Category: Blackjack

Cheating at Blackjack in Puerto Rico

by Harry J. McArdle
(From Blackjack Forum, Vol. VI #2, June 1986)
© 1986, 2006 Blackjack Forum

[Editor’s note: From the founding of Blackjack Forum in 1980 through 1986, when this article was submitted by Harry McArdle, numerous players had written about encountering high counts shoe after shoe while playing blackjack in Puerto Rico. The counts did not go down by the time the cut card was reached despite the fact that the cut card was placed only a half deck from the end of the shoe.

Although it’s been a long time since players have reported any signs of cheating at casinos in Puerto Rico, I am including this article in the library for historical interest and for its discussion of methods of cheating in blackjack shoe games. –A.S.]

In Puerto Rico in the early 70s, casinos like the El San Juan had all of their dealers deal from a shoe with two hands. They pulled cards from the shoe with the right hand. Their left hand held the front of the shoe. Their left thumb fed cards to their right fingers. Their left forearm covered the top of the shoe.

It occurred to me that this was conducive to second dealing as the left thumb could easily pull up the top card, allowing the right fingers to pull out the second from the top. Of course, most of the dealers were not second dealing. As with dealers out west who used the mechanic’s grip to no purpose, they only looked like they were second dealing…

In the 60s, I learned that the dealer schools of Las Vegas taught dealers to high low stack. [Editor’s note: I have not been able to verify this claim. —A.S.] The dealer trainees were told it was a form of shuffling. “Mixing ‘em up as you’re picking ‘em up” was the motto.

At the Four Queens in ’67, I made $700 by a combination of luck and the fact that I sat at first base and varied my bet with whether the last card played in the previous hand was high or low. In short, if the dealer was high-low stacking, I would bet low if the last card played was high and high if the last card played was low.

My luck at the Four Queens prompted me to seek out high-low stackers in Puerto Rico.

So, naturally I jumped at the chance to play first base against the finest, most thorough high-low stacker I’d ever seen. This guy was dealing at a $5 table, which was the most active since it faced the entrance to the casino and usually got the most business.

Usually, a high-low stacker will only intermittently high-low stack the deck. This guy was able to thoroughly high-low stack the deck. In retrospect, I guess he must have been false shuffling too, since the cards were coming out exactly high-low as he had picked them up, except when the cards came to me! I’ll explain.

I watched cards come out high, low, high, low until the dealer dealt the last card which, say, was high. I was sitting at first base and naturally would bet low as the next card would more likely be low. When the last card would be low, I’d bet high. But each of these times that I bet high I got the wrong card. I got a low card. Finally, it became obvious to me that I was not getting the next card when I raised my bet.

“I don’t mind you high-low stacking,” I said. “In fact, that’s why I sat here. But when you start second dealing, I think that’s going too far.”

“No puedo entender,” the dealer responded. “No comprendo su englise.”

“I don’t like cheating,” I said in a loud voice. The other players at the table nervously glanced around like they were looking for fire exits. The pit boss came over. “Clearly, sir, there is nothing wrong, but if you thought there was, then why didn’t you leave?”

I remained silent. When the pit boss left along with the other players, the dealer got his rocks off. Apparently, the word cheating turned him inside out. When we were alone together, he delivered a speech in really clear English. His tone was that of a man angered at me for belittling his skill.

“I don’t care where you go, here, Vegas, anywhere,” he said, “you won’t find a dealer who makes more money than I do, and the reason is that I’m the best. Nobody’s better than me. Nobody wins more than me. This is my game. You think you can come to my table and beat me at my game, you’re crazy. I’m the best. I’m a champ.”

A couple of weeks later, I approached a government inspector whom I knew to be honest (this one was honest!), and pointed out the dealer and asserted that he was high-low stacking and second dealing. The government inspector did not know what this meant. I tried to explain. The inspector promised to watch the dealer.

After that I did most of playing at the poorer casinos that could not afford such high-priced dealers.

But even at poorer places like the Borinquen, problems developed. One evening I continuously got positive counts every time the dealer reached the blank card that indicated reshuffling. Sure, the high cards could be behind the cut card. But every time? I began to suspect that all the cards were not there.

After a couple of hours I voiced my suspicions and asked for a count of the cards. In that warm, polite tone that is so common in Puerto Rico, the pit boss informed me that if I waited until 4 a.m., when the casino closed, he would give me the cards. The other players seemed satisfied. Even I had to admit that this was fair. So I waited three or more hours and kept getting positive counts. By closing time they all seemed to have forgotten their promise to give me the cards. So I reminded them.

The pit boss snapped his fingers.

“Four decks please,” he ordered of an underling.

“No,” I said. “I don’t want four decks, I want the four decks we’ve been playing with all evening. You said if I waited until closing time I could have them.”

“Oh no. That’s impossible. They have to return to the government inspector so he can check them.”

“I’ve been keeping track of them all evening and I don’t think they’re all there. I want to see the government inspector,” I answered.

I repeated my request for a count of the cards. He suggested that if I didn’t like things I play somewhere else. He would not permit a count of the cards and told me to leave and not return.

1979. Once again the lure of Puerto Rico’s warm women, sunshine and, of course, blackjack drew me back to that island in the sun.

What of the luxurious El San Juan? Well, it was eight years older and not as luxurious.

What about the blackjack? Well, the fast two-handed dealers of the early seventies were gone. In their place were the ordinary, nice, simple and not so simple Puerto Rican dealers of the type I remembered from the 60s.

The dealing was obviously honest but the counts were constantly very positive. By this time, I’d become a skillful cutter capable of bringing the high cards to the front more often than not. But all attempts failed. I still got positive counts at the cut card, just as at the Borinquen in 1982.

At the end of one shoe, I asked the dealer if he’d keep flashing the cards past the blank card. He started to but was stopped by the pit boss. I asked the pit boss to count the cards to see if they were all there. He told me he’d give them to me at the end of the evening. Déjà vu.

At 4 a.m. he reneged. By that time, however, I’d learned something. None of the dealers got to check the cards. They merely shuffled them. How the cards were presented to the dealers, I don’t know, but I got the impression that the dealers could not verify for me that all the cards were present.

I made a scene. A number of dealers converged on the area, more to see the outcome than to side with the casino. None of them asserted that they knew me to be wrong.

The next day at the Sheraton was a repeat but in the end they gave me the cards. However, I foolishly allowed them to return the cards to the boxes they came in before giving them to me. Without thinking, I failed to make sure that the boxes were empty before the cards were placed in them. So the fact that all the cards were ultimately there proves little.

I hope things get better in Puerto Rico, blackjackwise, since I really love that place.  ♠

Paranoia 101

by 98%
(From Blackjack Forum Volume XXII #3, Fall 2003)
© 2003 Blackjack Forum

Friends of mine who are not among the professional gamblers community often tell me that I am needlessly paranoid. Some blackjack players have even told me the same, sometimes going as far as laughing at my refusal to walk into a casino in their presence.

Perhaps they are right to make light of my paranoia, but I think they are wrong. In fact, I often wonder if I am paranoid enough about casino heat to make it in this business for long.

When I walk into a casino under the guise of a gambler who is relaxed and comfortable in his environment, I am on high alert, looking for any signs of trouble. Awareness is one of the most valuable weapons in any advantage player’s arsenal and it should be honed to a preternatural level by anyone who intends to become serious in his casino exploits.

