitting a two-card stiff when basic strategy tells you to stand, or hitting a pair when you should be splitting it. Such plays could be quite costly in the long run.

Few players would be tempted to hit a pair of jacks or kings in order to try for three of a kind, but more might be tempted to hit a pair of aces or eights instead of splitting. If you’ve got a pair of eights, the odds against being dealt a third eight in a 4-deck game are about 14-to-1. But the payout for making the hand is only 3-to-1! The actual cost to the player who makes this blunder-bet will, of course, depend on the dealer upcard.

As for those 3-card straight flushes, the odds against your making one of these hands are even worse. Assuming you start with two of the necessary cards, the odds against catching a straight flush on the next card dealt are almost 26-to-1, or about 51-to-1 if you’re foolish enough to try for an inside or closed end straight flush! Trying for that 3-to-1 payoff for making it is very costly to the player.

It’s unlikely that any practical card counting system could be devised to take advantage of these bonuses. It would be extremely rare that any variation from basic strategy, or your count strategy, would be the optimal way to play a hand in order to try for a bonus.

Recommended Strategy for Costa Rican Rummy

If you think the game of rummy is fun, and you’re intent on playing it since it’s the only form of blackjack they have in Costa Rica, here’s my recommended strategy:

Follow your normal card counting strategy for all playing decisions. It’s especially important that you take full advantage of the early surrender option, because this is the most valuable rule on the table.

(I don’t believe the “Archer Method” provided early surrender decisions. If not, you should either learn basic strategy for early surrender, available in most modern card counting books, or switch to a more recently developed counting system so that you can learn a few of the important indices for altering your strategy.)

Ignore the insurance vs. ten-up option. Never try for a bonus hand; just be happy when you collect on one during the course of your normal play. Don’t raise your bet until your count system indicates that your advantage has gone up by about 2% (with that unbalanced Archer Count, wait until a running count of +30!), and use as much of a betting spread as you can get away with (and afford).

If a casino with otherwise standard blackjack rules (i.e., blackjacks pay 3-to-2!) put all of those other Costa Rican rules and bonus hands in a game, it would be a very valuable game for a card counter. Even the basic strategy player would have the edge in such a game. But when blackjacks pay even money, forget it.

If you can use a very large spread, you might get slightly over the break even point in this Costa Rican rummy game. But don’t expect to make big bucks at it. ♠

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Review of Repeat Until Rich

Repeat Until Rich by Josh Axelrad (reviewed)

by Arnold Snyder

Josh Axelrad’s Repeat Until Rich: A Professional Card Counter’s Chronicle of the Blackjack War is an engrossing read by a former player on a notorious high-stakes team whose five-year blackjack career ended more or less when he found himself barred from just about every casino in the country. The stories have the ring of truth, especially for anyone who’s ever played at high stakes. His descriptions of the trials and travails of the traveling card counter’s life are often hilarious (if you’re a fan of black humor) and his cast of characters—from his teammates to the casino personnel to the cops he had to deal with—makes for one of the all-time great real-life adventure stories in print.

This is a beautifully written memoir, an easy read because there’s lots of dialogue, but you’ll find yourself reading it slowly to savor the scenes he creates. It covers Josh’s entire career as a professional blackjack player, from his initial introduction and training to his days of high stakes shuffle tracking and his ultimate “downfall” as a compulsive gambler. I admire his writing skills. Here he is describing a trip to Harrah’s in East Chicago:

“—and a ghetto like I’ve never seen, and I mean I’ve seen some. You have to drive over this quarry. The earth’s been hacked apart. The bridge goes right over the pit. It looks like some kind of an autopsy down there. You can feel the pain of the cliffs, you share in the agony, but that’s how you get to Indiana. And then, along the lake, it’s industrial wasteland, towers belching smoke, massive cylindrical units holding God knows what noxious shit, and in the middle of this—the casinos!”

Sure to bring fond memories to anyone who’s ever played at Harrah’s in Indiana.

Most of the blackjack play described in the book took place about eight to ten years ago, at a time when blackjack teams—big and small—were running rampant through the country. I knew some of Josh’s teammates and even sat down to a meal or two with them, including Josh, when they were in Vegas. For a number of years back then, various members of his team were regularly attending Max Rubin’s Blackjack Ball, and one of the team’s founders has even been nominated for the Blackjack Hall of Fame on the basis of the team’s success. None of this is in the book, but I’m telling you this so that when you read the book, you have my word that this book is written by a real player who was once the scourge of the casinos. And Josh Axelrad is his real name. Believe me, the casinos know who he is.

One moral of Josh’s story, if there is one, may be that even if you know how to win at gambling, you can’t do it if you’re a compulsive gambler. Josh made a lot of money for himself and for his blackjack team, and he even learned to beat online no-limit hold’em very handily when his casino career burned out. But then he blew it all in online games that he couldn’t beat and knew he couldn’t beat. He just wanted the action, the rush. He was bored with the tedium of playing the way you had to play to win. He also “flunked out” of Gamblers Anonymous, as he couldn’t buy into their group insistence that gambling professionally was a myth, as he knew from five years’ experience that it was not. He was also turned off by the group’s reliance on a “higher power” to see them through difficulties. To his credit, however, this book is not written to moralize or proselytize. It’s simply Josh’s personal story, told with disarming honesty, at times sarcastic, at times cynical, but always truthful.

The other moral of Josh’s story, however, if there is a second one, is that risk-taking really does pay off for the persistent soul who just keeps plugging away. The professional gambling risk ultimately turned out to be too dangerous for a person of his temperament. Still, he didn’t resign himself to a dead-end job, mumbling “yessirs” to the type of brain-dead corporate bozos he despised. He took the emotional risk of baring his soul in this book, an achievement beyond all of his gambling escapades. No one has ever told the story of the professional card counter quite like this. For all its craziness, meaningless greed, and wasted energy, it’s strangely exhilarating. If he continues to gamble with his words, instead of with his wallet, Josh Axelrad will continue to beat the odds. ♠

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Blackjack in Deadwood, South Dakota

Report on Deadwood Casinos and Blackjack Opportunities

by the Bison
(From Blackjack Forum XXIV #2, Spring 2005)
© Blackjack Forum 2005

Ah, yes, winter in the Black Hills, 10 below one day, 65 above the next. With summer being the main tourist season, winter weekdays are usually quiet in all casinos, with many not opening their blackjack tables until 3 or 4 pm. A couple of smaller casinos just have blackjack tables open on the weekends. If you want to play heads up, come during the day before 2:00 or 3:00 just about anywhere.

Most blackjack games in Deadwood, South Dakota are 6 decks, with a few sprinkles of others to be found. State law caps bets at $100, but most places will let you play as many spots as you want if you’re playing green or black. This is, however, mostly low rollerville, so card counters betting green and black will draw a little attention. Just look like a happy gambler and you can usually spread to your heart’s content.

The downside is that the smaller joints only book $50 max bets. The surveillance departments do not share information on card counters, according to a source. I would be surprised if a number of them actually have a surveillance department. The smaller ones are probably just taping everything in case they need it someday.

This area isn’t really looking for card counters. I think on a quick up and down visit of main street a player with a spotter could pull off several hands of black at the right count, then mosey on to the next one. Interested? Here is a rundown of the games that are worthwhile.

Blackjack Rules, Limits, Penetration, and Hours in Deadwood

Silverado, tables open 24/7, S17, 4.5/6 pen, DAS, Lucky Ladies, $100 max.

Tin Lizzie, 5/6 pen, S17, double action spots, only $50 max. Big spreads no trouble for a couple of shoes, then wander off.

Hickocks and Mineral Palace are 3/4 pen, H17, DAS, 50/100 max respectively.

Celebrity just opened a table, but it’s only open Friday through Sunday. The 4-deck pen is 75%, with S17, DAS, 100 max, with no mid shoe entry. However, I haven’t played this one yet to see if they enforce it.

Gold Dust has 5/6 pen, DAS, H17, and resplit aces on the shoe game.

Double Deck is H17, NoDAS, Double any 2. Penetration varies wildly.

Last but not least in Deadwood blackjack is First Gold Casino, home of the terrible double deck game with fantastic penetration. This double deck blackjack game has Reno rules, but is almost always dealt down to a few cards. No shuffle card. The casino just opened a single deck game with a $100 max.

That’s it for winter in South Dakota! ♠

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Blackjack in Reno – It’s Different

Reno Heat: Advice from a Professional Blackjack Player

by Syph
(From Blackjack Forum Online, August 2006)
© 2006 Blackjack Forum Online

I spent about six months or so card counting at the blackjack games in Reno, surviving solely off silver and green play.

Here are some thoughts and impressions. I emphasize that these are only my experiences, so feel free to reject them.

You might well know better.

You will get backed off, barred, and chased out.

I know everyone says you won’t get hassled at these stakes, but you will. Prepare for it. And the smaller the joint, the less gracious the reading of the riot act.

I was chased out of the Cal-Neva by half a dozen security guards. Twice. I believe my top bet was $14 the first time, $19 the second.

I was barred from the Sienna for spreading $5-$20. Looking back, the quickest I was ever backed off was spreading 1-4, with progressive betting in positive counts after wins. You know, count rises, you win, you double up the bet. For some reason, it would get me backed off within about 20 minutes every time I attempted this “cover” strategy.

It’s garbage, don’t use it. And I don’t care how long Don says he’s been backcounting shoes.

Now, on the other hand, I spent the entire week in Wendover playing strictly by the count, sometimes jumping from $5 to $100 and back to $5 in the same deck. I was not backed off once, and there was an amusing exchange between the dealer and the pit boss regarding my betting:

Dealer: “You’ve got to have the most erratic betting I’ve ever witnessed.”

Pit Boss: “It’s Canadian betting. Very effective.”

Then they comped me a room.

You know, most counters are so deathly concerned about trying to hide their spread that they all sorta end up looking like each other in the process. I found the more I spread, the less likely I was to be backed off. I think Arnold has mentioned Ken Uston made use of this phenomenon.

One final point, while playing in Reno. Always carry a disposable camera with you. That way, when they start taking your picture, you can take theirs. Trading these sorts of antics is playing a losing game, obviously. And if you find youself in such a situation you’ve done something really wrong, but it does tend to make one feel better at the end of the day.

Depths of Ignorance in Reno Casinos

The depths of ignorance in Reno casinos are unchartable.

Never underestimate the sheer stupidity, paranoia, and fear of the pit critters.

I once, trying to pass myself off as a mentally handicapped compulsive gambler, muttered …

“So, uhm … like, if all the aces get played I can’t get a blackjack?”

Man, you’ve never seen a Pit Boss’s head shoot up so fast, twisting left and right, seeking out the guilty perp. And as I slumped in my chair, I was reminded you simply can’t make a stupid enough comment to make them think you’re an idiot.

Reno Blackjack Dealers and Card Counters

Can’t we all just get along?

No, we can’t. Sorry.

I have so many instances of befriending blackjack dealers who would then identify me as a “mark” and consequently expect a little extra toke for the shared good fortune. And if they didn’t get it, they would turn on you faster than a fanged snake with a skin condition.

Even those who know better can get lured into this dynamic. In time, it will destroy your bankroll with 100% certainty. The dealers are exceptional hustlers, and once they identify a little bit of weakness, they will devour you.

It’s like a relationship. And what gets people into trouble in relationships is not having clearly defined roles. Your relationship with the dealer is of the utmost importance when you sit down, particularly for the first time. Every dollar won costs you $100 in wagers, and if you are to go by Certainty Equivalents and other fancy math… perhaps closer to $200.

Just try winning a few hundred in a session and flipping the girl a dollar. You will not make any friends. But if you do any more than that, you’re probably playing a losing game. And if you flip her enough to make her happy, I can guarantee you that you will be in the poor house.

Don’t kid yourself on this issue. Fluctuations are not the number one killer of success in card counting. In my experience, and from watching those around me, it’s really tipping that cute girl a dollar on every third win that destines a low stakes player to a flight back to home and a job.