Many of the ideas in this article have been discussed previously in the vast body of blackjack literature, but, in light of seeing many players in action in the casinos failing miserably to remain aware of their surroundings, instead becoming lost in their own worlds, I was inspired to reiterate some of these ideas and, in some cases, delve into them a little more deeply.

Recognizing Casino Heat

Many threats await an advantage player in the casinos, the most widely-discussed of which is casino heat. Heat is unavoidable once a player reaches a certain level of play, but its repercussions can be minimized by the aware player.

The first sign, especially when playing in a place where you should not be known or where you should be well-liked, is any sign of unfriendly recognition on the part of the security guards right when you walk in the door. Unless you have had interactions in the past with a guard that would warrant her remembering you, you should see no hint of recognition of you on her part.

If you do see unfriendly recognition, then that is a good sign that you could be in for some trouble if you elect to pursue your financial gain in this establishment. Recognition by a guard is only one potential threat here, as there is always the chance the eye has already picked you up from the moment you hit the property.

If one or more guards begin to follow you or start speaking into their headsets when you walk by, it is time to make for the door, because you are far too hot in this particular establishment to try and make any money. The wise decision is to leave and find a more welcoming house and give it some time before attempting to return.

Assuming you make it safely into the casino and into the table games area, then you can at least take some solace in the knowledge that you are not so well-known in the casino that everyone is looking for you.

Now, there are two cases that must be analyzed, the case that you are a known player and the case that you are unknown. In either case, the first thing you should do is attempt to locate the shift manager. She is your number one enemy on the casino floor, despite how well you think she likes you. It is of utmost importance to be mindful of this person’s whereabouts for the entire time you are in the casino. If you are going to be playing large, this will be easy to do, as she will, in all likelihood, be camped out at your table, especially if the wins or losses begin mounting.

After you have made a note of the shift manager’s location, it is time to proceed to the table and get down to business. You will, undoubtedly, be greeted or noticed by a floorperson at some point, probably when you buy in. Take a look at her face and her expressions. Is there any recognition? Is there any concern? Does she go to the phone and make any calls? Or, in the case that you are a regular, is she all smiles?

This is really the first big test, as most floorpersons are instructed to contact a higher-up should a known offender take a seat at a table. It will be immediately obvious if you have a big problem and you can then decide whether to take a backoff or make for the door.

After you have determined that playing is safe and that you are a welcome guest, the next few minutes will be quite instructive as to how you should proceed. If the phone starts ringing off the hook and the pit fills up with suits with concerned expressions on their faces, you might have a problem.

If they pull out their mug books and start flipping through them furiously, you might have a problem. However, if they cannot find your picture and cannot accurately evaluate your play, you stand a chance of making some money. It all depends on whether the chance of a barring is worth the expectation you figure to earn.

I recall one time in a casino where I ended up playing a three-hour session with most of the casino’s suits swarming the podium closest to my table. Their weighty mug book was out in plain view, and pictures were being passed this way and that and the phone did not stop ringing. Two suits, one of whom was the pit manager, had taken up a permanent post at my table.

It was clear they were very uncomfortable with my play, but they never made a move, and the opportunity was too good for me to just run out on, so I stayed and played. By the time they finally figured out what was going on, I was long gone with more than one pocket full of their chips.

Confusion is your friend. If they show any signs of uncertainty then you know you can take a shot. If you are marked for a barring, you will know immediately, as there will be no hesitation on their part to get the shift manager and possibly some security over to let you know you are not welcome.

In the example above, I played through the casino heat I was given because the conditions were right to do so. In most cases, I would have departed a casino were I getting heat like that, but I figured it was not as bad as it looked.

More Subtle Forms of Casino Heat

Sometimes, the floor will be more subtle in their evaluation of your play. A common method is to simply alert surveillance and have you watched from afar, all the while maintaining an air of calm in the pit. Your only defense against this procedure is to play a short session and hope that surveillance is not clever enough to make your play.

Fortunately, most floorpersons do not have the intestinal fortitude or comfort in their job security to remain calm in the face of big money and a possible advantage play, so they give themselves away by a glaring and growing unfriendliness that colors their aspect. It is common to have a suit watching if you are playing at a high level, but when the watching turns into glaring and the suit multiplies into many suits, you can bet you have the eye watching as well and there is something about you they do not like.

At this point, it is probably time to leave. This all seems like common sense, but I see no shortage of players who are so caught up in their game that they simply do not see the heat mounting around them. So, here is a message to everyone who is thinking too hard about his game: have a glance around every once in a while and practice harder so you do not have to focus on the cards. Do not start rubbernecking and looking all over the place, as that is a dead giveaway that you are up to something, but do try to be aware of where security is, who is watching you and where they are.

Many times a shift manager will be sneaky and lurk behind slot machines or in adjacent pits, stalking you from afar and discussing your play on the phone with surveillance, all the while assessing your overall mannerisms and characteristics. There is also the possibility that a counter catcher has been sent in to evaluate your play on the floor. While the vast majority of casinos do not employ such beasts, some do. If you find someone lurking around your table who shows up out of nowhere, either in the pit or out and about on the floor, who is taking too much interest in your game, you might want to consider some cheap cover, a break in the action or just leaving.

Another possibility is that a “special” dealer gets sent in. Many casinos have a dealer or two who actually knows how to count cards and will evaluate your play on behalf of the bosses. If you are suddenly faced with a dealer who seems to have come from nowhere or from a different pit and this dealer acts in a suspicious or thoughtful manner, you may have just gotten an additional counter at your table. So be careful.

Awareness is as important as a good act when you are playing a winning game in a casino. I recall one time when I was watching a novice playing with his friend on a table, where they had both been for a couple of hours. I noticed there was a lot of commotion with security and, within a few minutes, a large force of security was beginning to mount in groups in the area near the table.

I was getting concerned and tried to call a mutual friend to alert the player that he might want to consider getting out of there. After a few more minutes, a band of security about ten deep surrounded the back of the table, but I noticed they were all looking the other way. One of them disappeared behind a bank of video poker machines just behind the table and awakened a homeless man who was sleeping. The guards then escorted him out of the casino.

The player at the table never noticed any of this. While it was fortunate they were not after him, he never saw them coming and would have been caught completely off-guard had he been their mark and not the sleepy fellow passed out in front of the Double Bonus machine.

Casino Heat Brought on by Other Players

The threat of other advantage players is often dismissed and rarely discussed in the literature. Generally speaking, most other players pose no threat, but there are always exceptions.

It is usually not difficult to identify another advantage player in a casino. If you see him play, you will probably figure him out and, most of the time, you can spot a wiseguy just by looking at him.

If you identify another player in the casino as being an advantage player, you must proceed with caution, as he will probably be able to identify you, too. Unless you have some strange motivations beyond just making money (I will admit to this), it is wise to leave other players alone and seek out another table, preferably in another pit or another casino. Playing on his table will just give you a chance to pick up some additional heat and playing near him will give him a chance to observe you.

I know that I often do not want other players to see what I am doing because I like to keep the best opportunities to myself. And then there is the rare type of player who is actually friendly with the casino to the point that they let him work unmolested so long as he does not do too much damage. These players will often rat out other players in the casinos to score points with the bosses. This is yet another reason to avoid other advantage players in the casino.