Ok, I’m veering off topic. But the point is, the moment you sit down at the table you are being categorized. If you adopt a spineless persona, the dealer will come to expect a spineless persona, and all those tips that come from a spineless persona. You have become her bitch.

And once that identity is set, you have just fuct yourself (I apologize for the language, but this is kinda important). Conversely, if you never tip, she will also come to expect that as well. And the interesting thing is, provided you are consistent with your attitude, all will run smoothly. But if cracks start to form, then the trouble begins.

Whether you’re a non-tipper that decides to be gracious or a tipper who decides to be chintzy, problems start when you deviate from your identity. You are introducing weakness into the relationship, and weakness is punished severely in this game.

And don’t think that your tipping puts you in anyone’s good books. In my early days, I was tipping more than I was making in EV, but it didn’t prevent the backoffs. Remember, the backoffs come from above, and every tip you give is one less dollar the casino can make off you.

(One further thought, and this came from someone far more experienced than I. He recounted a story of how he witnessed a group of dealers together at the end of their shift, laughing about how much money they had collected from all the “losers” who had tipped them.

This is not the final word on the subject, but you would be better served viewing them in this light, than the urge to see them as struggling wage slaves trying to put food on their table. They WILL portray the latter identity, hold to the former.)

Card Counters and Reno Pit Staff

Beware of Greeks bearing gifts.

Subtitled: And you thought the blackjack dealer was evil …

Story time.

Nice Pit Boss: “You know, you should really be playing two hands on positive counts.”

Syph: “Yah, but I don’t want to wear out my welcome here. Besides, I think your dealer likes me.”

Nice Pit Boss: “She’s married. Let me get you a dinner.”

Syph: “Hey, thanks!”

While eating, the Nice Pit Boss joined Syph for dinner. They laughed and talked about the game. Turns out, the Nice Pit Boss used to be a card counter himself and even wrote a small book on the subject, and as the rapport developed, Syph popped the question:

Syph: “So, you don’t mind if I come in and play?”

Nice Pit Boss: “Son, I’ve been through three divorces… you think I care about this shit?”

The next night, the moment Syph raised his bet, the dealer shuffled. Then another early shuffle. And another. And one look over at the smirking Pit Boss told the story. An uncomfortable feeling of betrayal pierced Syph’s soul…

Syph: “Hey, I thought you said you didn’t care?”

And the Nice Pit Boss, with a benevolent smile and detached grace that would humble a buddhist and shame a trappist monk, responded:

“I don’t.”

(True story. In my defense, it happened relatively early in my career.)

Blackjack Card Counting and Surveillance in Reno

Be Kaiser Soze.

This article may be a little long winded, but I now need to address those who would like to try and be a bit more genuine than the rest of the cloak and dagger-like card counting community. I can respect this approach, but I must warn you, it won’t work. I know, I tried.

Ya gotta be more Kaiser Soze than Forrest Gump.

The simple reason is that Gump is just too easy of a target. And if there’s one truth in the casino industry, it’s that surveillance will go after the easiest perceived threat to justify its role.

Insofar as the surveillance personnel’s relation to you is concerned, they are not interested in protecting the game as much as they are interested in protecting their jobs. Your EV of a few dollars an hour isn’t really going to affect the bottom line much (though this has been argued), but card counters tend to stick out like a sore thumb. So while backing you off may have negligible impact on the casino’s EV, it has immense value (social, hierarchical, and economic) to a surveillance goon looking to move up, hold on to his job, or earn respect.

Remember that the surveillance guys don’t have the skills to catch the true threats to their bottom line, but they can obscure this by racking up large numbers of small time counters.

Reno Blackjack Wrap Up

Ok, so you’re spreading like a maniac, you’re flirting with the dealers, you’re not having dinner with the pit boss, and you’re keeping your sessions brief.

For myself, most of my backoffs happened when I got stuck for a good chunk, then spent the next six or seven hours digging myself out.

Don’t do this. Thirty minutes tops, and twenty would be better.

Now, you’ve asked about how the intel is in Reno. Unless it’s changed recently, I can assure you that (at least at low stakes) it is virtually non-existent. I would get backed off or barred during the day shift, then return for the graveyard. My grainy, black and white picture was probably in every book in Reno, but there was always a shift (or two) in the same casino that hadn’t gotten the memo. And, yes, I was probably backed off a dozen times at the Peppermill, hell… who wasn’t?

(Incidentally, this was the same Peppermill chain where they consequently comped me a room in Wendover a few months later. Same name on the player card. And they’re still sending me promos.)

I’ve never had problems getting a game.

So any concern about your name/image getting out can be laid to rest. If you are caught, it won’t even get around to the next shift. And this was first brought to my attention by a man who had been playing in Reno for 20 years.

‘Nuff said.

Needless to say, these are only my experiences. But as a guy who tried to live off a small bankroll in Reno, I thought I’d venture my two cents. Again, none of this is meant to replace your own experience, but if you are undecided on a certain area, I don’t mind giving a bit of a nudge. ♠

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How to Negotiate for Better Casino Comps

Redefining the Whale: Las Vegas Casino Comps for Smaller Fish

by Arnold Snyder
(From Blackjack Forum Vol. XXII #2, Summer 2002)
© Blackjack Forum 2002

OK, let’s look at the positive side of the September 11 terrorist attacks. We all know the negatives. Trying to fly anywhere these days is a royal pain in the butt. Anyone who looks the slightest bit foreign gets shaken down, searched and sometimes held for questioning. The government is now allowing itself to trample all of our civil rights in the name of national security. Then, there are all those dead people in New York…

But still, as Monte Python sings, “Let’s look at the bright side of life!”

Hey, those crazy Arabs who attended flight classes, but skipped out on Landing Gear 101, have inadvertently created some damn good blackjack conditions in Las Vegas… at least for high rollers.

Now I know some of you are thinking… “C’mon, Snyder, September 11 is a day that will live in infamy, a day of great national tragedy, the mass murder of thousands of innocent people… you can’t take this horror and turn it into a blackjack parable! We don’t recall seeing any headlines that read: Thousands Killed, But Great Deals for Gamblers in Vegas!”