The threat of other players goes beyond just being discovered, getting ratted out or having other people horn in on your good games and possibly even killing them in the future. I know of a couple of instances of diabolical wonging that was costly to the victims involved.

In one case, a middle-stakes player was plugging away, grinding out some nice expectation on a shoe and was wonged into by some high-stakes members of a prominent card counting team. Not only did they eat into his high count shoe, but he ended up getting associated with them on a flyer.

In another case, a player discovered that there was a card counter busy at work on a shoe game. He decided that it was more fun to sit at the bar and have a few drinks than it was to count down shoes, so he just enjoyed his beverages and, as soon as the counter started upping his bets, he walked over and wonged right into his shoe with big bets of his own. Amazingly, it took the hapless counter several shoes before he realized the other man was filching his advantageous shoes.

This sort of thing happened to me on one occasion as well. I was sitting on a table with just one other player and a card counter arrived and sat on first base. He was just spreading nickels and did not seem to notice what I was doing, so I figured he would be harmless, but, as it happened, he ended up costing me some money.

At the beginning of a deck, he did not yet have his bet in the circle and the dealer accidentally exposed the first card as she was about to deal it to him. He waved it off after glancing at it, proclaiming his intention to sit out the first round. Before I could react and pull back my bet, the six of spades came flying my way and, sure enough, turned into a hard sixteen when the second card was dealt.

Needless to say, I was irked. There are plenty of countermeasures you can take against this sort of aggression without giving yourself up to the casino, but I will leave it to the reader to devise his own plan.

My response to the guy who let me eat that six was to start discussing card counting with him in an audible fashion. It did not take him very long to leave.

Heat from Players Who Are Cheating

Many authorities and players dismiss cheating on the premise that no casino would tolerate or engage in cheating because their gaming license is far too valuable to risk. That sounds logical until you dig deeper into the world of cheating.

I have witnessed cheating and I know of many others who have too. If you are aware and if you spend enough time in a casino, you will too. This topic has been discussed in detail in countless books on blackjack and casino gambling in general, so I will not attempt to offer any new pointers, beyond suggesting that people read the books and familiarize themselves with cheating techniques and, most importantly, always be on guard.

One aspect of cheating that is not discussed very often is the threat of being in the presence of player cheating. If you discover that the players near you are trying to take a shot or making some untoward moves or if you just sense trouble, you should consider leaving.

While you are not a cheater and you are playing with a legal technique, it will undoubtedly be a real headache convincing the casino, Gaming Control and maybe even a jury that you were just in the wrong place at the wrong time.

Criminal Activity

While it is true that cheating is a criminal activity, far worse things can and do transpire in casinos and sometimes advantage players can be the targets of sinister acts.

If you are playing big and have a mountain of money and chips in front of you, you had better believe other people are going to take notice. If one of those people happens to be a thief or mugger, you could have trouble awaiting you when you leave the casino or if you leave your chips unattended at any point. Many people leave their chips on the table when they go to the restroom or take a break but only bad things can happen if you do that. Remember, the casino is not responsible for your loss if some thief runs up and takes your big stack of black chips and runs out of the casino.

Most of these people are caught, but some get away and there are other ways to reserve your seat for a couple of minutes. A single red chip and a request to the boss to reserve your seat will do the trick. Your first defense is to be aware of anyone eyeballing you or your money in a threatening manner. Most crooks are very careful when operating in an area of high surveillance such as a casino, so you may not get a chance to glimpse them casing you. When you finally do decide to leave, be aware of anyone trailing you or watching where you go.

As it happens, this is a good defense against being followed by suits and Griffin agents as well. One of my favorite activities when making my casino rounds is to follow other advantage players around and see what they are doing. I have yet to get caught, and I am neither subtle nor an expert in stealthily shadowing people; muggers and some private investigators are.

Once you have arrived safely at your car or cab, you are still far from being completely out of danger. There was a case not too long ago in Las Vegas of a man who had a large win at the blackjack tables being followed back to his apartment complex and mugged at gunpoint for his wad of cash. That would be an unpleasant bankroll hit, to be sure.

So, when you leave the casino, watch out for people lurking nearby and watching you. Furthermore, check to see if you are being followed once you have begun your drive or cab ride to your next destination. If you think you are being followed, then take an indirect route to your car or eventual destination and linger in safe places where the threat of theft is not likely to manifest itself.

Awareness

At the heart of this article is the need for an increased sense of awareness on the part of the advantage player. For some people, this comes naturally, but for others it most definitely does not.

While I am still far from having the level of awareness I want, I have learned a couple of things. First, awareness can and should be trained. Casino experience can help with this and, over time, your awareness can improve, but then again, I know of a few seasoned players who are basically out to lunch all the time, even when at the tables.

When you go about your life, do you often wander off into your own world or do you keep yourself apprised of the situation at hand, wherever you are? There is a time and place for introspection, thinking and all around downtime, but it is not when you are out in public. I reserve those things for when I have time to myself at home. The world is a dangerous place and you never know when you might be blindsided when you are out in it. Not to mention, you might just miss out on something hilarious that could make your day!

I like to get an idea of everything around me when I walk around. Who is behind me? Why is that man looking at me? Where have I seen that car before?

I try to view life as a series of scenes in which I have cast myself, taking into account my position, motivations and movements and the relative positions, presumed motivations and movements of all other actors and objects in every scene. Pay attention to every little detail everywhere you go. Try to read the faces and body language of the people around you. Be aware of every sight and sound as they are all clues to what the future holds for you over the next few seconds or minutes. This may sound like sheer insanity, but heightening your awareness will pay off greatly in the casino, whatever your game.

I am no psychologist and my opinion on the human mind is that of an uninformed advantage player, but I believe there is a connection between memory and awareness. I find that working on my memory from time to time and trying to remember the details of the scenes through which I pass in the course of a day have given me an overall improvement in my general awareness.

Likewise, remembering a scene from the last time you visited a location, be it a casino or anywhere else, can tip you off to when things are not quite right if you find yourself there again and something has changed. In short, pay attention and, if you see me watching you, be sure not to make a beeline to a valuable casino opportunity that you do not want to share. ♠

A System for Beating the Over/Under Side Bet

by Arnold Snyder

© 1989 Arnold Snyder

Introduction

Much of this report will seem too technical for the average player. If you don’t quite grasp some of the mathematical concepts, don’t worry about it. The over/under card counting system described is simple and easy to apply. Just follow the recommendations and you should have no trouble. The more technical explanations are for the math-heads who will hopefully appreciate the full story. –A.S.

The Over/Under Rule

At the time of this writing (August, 1989) the only U.S. casino that offers the over/under rule at its blackjack tables is Caesars Tahoe in Stateline, Nevada. [Editor’s note: As of 2006, the Over/Under rule is not offered in the U.S. However, it is offered in casinos in Eastern Europe, Asia, and elsewhere.] Caesars has a two-year exclusive contract with the developer of this rule variation to offer this game in the U.S. In the summer of 1990, the developer may market this rule variation to other U.S. casinos.

Note: Technically, the “rule” of a game cannot be protected by copyright or patent. However, the over/under bet requires an alteration of the blackjack table layout in order to facilitate the side bet. The developer, Mr. Ken Perrie, a Caesars’ pit boss, owns the rights to the design of his unique table layout.