Oh, ye of little faith. I don’t make up the news, I just report it. And the fact is: Osama bin Laden, nut case that he is, has significantly changed the face of high stakes blackjack in Las Vegas. Stick with me, gang. There’s a story here…

The economic effects of September 11 on the casino industry have been phenomenal, with various gaming regions reporting both dramatic increases and decreases in business. Las Vegas, for instance, saw its hotel occupancy rate immediately nose-dive from the 97+% average down into the mid-70% levels, resulting in massive layoffs, stalled and canceled construction projects, and an economic recession that has forced the bankruptcy of at least one major Strip casino. The struggling Aladdin, for instance, which had been aggressively pursuing refinancing negotiations throughout the Summer of 2001, put itself on the auction block after September 11.

All of the Las Vegas casinos have been hurting since September 11, but the major Strip casinos have been hardest hit. There is a big difference between the effects on mega-casinos like Caesars or Bellagio, and locals’ joints like Palace Station or Sam’s Town. Unlike the Strip casinos, the locals’ joints didn’t physically lose their customers. The cutbacks and layoffs meant that some of the locals had less money in their pockets, but most of them were still there.

The big joints, on the other hand, depend on tourists who fly in from all over the world. The big joints also cater to a segment of the customer base that the locals’ joints totally ignore: the whales, those players who fly in with six and seven-digit credit lines, or front money, then play baccarat, blackjack, or Pai Gow, for anywhere from $10,000 to $100,000 per hand.

These whales are not a small profit factor for the Strip casinos. As an example of how much these big players can mean to the carpet joints, consider the fact that virtually every major casino on the Strip — except for Bellagio — reported a dramatic reduction in table game win for the month of September, 2001. Why did Bellagio have a great month? Because noted whale of whales Kerry Packer happened to be staying at Bellagio the week of September 11, and he was unable to leave when all international flights were canceled! Bellagio cleaned up on his extended vacation there. Come October, like the rest, Bellagio was hurting too.

One major factor in the disappearance of the whales from Vegas’s VIP rooms was Japan Air Lines’ (JAL) cancellation of all non-stop flights into Las Vegas. JAL had a near monopoly on flights to Vegas from ports in the Far East.

It should also be noted that JAL did not cancel their Vegas flights because the airline was afraid to fly into the US. They did not cancel their flights until it became clear that there were no longer enough passengers to make these flights economically feasible. People all over the world were afraid to fly. The junkets from Tokyo and Hong Kong that typically brought in the highest of the high rollers were no more. The Strip casino VIP rooms were empty.

Not all casinos throughout the US suffered like Las Vegas did. California’s Indian casinos thrived, as gamblers avoided even short domestic flights. Likewise, Detroit’s casinos saw an increase in business as a direct result of the September 11 events. Since nobody actually flew into Detroit to gamble, the flight paranoia meant fewer Detroiters were flying out of the city.

Also, those players in Michigan and Ohio who would normally drive across the Ambassador Bridge to gamble in Canada’s Windsor Casino, stayed to play in Detroit so they wouldn’t have to put up with the security delays and hassles of crossing the Canadian border. Customs was a nightmare.

What many of the big Vegas Strip casinos learned from September 11 was that a small handful of high-end players meant the difference to them between profit and loss. One player betting $10,000 per hand was worth a thousand players betting $10 per hand. An individual player’s result (such as the result of a Kerry Packer) can sometimes change the bottom line result for an entire month!

The big Vegas casinos had to make some quick decisions after September 11. If JAL wasn’t going to fly the whales in, then there was no use even trying to get the “regulars” to come back to the VIP rooms. The regulars were oceans away. What Vegas needed in its VIP rooms was a new group of regulars. Although domestic US flights also had severe cutbacks, and many Americans were frankly afraid to fly, at least the domestic flights still existed, so the Vegas casinos were simply faced with the problem of figuring out how US players could be lured back into the air.

Money talks.

The casino bigwigs looked at the way they marketed their games to the overseas whale market. Whales lived in a world of comps unknown to the average player, including most players who counted themselves as “high rollers.” Whales typically got not only the standard RFB (room, food, beverage) comp, for themselves and their friends and families, but they also got their airfare which in many cases meant the cost of the fuel and the pilots for their private jets.

Then there were gifts: jewelry, watches, shopping trips to designer stores, tickets to concerts, sporting events. There were invitation-only tournaments, sometimes with six-digit prizes and no entry fees or buy-ins. There were the loss “rebates,” running as high as 20%, 30% or more, depending on the player’s credit line and betting level. A loss rebate is just what it sounds like: if the player has a 20% rebate deal, and he loses $500,000, he’ll get 20% back ($100,000) as “walking money” when he leaves. And then there was up-front money itself. Come in with a million bucks, and get an “extra” $20K or more in chips, just for showing up! Just a little incentive.

So, since the overseas whale market was gone, the casinos needed a new class of domestic whale who could be convinced to fly in and take one of the empty VIP seats. There weren’t a whole lot of domestic players in the multi-million-dollar action category, so the casino marketing execs instructed their hosts to go after the high-end US players who were a level down from the whales, the players who normally put up front money or had credit lines from $25,000 to $100,000. These new mini-whales started getting offers from hosts that included all the typical whale bait.

For the first time, a player who came in with a $100,000 credit line got an inkling of what it was like to be a player who came in with a million. For high-end advantage players, Las Vegas has become vastly more advantageous since September 11, 2001. Some of the new comp opportunities have little dollar value, but others are valuable enough to make a mediocre game a highly advantageous game. Let’s look at, and analyze, some of the complimentaries that are being made available to mini-whales these days.

Butler Service Comps for Whales

Unless you’re trying to impress your date, having a six-room suite with fresh flowers and fruit bowls changed daily, and butler service, has no dollar value. Whales have always gotten butler service in their rooms. Now, with a lot of the penthouse suites empty, casinos are starting to give these rooms to lower end players. And what is the difference between butler service and regular room service. Does it really matter if the person who brings the food up to your room is dressed like a butler?