Bets on the regular blackjack hand are placed in the large central circle (the normal betting spot). Optional over/under side bets may be placed in the small circles to the left and right of the center circle. The side bet circles will be labelled “over” and “under.”

How the Over/Under Bet Works

As with the normal blackjack bet, over/under bets must be placed prior to the deal. Over/under bets are always optional side-bets. No player at an over/under game is ever required to place an over/under bet.

The player who places a bet in the over circle is betting that his first two cards will total more than 13. The player who places a bet in the under circle is betting that his first two cards will total less than 13. These are even money bets. Aces always count as one when determining totals for the over/under bet. King, Queen, Jack and 10 all count as ten. All other denominations count as their face values.

Over/Under Restrictions

No player may place an over/under bet unless he is betting on a regular blackjack hand. The amount bet on over or under may never exceed the amount bet on the blackjack hand. At Caesars Tahoe at this time, no over or under bet may ever exceed $100.

All over/under bets are settled prior to the play of the blackjack hands. The outcome of over/under bets have no effect on any aspect of the blackjack game.

Analysis of the Over/Under Game

Compared to regular blackjack, the over/under game is easy to analyze. By considering all possible two-card totals, it is a straightforward calculation to count how many of these hands total over 13, and how many total under 13.

If we assume that the player will bet one unit on every hand that his hand will total over 13, then compare the results of his wins and losses, we see that he will lose about 6 1/2% of his total amount bet. If he always bets on the under side, he will lose slightly more than 10% of his total under bets. The house obtains its advantage from the fact that the house always wins over and under bets on player totals of exactly 13.

So, “basic strategy” for the over/under bets is to never bet on either side. The house has the advantage either way in the long run.

However, it is also obvious that this house advantage will change throughout the course of the game. An excess of high cards remaining to be dealt would make a hand totaling over 13 more probable. And an excess of low cards will make an under 13 hand more probable.

In order to devise an optimal card counting system that will tell us when the over or under bets have become advantageous, we must first figure out the effects of removing each of the individual cards. Again, this is a very straightforward mathematical calculation. It is done exactly like the initial calculation we did to determine the house advantage off the top of the six-deck shoe [editor’s note: analysis of 1, 2, 4 and 8 deck Over/Under games is included in the supplement at the end of this report], except that we remove one of each denomination of card in turn, refiguring the outcome on the over and under bets.

We will find, for instance, that when we remove one ten-valued card, we come up with slightly fewer possible two-card hands that will total over 13, and slightly more two-card hands that will total under 13. The difference between the house advantage off the top and minus one ten tells us the effect of removing a ten. Note that each card will have two effects of removal—one effect on the over bet, and a different effect on the under bet.

These are the approximate effects of removal in percent for each denomination of card in the 6-deck over/under game (for effects of removal in 1, 2, 4, and 8-deck games, see the supplement at the end of this report):

Effects of Removal in the 6-Deck Over/Under Game

	A	2	3	4	5	6	7	8	9	10
Over:	+0.60	+0.60	+0.60	+0.20	+0.11	+0.01	-0.09	-0.19	-0.29	-0.39
Under:	-0.71	-0.71	-0.31	-0.21	-0.11	-0.01	+0.08	+0.18	+0.28	+0.38

These effects are much greater than those for regular blackjack. The removal of one ace, for instance, in a 6-deck blackjack game, has an effect of approximately -0.10% on your regular blackjack hand. Removing an ace has 6 times this effect on any over bet, and seven times this effect on an under bet.

It is easy to see why the ace and deuce, for instance, have such high effects of removal. Consider that if either one of your cards is an ace or a deuce, you could not possibly lose the under bet, nor could you possibly win the over bet.

Also note that these effects of removal are for removing just one card from the top of a 6-deck shoe. In regular blackjack, effects of removal are usually given for removing one card from the top of a single deck. The effect of removing an ace from a single deck is approximately -0.6% on your regular blackjack hand. If the over/under bet were allowed in a single-deck game [editor’s note: 1, 2, 4 and 8-deck games with the Over/Under rule later became available], the effects of removing one ace would be -4.40% on the under bet, and +3.73% on the over bet.

In other words, even though the house advantage over you on the over bet in a single-deck game is about 6.8%, the removal of just one ace and one deuce in a single-deck over/under game would put the edge in your favor by almost 0.7%! Although there are no single-deck over/under games at this time, the volatile swings in advantage caused by the effects of removal make even the 6-deck game a profitable game for card counters. Removal of a single ace, deuce, or three, for instance, from the 6-deck shoe has more effect on your over/under betting opportunities than the removal of any of these cards would in a single-deck regular blackjack game.

Devising an Over/Under Card Counting System

First let’s look at how well some common blackjack card counting systems correlate to the over/under bet:

Correlation of Various Card Counting Systems to the Over/Under Bet

COUNT SYSTEM	A	2	3	4	5	6	7	8	9	10	UND	OVR
EINSTEIN/HI OPT I
	0	0	1	1	1	1	0	0	0	-1	-0.56	0.64
DHM/GORDON
	0	1	1	1	1	0	0	0	0	-1	-0.74	0.79
GRIFFIN-1
	0	0	0	1	1	1	1	0	0	-1	-0.46	0.46
BRAUN +-/DUBNER/HI-LO
	-1	1	1	1	1	1	0	0	0	-1	-0.50	0.57
USTON +-
	-1	0	1	1	1	1	1	0	0	-1	-0.32	0.41
REVERE ADVANCED +-
	0	1	1	1	1	1	0	0	-1	-1	-0.73	0.78
CANFIELD EXPERT
	0	0	1	1	1	1	1	0	-1	-1	-0.55	0.62
ITA GREEN FOUNTAIN
	-1	1	1	1	1	1	1	0	-1	-1	-0.50	0.56
HI OPT II/STEPPINE
	0	1	1	2	2	1	1	0	0	-2	-0.64	0.67
ANDERSON/REPPERT
	-2	1	1	1	0	1	1	0	-1	-1	-0.30	0.38
R&T POINT COUNT
	0	1	1	2	2	2	0	0	0	-2	-0.63	0.66
REVERE POINT COUNT
	-2	1	2	2	2	2	1	0	0	-2	-0.42	0.50
CANFIELD MASTER/GRIFFIN-2
	0	1	1	2	2	2	1	0	-1	-2	-0.64	0.66
WONG’S HALVES
	-1	0.5	1	1	1.5	1	0.5	0	-0.5	-1	-0.44	0.51
GRIFFIN-3/USTON ADVANCED
	0	1	2	2	3	2	2	1	-1	-3	-0.61	0.65
REVERE ADVANCED (’71)
	-4	2	3	3	4	3	2	0	-1	-3	-0.38	0.46
REVERE ADVANCED (’74)
	0	2	2	3	4	2	1	0	-2	-3	-0.68	0.71
ZEN
	-1	1	1	2	2	2	1	0	0	-2	-0.51	0.55

Note that the most common counting systems correlate poorly. Hi-Opt I has about a 64% correlation on the over bet, and about 56% on the under bet. The High-Low is worse; 57% over and 50% under. The Zen Count’s about the same. The Uston +/- is terrible. The best normal card counting system for this game is the DHM (a mail order card counting system of years gone by, no longer in print.) Second best is the Revere Advanced +/-, another ancient system no longer in wide usage. Third best is the 1974 Revere Advanced Point Count, which correlates 71% on the over bet and 68% on the under bet. But this is another system that is not widely available, and a difficult level 4 strategy that would be unwieldy for most players.