“Whales get real butler service, and that means a lot of things,” says one player who wishes to remain anonymous. “If you call for your breakfast, you can ask to have the pot of coffee brought up right away, and it will be there in a minute. You can ask for a copy of Sports Illustrated or some other magazine, and the butler will pick it up in the gift shop for you and deliver it with your breakfast.

“Also, if it’s real butler service, you won’t ever see a bill. He’ll bring the food, set the table, and disappear. With room service, you can be sure you’re going to sign for whatever you order. When you have butler service, the casino has already decided up front that everything you ask for is comped. Now that some of the smaller fish are getting into the luxury suites that were meant for the whales, casinos are sometimes telling these players they have butler service when they really don’t. If the ‘butler’ asks you to sign for the food, that’s not butler service.

Butlers will pick up your tickets at the box office, press your pants, you name it. And they never hold a hand out for a tip. They’re servants. You leave money for them in an envelope when you leave, and you should be generous.”

Gifts for Whales

Players who get rooms with butlers also typically get gifts, which range from small (flowers, chocolates, wine, champagne, etc.) to medium (jackets, luggage, designer shirts, and the like) to lavish (watches, jewelry, artwork, and more). There is also very little dollar value to most of these gifts, at least from the perspective of the advantage player. A typical gift watch for a mini-whale, which might sell for $2000 in a jewelry store, probably wouldn’t get more than a couple of hundred bucks on Ebay. You might as well just keep the watch.

A High Value Casino Comp: Shopping Trips

Many casinos are now offering shopping trips to their mini-whales. You’ll be set loose in a store with a dollar limit of anywhere from $500 to $15,000, depending on your level of action. The casino picks up the tab, usually by special arrangement with the store(s) involved. The shopping comp, which sounds extremely valuable, is also of limited dollar value in the real world. As explained by one advantage player:

“I got an invitation to a $1000 shopping spree at Neiman Marcus. I thought fantastic, since I would never shop there otherwise — all that overpriced designer crap. I figured I’d go spend my thousand bucks, then return everything later and walk with the cash! Unfortunately, as I discovered, you can’t return anything for cash. Not allowed. You either have to get something you actually want, or maybe a gift for your wife, or something you might be able to sell to one of your friends at a discount… a thousand bucks doesn’t go very far in Neiman Marcus.”

Casino-comped shopping-trip purchases cannot be returned to the store(s) for cash refunds because the casinos negotiate special deals with the stores to pay the wholesale price on a no-refund basis. If you get a $600 silk shirt, you can be sure that the casino is not paying anywhere near $600 to the store. As another player describes it:

“The whole shopping trip comp is to make rich jerks feel important. It’s like ordering a bottle of Dom Perignon from room service. Most of the big casinos list Dom at anywhere from $250 to $350 on their room service menus. They don’t even specify the vintage. I can almost guarantee you’ll get a 1992 bottle, since — as Dom goes — that’s the cheap stuff. You can get that in any liquor store for about $99 a bottle, so I would guess the wholesale price is $50 or less.

“If you’ve got a million-dollar credit line, on the other hand, you’re not going to get the 92 Dom because they figure you probably know the value of it. You’ll get the good stuff. If your credit line is only fifty thousand, they’ll figure you don’t know Dom from Cold Duck. You get the 92. You think they’re comping you a $300 bottle of champagne, but it’s just to make you feel important.

“By putting outrageous prices on room service items, they can also max out their ‘soft comps’ so that they can avoid paying any ‘hard comps’ if you turn out to be a phony. For example, let’s say you put $100K in the cage when you arrive, then you never place a bet of more than $1000, and you rarely even bet this much. They’ve got you down as a $400-500 average bettor. They know that the $100K front money was just for show. You never really gave them a shot at your bankroll.

“When you try to get your airfare, they can point to your $1500 per night suite, and your thousands of dollars in room service charges, and your $2000 shopping trip, and tell you that you don’t have sufficient play to qualify you for $1200 airfare. Airfare is always a hard comp. If they give you $1200, then it’s $1200 cash. There’s no kickback from the airlines.

“For this reason, if you think you’ve got a shot at getting your airfare, skip the Dom and the caviar. In fact, tell them you just want a small regular room because you’re afraid of heights, or you hate elevators. Tell them your wife hates shopping! Minimize the soft comps, and you might see some airfare cash when you leave. Of course, if you are putting a half-million on deposit and playing long hours, with an average bet of a couple thousand, you don’t have to scrimp on anything. You’ll get your airfare and lots more.”

Comped Event Tickets

Says one pro: “When I was playing at a lower level — chunky black action — I used to milk event tickets for money. Fight tickets, concerts, shows — you can sell all of those tickets pretty easily, especially if the event is sold out. And, because the casinos comp so many tickets, it’s hard to find a show that’s not sold out!

“Event tickets are one of the easiest to get soft comps there is, unless it’s some major event that everyone really does want to attend. You simply tell your host to get you as many tickets as he can come up with because you have a whole group of friends in town, and you want to take them all. I used to scalp fight tickets right outside the entry gate. You’ve got to be cool, just wait until someone meets your eyes. There are always people who show up looking for tickets.

“Now that I’m more of a whale, I can’t pull this off so easily. If I’m trying to pass myself off as some millionaire gambler, I can’t be seen hawking tickets like a two-bit hustler. It’s important to uphold the image at all times.

“If I don’t personally know someone who will buy the tickets from me, then I’ll just go to the event myself. But it’s painful sitting in $800 seats with a friend, knowing that some fight fan would have given me $1200 each for the tickets. Especially when I don’t care that much about boxing. But image is everything at this level of play. If I really don’t care about the event — I had tickets to the Madonna concert last year — I’ll give the tickets to a host or a boss or someone in marketing.

“I recently took a buddy to a comped fight — fantastic seats — and found myself sitting next to one of the casino marketing execs and his wife whom I’d met briefly on a previous trip. This was my host’s boss, and he recognized me.

“Turns out he was the person who had scored these tickets, and he knew I would be sitting next to him. Imagine the questions that might be raised if I didn’t show up in those seats, especially if I later told my host how much I enjoyed the fight! Even worse, what if the marketing guy asked whoever did show up in my seat where he’d gotten his tickets, what he’d paid for the seats… When you’re playing blackjack for thousands per hand, you can’t afford to look cheap or phony to anyone.”

Air Fare Casino Comps for Whales

In the new edition of Comp City: A Guide to Free Casino Vacations (Huntington Press, 2001), Max Rubin describes an airfare comp scam that big players have been using for many years, in different variations. According to Max:

“…buy your tickets at the lowest discount available, nonrefundable. Then, at the last minute, buy a first-class round-trip ticket from a travel agent… When you get to your destination, play in two different hotels… After a long play in the hotel you’re not staying in, show your host the expensive tickets and snivel, telling him how much you lost and how you didn’t even stay at his hotel… and pleeeeease help me out here, I’m tapped and my wife’s going to kill me and can you make reservations for my next trip?…

“Then take that same first class ticket to the joint you’re staying at and tell the host there how you paid for all your own lunches, but you’re tapped and cripes, you’d like to come back but if you go home empty, you’re gonna get killed… Be polite, but persistent, and you’ll likely get at least a portion of your high-cost first-class airfare picked up by both places. Then fly home on your budget ticket and cash in the first class beauties.”

I have heard many variations of this airfare scam through the years, with various numbers of first class tickets being purchased and reimbursed by various numbers of casinos. In Burning the Tables in Las Vegas (Huntington Press, 1999), Ian Andersen says that when he visits Las Vegas, he checks into multiple hotels, under different names, for the same trip, and plays at all of them.

He explains: “I buy several sets of open first-class airfares, one for each of my registered monikers. I submit the proper ticket to the VIP host at each joint for a refund. They’ll call up my action on the computer. Assuming my play warrants a refund, they fork over the cash with no questions asked.”

Ian describes how the ploy works for a high roller who “deserves” the airfare comps, as opposed to Max who describes a player who is trying to get more than he “deserves” with the argument that he has lost so much money at the tables. Ian’s method would probably not work so well these days. Purchasing airline tickets under multiple fake names could be dangerous in today’s terrorist-paranoid world.

Likewise, displaying all those fake ID’s, along with the tickets, in Las Vegas hotels, would take a lot of nerve. The level of play required for airfare reimbursement would more often than not require the casino to file a Cash Transaction Report (CTR) with the IRS. This would require the player to show both a picture ID and provide his Social Security Number to the casino. Post September 11, all of these phony ID ploys are much more dangerous, and likely illegal. Max’s whining act is at least not liable for criminal charges.

Ironically, the casinos are well aware that there are big players pulling this airfare scam, and they have known it for many years. In fact, the above quote from the second edition of Comp City, which came out in 2001, is almost identical to what Max wrote in his 1994 first edition.

One casino exec told me, “I don’t care one bit if a player is flying coach but getting us to reimburse first class. Why should I care as long as he gives us the action? We don’t even look at the ticket for our big players. We ask them how much the airfare was, and we give them the cash. In fact, we usually round up. If he says $1850, we’ll just give him an envelope with an even $2000. What do we care if he actually rode in on a motor scooter?”

In Kevin Blackwood’s recent novel, The Counter (Wooden Pagoda Press, 2002), reviewed in the Spring 2002 issue of Blackjack Forum, the author describes a fictional player who must be the ultimate airfare scammer. Since he lives in Vegas, he doesn’t even fly coach to get there. Yet he gets reimbursed for hundreds of round-trip first-class airfares every year by purchasing multiple tickets every week, as if he and his wife are flying in from Cleveland. This character purchases his tickets from a travel agent friend, then returns them to the same agent. He is portrayed as having made half a million dollars in the past two years on phony airfare reimbursements.

This, of course, is pure fantasy. Whereas Ian Andersen describes a workable ploy whereby a big player with multiple IDs might get multiple airfare reimbursements for the same trip under different names, and Max Rubin describes a player who is not such a big player getting multiple reimbursements under his own name, it is highly unlikely that any big player could have enough fake IDs to get multiple reimbursements each week, 50 weeks per year, for years on end.

The number of Las Vegas casinos that take action big enough to qualify a player for reimbursement of two first-class round-trip tickets from Cleveland is small — maybe a dozen or so. And the amount of action required for this reimbursement would be substantial in both hours and average bet.

No player could play that many hours per week, week after week. And any player who did put that many hours on the tables every week, with average bets in the multiple thousands, at the same dozen joints, would become so well- known so fast that his fake names would unravel in no time. There is just too much communication in the industry about the big players.

Most of the big Las Vegas casinos are owned by one of three different groups: The MGM/Mirage group, which owns MGM, Mirage, Bellagio, Golden Nugget, New York New York, and Treasure Island; The Park Place Entertainment Group, which owns Caesars, Paris, Hilton, Flamingo, and Bally’s; and the Mandalay Group, which owns Mandalay Bay, Luxor, Excalibur, Circus Circus, and Monte Carlo. All of these groups have cross-over management and marketing execs.

Even if the casinos were so ignorant that they never noticed the same face continually popping up under different names, what would the airlines think of a travel agent who purchased and returned hundreds of first-class tickets every year, for the same passengers, none of whom actually ever flew anywhere? The concept reeks of a scam. Even if you could find a travel agent willing to do this, it would not be long until the feds were investigating.

In any case, the new “ticketless” travel option that most airlines now offer has made it much easier for players to pick up multiple airfare reimbursements. Some years back, when the scam first came to the casinos’ attention, many casinos started rubber-stamping the airline tickets “PAID,” with their casino name. It took a lot of guts to ask for a second reimbursement at a different casino, when they could see that you were already reimbursed elsewhere.

Now, with so many people purchasing tickets on the Internet, or through 800-numbers, “ticketless” itineraries are simply emailed or faxed to the purchaser. By printing out multiple copies of the itinerary, it doesn’t matter if a casino stamps it “PAID.” You can use a clean copy for the other casino(s) where you play.