Considering the fact that the effects of removal indicate to us that over/under betting opportunities provide far more profit potential in this 6-deck game than regular blackjack, let’s devise some card counting systems specifically aimed at attacking the over/under. Here are six possible over/under counts:

Six Possible Over/Under Counts

COUNT	A	2	3	4	5	6	7	8	9	10	UND	OVR
Count 1	1	1	1	1	0	0	0	0	0	-1	-0.90	0.92
Count 2	1	1	1	1	1	0	0	0	-1	-1	-0.89	0.91
Count 3	1	1	1	1	1	1	0	-1	-1	-1	-0.86	0.88
Count 4	2	2	2	0	0	0	0	-1	-1	-1	-0.94	0.97
Count 5	2	2	1	1	0	0	0	-1	-1	-1	-0.98	0.96
Count 6	2	2	2	1	1	0	0	0	0	-2	-0.91	0.94

We can see here that Count #4 and Count #5, both level two systems, correlate the best. My choice of system, however, is Count #1, for a number of reasons. First of all, as a level 1 system, it’s the easiest to learn and use. Second, if I assume that your are going to be using your over/under count not only to make over/under betting decisions, but also to play your regular blackjack hand, Count #1 is the best all-purpose card counting system. It has an insurance efficiency of 85%, the same as Hi-Opt I, and a playing efficiency of 47%, not that much worse than the High-Low’s 51%. For convenience, let’s call Count #1 the “Over/Under Count.”

The Over/Under Count

	A	2	3	4	5	6	7	8	9	10	UND	OVR
The Over/Under Count	1	1	1	1	0	0	0	0	0	-1	-0.90	0.92

Although it is possible to develop many multi-parameter approaches that would optimize potential profits on both the over/under bets and the regular blackjack hand, I would not consider these more difficult strategies to be worth the trouble. Having a system with a high betting correlation for your regular blackjack hand is useless. The over/under bets are much more important. And to strive for a playing efficiency of 60%, or even 70%, in a 6-deck game, is a waste of time. The potential strategy gains are extremely small.

The vast majority of your profit potential will come from betting accurately on your over/under opportunities. You only want to be and play the regular blackjack hand well enough to reduce the ½% house advantage to as near a break even point as possible. You can’t table hop over/under games. You’re likely to miss betting opportunities on the under side when the count is negative.

For extreme ease, if you are already using a balanced level 1 card counting system, such as Hi-Opt I or the Hi-Lo count, you could use the same strategy tables to play your hand using the Over/Under Count, and you will be playing your regular blackjack hand with great accuracy. This is a count-per-deck strategy chart drawn up specifically for using the Over/Under Count to play your blackjack hands.

Count Per Deck Strategy Chart for the Over/Under Count

	2	3	4	5	6	7	8	9	10	A
16							+5	+3	0	+3
15									+5
14	-4
13	0	-2	-3	-4
12	+4	+2	+1	-1	-2
A7									+5	0
11								-4	-4	-1
10							-5	-2		+3
9	+1	-1	-4			+4
8				+4	+2
Insurance: +3

The next step in analyzing this game is to figure out the value of each point-per-deck; in other words, how much does your (dis)advantage change with each true count? The value of a point is a function of the effects o9f removal and the assigned point values. Since we have different effects of removal for the over bet, the under bet, and the regular blackjack hand, each true count will technically have three different values.

If you have a background in statistics, you may calculate the value of a true point for each of the three possible bets by dividing the inner products of the effects of removal and their respective assigned point values by the sum of the squares of the point values. Note that you should first multiply the 6-deck effects of removal for the over and under bets by 6, in order to obtain the effects of removal per deck. The effects of removal for the regular blackjack hand are in Peter Griffin’s Theory of Blackjack, as well as numerous other publications. Griffin also explains how to find the inner product.

Fortunately, Sam Case has a computer program that spits out this data in a fraction of a second. You don’t have to do the math, or even understand it. Just trust me that each true count using the Over/Under Count described above has the following values:

Over/Under True Count Values

Over bet:	2.70%
Under bet:	2.58%
Regular blackjack hand:	0.35%

Do note that each true count with this system affects your regular blackjack advantage by only -.35%, instead of the 0.5% we usually expect with level one systems. This is due to the lower betting correlation, caused primarily by assigning a plus value to the ace. We are willing to relinquish the betting accuracy on our blackjack hand since the over/under bets offer so much more profit potential.

Caesars Tahoe’s 6-deck games use downtown Vegas rules with double after splits. The player’s starting advantage in this game is -0.54%. The following chart shows your expectation in percent on each of the three possible bets you may make at various true counts.

6-Deck Expectation for Various True Counts

True Count	Blackjack Bet	Over Bet	Under Bet
-9	-3.69	-30.85	+13.15
-8	-3.34	-28.15	+10.57
-7	-2.99	-25.45	+7.99
-6	-2.64	-22.75	+5.41
-5	-2.29	-20.05	+2.83
-4	-1.94	-17.35	+0.25
-3	-1.59	-14.65	-2.33
-2	-1.24	-11.95	-4.91
-1	-0.89	-9.25	-7.49
0	-0.54	-6.55	-10.07
+1	-0.19	-3.85	-12.65
+2	+0.16	-1.15	-15.23
+3	+0.51	+1.55	-17.81
+4	+0.86	+4.25	-20.39
+5	+1.21	+6.95	-22.97
+6	+1.56	+9.65	-25.55
+7	+1.91	+12.35	-28.13
+8	+2.26	+15.05	-30.71
+9	+2.61	+17.75	-33.39

Now, we’re ready to devise a strategy for attacking this game. One of the nice features about the over/under bets is that you never have to place them. This means that all of the negative advantages that occur on these bets at various counts will have no effect on your expectation since you will not be betting. So, let’s simplify the above chart to show the effective player/house advantages at each true count, assuming that the player only bets on over or under when the player has the edge.

It can also be shown that if we place two equal simultaneous bets on events with different expectations, our combined expectation is the same as if we had placed one bet of the total amount on the average of the two expectations. For instance, the expectation on your blackjack hand at a true count of +3 is +0.51%. The expectation on the over bet is +1.55%. Therefore, if I place a $100 bet on each of these, I would expect to profit in the long run 51 cents on my blackjack hand and $1.55 on the over bet. This is a total profit of $2.06 on the $200 of total action. $2.06 is 1.03% of $200. 1.03% is also the average of .51% and 1.55%.

This means that we can further simplify the chart of our expectations at various true counts by averaging our advantages when we place simultaneous bets. The following simplified chart shows your actual expectations at various true counts when you place over or under bets when you have the advantage.

Expectation at Various Over/Under Count True Counts with the Over/Under Bet

Count	% Expectation
-9	+4.73*
-8	+3.62*
-7	+2.50*
-6	+1.39*
-5	+0.27*
-4	-0.85*
-3	-1.59
-2	-1.24
-1	-0.89
0	-0.54
+1	-0.19
+2	+0.16
+3	+1.03*
+4	+2.56*
+5	+4.08*
+6	+5.61*
+7	+7.13*
+8	+8.65*
+9	+10.18*
* Combined blackjack and over/under bets

Now you can see why this is such a nice game for card counters. Not only does your advantage go up on both positive and negative counts—and quite a bit higher than a card counter’s advantage every rises—but the house never has an advantage over you of much more than 1 ½%.

We can now analyze your profit potential in this game using standard 6-deck frequency distributions. The frequency distributions for this count are identical to those for the Hi-Opt I counting system.

I visited Caesars Tahoe in June of 1989, and again in August, in order to play the over/under games and observe the shuffling standards. There is a wide variance in deck penetration on Caesars’ 6-deck games. On an average, most dealers deal out about 4 ½ decks, or 75% between shuffles. During both of my visits, however, I was able to find dealers who dealt out 5 decks. You will also see dealers who do not deal out much more than 4 decks.

As with any blackjack game, deep penetration is important for card counters. These are frequency distributions, in hands-per-hundred for the Over/Under Count, assuming 4 decks dealt out, 4 ½ decks dealt out, and 5 decks dealt out.

Over/Under Count Frequency Distributions

True Count	4 Decks Dealt	4.5 Decks Dealt	5 Decks Dealt
-9	0	0	0.5
-8	0	0.5	0.5
-7	0.5	0.5	1
-6	0.5	1	1.5
-5	1	1	1.5
-4	2	2	2.5
-3	3	3.5	4
-2	8	7.5	7
-1	14	14	13
0	42	40	37
+1	14	14	13
+2	8	7.5	7
+3	3	3.5	4
+4	2	2	2.5
+5	1	1	1.5
+6	0.5	1	1.5
+7	0.5	0.5	1
+8	0	0.5	0.5
+9	0	0	0.5

If you are mathematically inclined, you may use these frequency distributions to estimate your potential advantage and win rate in dollars with various betting approaches. My analysis yields the following data.

Flat Betting

For the over/under game, we’ll define flat betting as placing the same size bet on all of your blackjack hands, but also placing a bet of the same amount on either the over or under only when it is advantageous to do so. Using the Over/Under Count, this means placing an over bet when your true count is +3 or more, and placing an under bet when your true count is -4 or less.

Flat betting is not a good approach to this game, though it is moderately favorable when the penetration is deep. If only 4 decks are being dealt out, your expectation is -0.1%. If 4 ½ decks are dealt out, your expectation is 0.1%.

In other words, with normal penetration, you will be playing a break even game. If 5 decks are dealt out, your expectation goes up to +0.4%. With $100 bets, and 100 hands per hour, this would be a potential win rate of about $50 per hour. If you have a large bankroll and you can afford the potential fluctuation, this approach may appeal to you—especially if you’re playing for comps. Generally, I do not advise serious players to risk so much for so little. It is remarkable that you are able to get any advantage at all flat-betting a 6-deck game, playing through all negative counts.

1-to-2 Spread

You bet one unit on your blackjack hand when the true count is between -5 and +2. Below -5, or above +2, you bet 2 units. At -4 or below, you match your blackjack bet with an under bet. This means you will be betting one unit on under at -4 and -5, and two units on the under at -6 or below. At +3 or above, you match your two unit blackjack bet with a 2 unit over bet.

With 4 decks dealt out, your expectation is +0.2%, nothing to write home about. With 4 ½ decks dealt out, you’ll expect to win at the rate of about 0.5%. With 5 decks dealt out, you’ll have a full 1% expectation. Spreading from $50 to $100, this would make you about $75 per hundred hands.

1-to-4 Spread

I analyzed this spread with a 1 unit bet on the blackjack hand from -4 to +1; 2 unit blackjack bets at -5 and +2; 4 unit blackjack bets below -5 and above +2. Under bets match the blackjack bets (1, 2 or 4 units) at -4 and below. Over bets match the blackjack bets (4 units only) at +3 and above.

With 4 decks dealt out, this spread will get you an advantage of about 0.7%, not bad for the poor shuffle point. 4 ½ decks dealt out will get you a 1.1% advantage. And with 5 decks dealt out, your expectation is about 1.6%, or about $88 per hundred hands.

You may have noticed that the percentage advantage seems to be climbing with larger spreads faster than the $ expectation. For instance, flat-betting $100 chips with 5 decks out provides a 0.4% advantage, and about $50/hour. Using a 1-to-4 spread, your advantage climbs to 1.6%, but $ expectation is only $88/hour.

The reason for this is that we are obtaining the larger spread by lowering the minimum bet, as opposed to raising the maximum. Since the maximum bet allowed is $100, I’m analyzing the maximum potential dollar return for players who can afford it. Smaller stakes players would find that their $ win rate advanced as expected if they raised their top bets. For instance, flat betting $25 chips, with 5 decks dealt out, would net about $12 per hour. Spreading from $25 to $50 would get you about $38 per hour. And spreading from $25 to $100 would take in about $88 per hour.

I’m analyzing this game with conservative spreads so that you can see that it is not difficult to get the best of this 6-deck game, even with a small spread. Remember, if you’re barred at Caesars Tahoe, there are no other casinos in this country that offer over/under games at this time. Brave fools who either have, or believe they have, incredible acts, may use the frequency distributions provided to discover that they will have no trouble killing the game, even with only 4 decks dealt, with a spread of $5 to $100. Good luck!

Players with substantial bankrolls, who are put off by the limitations of the $100 max bet, may be tempted to analyze the potential win rates if you spread to multiple hands when the over/under bets are favorable. Such tactics will greatly increase your expectation. If you are spreading from $25 to $100 on one hand, using the 1-to-4 strategy described above, and playing a second hand only when the true count is at +3 and above, or -6 and below, your expectation would be about 2.2%, and about $190/hour.

Over/Under Count Bankroll Requirements

One of the nice things about the over/under bet is that it is a true side bet. Betting $100 each on your blackjack hand and the over bet, simultaneously, is not the same thing, as far as fluctuations go, as betting $200 on your blackjack hand, or even playing two simultaneous blackjack hands. The reason for this is that the over/under bets are not affected by the dealer’s upcards.

When you are playing simultaneous blackjack hands, you must account for the covariance. In other words, if the dealer gets a total of 20, both of your hands are going up against this strong total. If the dealer gets a natural, neither of your hands win money. But over/under bets are not tied to the dealer’s hand in any way. If you place an over bet, and you are dealt a total of 14, you win regardless of what the dealer has.

In fact, one of the first things you will notice when playing this game is how the over bet, especially, acts as a hedge against most of your losing stiffs when you have a big bet out. Much of the pain of being dealt a 14, 15 or 16 vs. a dealer 10, when you’ve got a big bet on the table, is eased by collecting on the over bet prior to having to play your miserable stiff.

Another nice feature of the over/under bets is that your advantage climbs so dramatically with each true count. A blackjack player whose moderate bankroll would never allow bets above $25 would not infrequently be able to place $100 over/under bets, because his combined blackjack and over/under advantage will be 4% or more. This is virtually unheard of in any “normal” 6-deck game.