One way to judge your whale status at any casino is by how they handle your airfare reimbursement. If they want to see the ticket (or itinerary), and then (usually) photocopy it, and have you sign a receipt for the exact amount paid, you’re not very high on the whale scale. If, on the other hand, the host just hands you an envelope with money in it, no questions asked, you’ve arrived at the top. Of the comps available to the new breed of mini-whale, airfare is the first one with real dollar value. It’s always paid in cash, and the amount can be substantial.

Beyond Comp City…

Most of the above comps are discussed at great length in Max Rubin’s seminal work on the subject, Comp City. Max never gets into some of the whale category comps, as up until recently these have been just too unavailable to all but the chosen few who came to town with millions to lose. So, let’s look beyond Max into some of the comps that casinos are dangling in front of mini-whales today.

Money Comps for Whales

One very valuable comp, formerly available only to whales, is money. That’s right, most of the big casinos will flat-out comp you money. They won’t give it to you in cash, per se, but it has virtually the same value as cash.

Some casinos call these cash comps “bonus” chips, or “promotional” chips, or “casino action” chips. One player explains it like this: “If I go in with $100,000 front money, the casino gives me an extra $2,000 in ‘promotional’ chips as soon as I put the money in the cage. Two thousand bucks right off the top, just that easy. My host told me that I could get this extra $2000 for every $100K I come in with. If I had $500,000 to put in the cage, they’d give me $10,000 extra right off the top!”

Technically, this is just a high-end variation of what many casinos have provided their low-end players for many years. If you’ve got a “fun book” from some local motel in Vegas, there’s quite likely a coupon within it good for a roll of nickels ($2.00) at one of the casinos that’s trying to lure in slot players.

I’m not sure which casino invented the concept of “casino action” chips as a bait for players, but Bob Stupak raised it to an art form back in the 80s at his Vegas World Casino (now the Stratosphere). I can’t remember all the various offers made to players by Vegas World, but typically if a player checked into their hotel for the weekend, he could get back nearly all of his hotel charge in promotional “casino action” chips. These looked more or less like regular gaming chips, except that players were not allowed to cash them in at the cage — they had to be played at the tables.

Also, they did not have the full dollar value of regular casino gaming chips, because they could only be used for one play. If you bet a $5 casino action chip and won the bet, you’d get the $5, but the casino action chip would be taken away. This cut the value of a casino action chip by slightly more than half. What cut it even further was the fact that they could be used on “even money bets only” at the tables. A player who was dealt a blackjack on his casino-action-chip hand, learned to his dismay that he would only be paid even money.

In the 90s, Caesars Palace started using promotional chips to lure in bigger fish. During slow periods, they would send coupons to their high-end customers offering them casino chips valued at $100 up to $500, depending on the player’s prior history. In the mid-90s, MGM began making similar offers. Typically, no play was required, nor was front money necessary, though often the player was required to check in at the hotel in order to get the promotional chip from the cage.

At different casinos today, these promotional chips work differently. At the MGM/Mirage properties, the bonus chips that are given to big players have full-dollar value because you may continue to play the chips until they lose. You still can’t cash in a promotional chip, but you win real chips with them, and if you are there to play, this is real money. I’ve heard a few stories about players who started play with a $500 promo chip, then won numerous bets in succession, and finished playing through the entire weekend at the black chip level without ever having to dig into their own pockets!

It may sound incredible that any player might be provided with thousands of dollars in promo chips, but the fact is, if you are going into a casino with $100,000 front money, the casino will be expecting you to have average bets of a couple of thousand dollars. They’re really just giving you one average bet! And if your average bet is not in this range, then you will be unlikely to get this promotional chip offer in the future. Casinos hate it when players put up front money “for show.” They expect you to gamble with the money you come in with, not just flash it for comps.

Says one pro: “If you are playing at the level where you are putting up substantial front money, and the casinos are giving you bonus chips up front, you really are expected to give them satisfactory action, in both average bet and the number of hours you play. This type of promotional bonus is always arranged by your host, and you’ll know what to expect from them, and what they expect from you, before you arrive. If I go in with $200K, and they bump it up to $205K, that’s a real nice head start on a playing trip.

“Before you get to that level, however, you will probably pass through the lower-end comp, where the casino marketing department just sends you a flyer with a coupon for a $200 promotional chip, or a $500 promotional chip, or whatever they feel your past play warrants. These coupons are always dated, and usually have a very small range of dates when you can pick up your chip from the cashier.

In almost every case, the chip offer is combined with a free room for 2-3 nights during the valid dates, weekends usually excluded. If you don’t want to pass up the opportunity to get the chip, but you really don’t want to play at this casino, then your best bet is to check in, get your chip, play it on a table, then leave the pit without showing them any other play during your stay there.

It’s crazy how in most casinos marketing and pit operations are so disconnected that you won’t even show up in the computer as having played there, provided you never give the boss your player’s card. I know one player who got one of these $500 chip offers from the same casino many months in succession, despite completely burning them on the comped room and giving them no action whatsoever except for the promo chip.”

The Best Casino Comp: Loss Rebates

Another high-end comp being offered to mini-whales, formerly available only to the highest level of whales, is the “loss rebate,” or “discount,” as some casinos call it. The rebate is exactly what it sounds like: if you lose, you will get back a percentage of your loss when you leave.

In Comp City, Max Rubin discusses the concept of “walking money,” and loss rebates are just a high-end variation of this age-old pat-on-the-back-and-handshake, with a little green pressed into the player’s palm. There has long been a tradition in the casino industry that if a player taps out (loses everything he came in with), the casino will give him a hundred bucks or so in order to get him home with something in his pockets (or even to pay for the bus ride!). Walking money was simply a courtesy extended to “good” customers.

The loss rebate offered to whales and mini-whales is a creative take on walking money, except that it is not necessary for the player to go broke, and the amount of the rebate is agreed upon in advance of the player posting his front money.

Various casinos have various rebate programs. Some require the player to put up a specified amount of front money — which might range from $50,000 to $250,000. Some require a specific loss in order to qualify for the rebate, which again might be $50,000, or $100,000, or more. Some have rebate schedules that change as the amount of the loss, or the amount of front money changes.