For this reason, even if you can’t afford to spread from 1-to-4 according to the strategy I’ve outlined, with your 4 unit bet placed at +3 or above, you may be able to use this spread if you wait for higher advantages for your big bet. At +3, your combined advantage is about 1%; at +4, it’s about 2 ½%; at +5, it’s more than 4%! If you get into the deeply dealt games, you will see opportunities like this regularly.

General guidelines: With a very small bankroll—say $1000—plan on spreading from $5 to $10 for most of your play according to the betting guidelines above. But look for deeply dealt games and don’t hesitate to put a $20 bet on the table if the true count goes to +5 or more. As with any other blackjack game, you’re not going to be able to make a living wage if your total bankroll is $1000. If you’ve got a $5000 bankroll, you will be able to play with quarter chips, and you will have many occasions to place the max $100 bets. But be aware of any substantial negative swings, and cut back your bets accordingly.

Future of the Over/Under Side Bet

Will the over/under game survive? Caesars Tahoe has been offering it on six tables now for more than a year, which indicates a better chance for longevity than most gimmick games. Caesars knows that card counters are attacking the game, and for the most part they’ve been welcoming them. This is because most card counters are using standard card counting systems to determine when to bet over and under, and such systems correlate poorly to the over/under effects of removal.

With the Hi-Lo card counting system, for example, you do not have an advantage on the over bet until your true count is +5 (as opposed to +3 with the Over/Under Count), and you do not have an advantage on the under bet until your true count is -8 (as opposed to -4 with the Over/Under). This means that with 4 ½ decks dealt out, the Hi-Low count would accurately recognize 3 ½ over/under betting opportunities per 100 hands. The Over/Under Count would recognize 13 ½ betting opportunities.

Most card counters using normal blackjack systems will bet far too often when the house has the advantage, simply because their blackjack systems are not designed to identify over/under opportunities. You cannot beat this game with a small spread and a normal blackjack card counting system.

So, despite this report, I suspect Caesars will continue to profit substantially from both card counters and non-counters at their over/under tables.

Player Advantage with Various Over/Under Betting Strategies in 6-Deck Games

	4 Decks Dealt	4.5 Decks Dealt	5 Decks Dealt
Flat Bet	-0.12%	+0.07%	+0.41%
1-2 Spread	+0.22%	+0.52%	+1.01%
1-4 Spread	+0.67%	+1.08%	+1.61%

Over/Under Supplement for 1, 2, 4 and 8 deck Games

Since the initial Over/Under Report was published a few months ago, one- and two-deck over/under games have appeared in Reno. Others using various numbers of decks are reportedly being offered on cruise ships and in overseas casinos. This supplement to the Over/Under Report will aid you in beating these games with any number of decks.

Assumptions

Each page of this supplement analyzes Over/Under games with a different number of decks: 1, 2, 4, 6, and 8. At the top of each page is the number of decks in play, and the assumed rules. If you are playing in a game with a different set of rules, adjust the advantages accordingly.

For example, I’ve analyzed the 2-deck game with Reno rules. The advantage at a true count of 0 is -0.7. If you find a 2-deck Vegas Strip rules game, your advantage at 0 would be -0.3. All of the figures in the advantage column should be adjusted accordingly.

For ease of use, I have analyzed your expectation with a flat bet, a 1-2 spread, and a 1-4 spread. If you are playing in a game with a different set of rules, you may approximate your advantage simply by adding or subtracting, as appropriate, the difference in your starting advantage from the “win rates” shown.

All frequency distributions assume the Over/Under Count is being used as described in the report.

Note: These frequency distributions were obtained via computer simulation with “fixed” shuffle points, so they are not symmetrical. The simulations also used a different method of rounding than the mathematical model used for the Report. For this reason, the 6-deck distribution in the supplement is different from that in the report. You may note that the 6-deck win rates in the supplement are 0.1% to 0.2% lower than in the Report. The win rates are more accurate in the supplement.

1-Deck (Reno Rules) Over/Under Count Win Rates

Count	Advantage	65%	75%	85%
-25	26.6	0	0	0.1
-24	21.5	0	0	0.1
-23	20.4	0	0	0.1
-22	19.3	0	0	0.1
-21	18.2	0	0	0.1
-20	17.1	0	0.1	0.1
-19	16.0	0	0.1	0.1
-18	14.9	0.1	0.1	0.1
-17	13.8	0.1	0.2	0.2
-16	12.6	0.1	0.2	0.3
-15	11.5	0.1	0.3	0.3
-14	10.4	0.1	0.4	0.5
-13	9.3	0.2	0.3	0.5
-12	8.2	0.4	0.6	0.7
-11	7.1	0.3	0.4	0.6
-10	6.0	0.8	1	1.2
-9	4.8	0.8	1.1	1.5
-8	3.7	1.2	1.3	1.5
-7	2.6	2.3	2.3	2.5
-6	1.5	2	2.4	2.1
-5	0.4	3.4	3.4	3.5
-4	-0.7	4.7	4.1	4.6
-3	-1.5	5.6	6.5	6.0
-2	-1.1	8.3	7.5	6.5
-1	-0.8	7.5	6.6	5.8
0	-0.4	30	28	26.8
+1	-0.1	6.3	5.6	4.9
+2	0.3	7.1	6.3	5.6
+3	1.1	4.7	5.7	5.2
+4	2.7	3.6	3.2	3.8
+5	4.2	3.3	3.3	3.4
+6	5.7	1.6	2.0	1.8
+7	7.2	1.8	2.1	2.3
+8	8.8	1	1	1.2
+9	10.3	0.8	1.1	1.4
+10	11.8	0.6	0.9	1.1
+11	13.3	0.3	0.3	0.5
+12	14.9	0.3	0.5	0.6
+13	16.4	0.2	0.3	0.4
+14	17.9	0.1	0.2	0.4
+15	19.4	0.1	0.1	0.2
+16	21.0	0.1	0.1	0.3
+17	22.5	0.1	0.1	0.2
+18	24.0	0	0.1	0.1
+19	25.5	0	0.1	0.1
+20	27.1	0	0.1	0.1
+21	28.6	0	0	0.1
+22	30.1	0	0	0.1
+23	31.6	0	0	0.1
+24	33.2	0	0	0.1
+25	34.8	0	0	0.1
Win Rate (%)
Flat Bet:		1.6	2.2	3.1
1-2 Spread:		2.5	3.1	4.1
1-4 Spread:		3.2	3.9	4.9