For instance, you might be offered a 5% rebate if you lose $50,000, a 10% rebate if you lose $100,000, and a 15% rebate if you lose $250,000 or more. The purpose of this graduated rebate is to keep you in action after you’ve lost a significant amount. Those in the whale category, who come to town with millions, have reportedly been offered loss rebates as high as 25% to 30%.

As a card counter, this type of program will likely have you salivating. Imagine the value of having every major loss cut by 10%. In fact, consider the result if you just played a break-even game with the house, with a 10% rebate deal, and you always played until you either won or lost $100,000. Over time, you would win half of your sessions, and lose half, but every time you lost you’d only lose $90,000. On average, you’d be making $5000 every time you played! If you played every weekend, you’d profit more than a quarter million dollars a year, just by playing even with the house!

Unfortunately, this is one of those things that sounds better on paper than it would work in the real world. In Extra Stuff: Gambling Ramblings (Huntington Press, 1991), Peter Griffin discusses and analyzes a number of loss rebate propositions that he had heard of being made to various high level players.

One of these rebates was negotiated by a wealthy sheik who wanted half of his loss returned (a 50% discount on losses!), provided he would bet $10,000 per spin at roulette. Griffin shows that with a rebate of this magnitude, even at a terrible game like double-0 roulette (5.26% house edge), the sheik would clean their clocks to the tune of about $87,000 per trip, if he always played for exactly 234 spins, and also always bet the numbers (35:1 payout), rather than the even money bets (red/black, odd/even, etc.).

It certainly isn’t intuitive to me that the way to make money on this rebate deal would be to bet the long shots, but that’s a different story. What is most important from Griffin’s analysis as far as blackjack players are concerned is that if the sheik were playing the even-money payoff bets, instead of the numbers, then the optimal number of spins for him to have the best edge over the house would be 7, not 234. In fact, if he played more than 28 spins on these even-money bets, then even despite a 50% loss rebate, the edge would swing back to the house.

Griffin further analyzes the optimal play with a loss rebate of only 10%, where the player is making even money bets in a game like craps, where the house has only a 1.4% edge on the pass line. In this case, the optimal number of bets the player should make is only 3, and if he makes more than 11 bets, the overall edge swings back to the house.

This is very enlightening for any player who decides he wants to “milk” loss rebates, with a strategy which assumes that he will win half the time and lose half the time, give or take the flux and a relatively small house edge. If the house has any edge over you at all, it does not take much play on your part before the rebate value has been cut sufficiently to make your continued play a negative expectation.

Of course, the bigger question is, can you play a winning game at the multiple-thousand-dollar level? At this level, where you are definitely one of the biggest players in the house, especially with a loss rebate deal, the scrutiny will be intense.

Can you pull off card counting (or other advantage play) in such circumstances? How much camouflage will you have to lay, both playing camo and betting camo, to keep the bosses smiling and the eye upstairs happy with your play? Rebate deals can have a huge value for advantage players who can actually get away with advantage play, or even break-even play, at that level of action, but few can probably do this for long.

That’s why, although the casino industry is aware of Griffin’s analysis of rebate value, they continue to woo gamblers with discounted losses. They know that with modest rebates, and a small house edge, it doesn’t take them long before they have the best of it. Try playing craps for less than 11 rolls of the dice and see if you qualify for a rebate, regardless of your bet size, your credit line, or how much front money you put in the cage.

Hookers for Whales

Here is another one you won’t find in Comp City: sex. In fact, Max writes: “Contrary to popular belief, hotels do not send hookers to high-rollers’ rooms. Gambling destinations are becoming more and more family-oriented, and a casino, no matter how big the player, would risk losing its gaming license if it supplied gamblers with women.”

Max, this just ain’t true anymore. (Well, it’s true a casino might be risking its license, but it’s not true they wouldn’t risk it!) A host at a major Las Vegas casino recently offered one mini-whale an invitation to a “pajama party” in one of the casino’s penthouse suites.

“He told me I didn’t have to wear pajamas myself, but there would be a good selection of women there who would be in their nighties, and ready to go back to the players’ rooms with them. He said there would be drinks and hors d’oeuvres, and that only their ‘best’ players were invited. ‘Best’ to them means the biggest losers, or expected losers, I guess. I was actually shocked, but I just told him I never paid for sex. He said the women were already paid for, and to just think of it as a comp.”

Whether a casino might really be risking its license on something like this is debatable. Technically, the casino is not offering a sex partner to its customer; the casino host is offering this goodie. Or, you can be sure that would be their argument! You can be sure the casino itself would wash its hands of this matter. “We didn’t know nothin’ about it, judge!” You can also be sure that the host is not pulling money out his own pocket to procure sexual favors for players. One way or another, that host will be reimbursed for his efforts and costs.

Says another big player: “I was invited to a major casino in Mississippi, and my host asked me if I wanted a girl for the weekend. I asked him what he meant, and he said, ‘She’ll eat with you, she’ll sleep with you, she’ll stay with you all weekend. Just make sure you don’t bring your wife.’”

Shades of pre-Castro Cuba! If you were a casino gambler back in the 50s, when Nevada boasted the only legal casinos in the US, many East-coasters chose Havana over Vegas. The flights were cheaper and the casino-hotel accommodations were first rate. Casinos were not family affairs back them. There were no theme parks for the kiddies. In Batista’s casinos, for an extra fifty bucks or so, a hotel guest could get a girl (or boy) companion for the whole weekend. The big players were often comped this luxury.

I can definitely state that there’s no dollar value to this type of comp for advantage players. I’m not even sure if this would be considered a soft comp or a hard comp, pardon the pun(s). But as I doubt this is a cheap comp for the casino, you may want to tell your host that whatever they’re paying the girl, you’d rather have it in promo chips. I mean, we are in this for the money, aren’t we guys?

In any case, the competition for high-end players is obviously getting fierce. The day of the mini-whale is here. ♠

[Note from Arnold Snyder: For more information on casino comps and high rollers (whales), see Deke Castleman’s Whale Hunt in the Desert: Secrets of a Vegas Superhost.]