2-Deck (Reno Rules) Over/Under Count Win Rates

Count	Advantage	65%	75%	85%
-19	15.7	0	0	0.1
-18	14.5	0	0	0.1
-17	13.4	0	0	0.1
-16	12.3	0	0.1	0.1
-15	11.2	0	0.1	0.1
-14	10.1	0	0.1	0.2
-13	9.0	0.1	0.1	0.2
-12	7.9	0.1	0.2	0.4
-11	6.8	0.1	0.3	0.4
-10	5.7	0.2	0.4	0.6
-9	4.6	0.4	0.6	0.9
-8	3.4	0.7	0.9	1.2
-7	2.3	1.1	1.5	1.8
-6	1.2	1.5	1.8	2.0
-5	0.1	2.6	2.9	3.1
-4	-1.0	4.0	4.1	4.1
-3	-1.8	6.0	6.3	5.8
-2	-1.4	9.5	9.1	9.0
-1	-1.1	16.2	14.6	13
0	-0.7	19.6	18.5	17.7
+1	-0.4	14.6	13.2	11.8
+2	0	8.4	8.1	8.1
+3	0.9	5.3	5.6	5.3
+4	2.4	3.6	3.6	3.8
+5	3.9	2.3	2.6	2.9
+6	5.4	1.3	1.6	1.7
+7	7	1.0	1.3	1.6
+8	8.5	0.6	0.8	1
+9	10	0.3	0.5	0.8
+10	11.5	0.2	0.4	0.6
+11	13	0.1	0.2	0.3
+12	14.6	0.1	0.1	0.3
+13	16.1	0.1	0.1	0.2
+14	17.6	0	0.1	0.2
+15	19.1	0	0.1	0.1
+16	21.2	0	0.1	0.1
+17	22.7	0	0	0.1
+18	24.2	0	0	0.1
+19	25.7	0	0	0.1
Win Rate (%)
Flat bet:		0.5	0.9	1.5
1-2 spread:		1.1	1.6	2.3
1-4 spread:		1.7	2.3	3.1

4-Deck (Reno Rules) Over/Under Count Win Rates

Count	Advantage	65%	75%	85%
-14	10.4	0	0	0.1
-13	9.3	0	0	0.1
-12	8.1	0	0.1	0.1
-11	7.0	0	0.1	0.2
-10	5.9	0.1	0.1	0.3
-9	4.8	0.1	0.2	0.4
-8	3.7	0.2	0.4	0.6
-7	2.6	0.4	0.7	1.0
-6	1.5	0.7	1.0	1.4
-5	0.3	1.5	1.8	2.2
-4	-0.8	2.8	3.2	3.5
-3	-1.5	5.2	5.4	5.6
-2	-1.2	9.5	9.3	9.0
-1	-0.8	18.4	17.2	16.1
0	-0.5	26.6	23.9	22.4
+1	-0.1	16.6	15.8	14.8
+2	0.2	8.5	8.8	8.2
+3	1.1	4.6	5.1	5.1
+4	2.6	2.5	3.0	3.3
+5	4.1	1.3	1.6	2.0
+6	5.7	0.5	1.0	1.3
+7	7.2	0.3	0.6	0.8
+8	8.7	0.1	0.3	0.5
+9	10.2	0.1	0.2	0.4
+10	11.8	0	0.1	0.2
+11	13.3	0	0.1	0.1
+12	14.8	0	0	0.1
+13	16.3	0	0	0.1
+14	17.9	0	0	0.1
Win Rate (%)
Flat bet:		0	0.3	0.7
1-2 spread:		0.4	0.9	1.4
1-4 spread:		0.9	1.4	2

6-Deck (Reno Rules) Over/Under Count Win Rates

Count	Advantage	65%	75%	85%
-12	8	0	0	0.1
-11	6.9	0	0	0.1
-10	5.8	0	0.1	0.1
-9	4.7	0	0.1	0.2
-8	3.6	0.1	0.1	0.3
-7	2.5	0.1	0.3	0.6
-6	1.4	0.3	0.6	0.9
-5	0.3	0.8	1.3	1.7
-4	-0.9	1.8	2.4	2.8
-3	-1.6	4.2	4.6	5
-2	-1.2	8.8	8.9	8.9
-1	-0.9	18.7	17.9	17.1
0	-0.5	32.1	29.3	26.6
+1	-0.2	17.6	17	16.1
+2	0.2	8.3	8.4	8.4
+3	1	4	4.4	4.6
+4	2.6	1.9	2.1	2.6
+5	4.1	0.8	1.2	1.6
+6	5.6	0.3	0.7	0.9
+7	7.1	0.1	0.3	0.6
+8	8.7	0.1	0.1	0.3
+9	10.2	0	0.1	0.2
+10	11.7	0	0.1	0.1
+11	13.2	0	0	0.1
+12	14.8	0	0	0.1
Win Rate (%)
Flat bet:		-0.2	0	0.3
1-2 spread:		0.1	0.4	0.8
1-4 spread:		0.5	0.9	1.4

8-Deck (Reno Rules) Over/Under Count Win Rates

Count	Advantage	65%	75%	85%
-11	7	0	0	0.1
-10	5.9	0	0	0.1
-9	4.8	0	0	0.1
-8	3.7	0	0.1	0.2
-7	2.6	0.1	0.2	0.4
-6	1.4	0.2	0.4	0.7
-5	0.4	0.4	0.9	1.3
-4	-0.8	1.3	1.8	2.5
-3	-1.5	3.3	3.9	4.4
-2	-1.2	8.1	8.5	8.5
-1	-0.8	19.6	18.4	17.4
0	-0.5	36	33.1	30
+1	-0.1	18.4	17.6	16.8
+2	0.3	7.6	8.1	8.1
+3	1.1	3	3.7	4.2
+4	2.7	1.2	1.8	2.3
+5	4.2	0.5	0.8	1.3
+6	5.7	0.2	0.4	0.7
+7	7.2	0.1	0.2	0.4
+8	8.7	0	0.1	0.2
+9	10.3	0	0	0.1
+10	11.8	0	0	0.1
+11	13.3	0	0	0.1
Win Rate (%)
Flat bet:		-0.3	-0.1	0.2
1-2 spread:		0	0.2	0.6
1-4 spread:		0.3	0.6	1.2

On the Road to Nevada’s Nowhere Towns

by Barry Meadow
(From Blackjack Forum XX #2, Summer 2000)
© Blackjack Forum 2000

[Barry Meadow is the author of Blackjack Autumn: A True Tale of Life, Death, and Splitting Tens in Winnemucca .]

The road is long, With many a-winding turn, That leads us to who knows where, Who knows where…

Uh, I know where. I’ve been there.

Most of us have doubled down and split pairs all over Las Vegas and Reno.

Some of us have comp-hustled in Laughlin or surrendered in Lake Tahoe. But I say if you’re going to play serious blackjack in Nevada, hit the road.

That means blackjack in Tonopah and McDermitt and Ely and Jackpot and every other place you’ve seen on the map, only it was too damn far or too damn cold and why the heck would you drive a hundred miles to Lovelock when there was exactly one blackjack table in town and you’d look like a stalker trying to wong it?

I’ve been here, and there, and everywhere in Nevada. I counted cards at blackjack in every casino in the state during a two-month trip last year which consisted of me, a suitcase, and $8000. No entourage, no pals, no nothing but yours truly and one open road.

Every day, I’d record my observations on a tiny tape machine. I made more recordings in garages than a Seattle grunge band. And by the time I finished my trip, 192 casinos later, my laptop computer was in worse shape than Andy Sipowicz.

And so was I.

The name of the book is Blackjack Autumn, and if you don’t buy a copy right this minute, shame on you. The subtitle is A True Tale of Life, Death, and Splitting Tens in Winnemucca.

I should point out that the count was really, really good at the time. Once I played in a one-deck game dealt all the way to the bottom. Boy, it sure was fun taking insurance on a plus count when only two cards remained to be dealt!

Then again, there was the casino that featured a grand total of one player — me again — and seven pit employees, none of whom had anything better to do than watch me try to earn a few dollars.

At times I was the crusher, while at other times I was the crushee.

I’ve seen a blackjack dealer pull out more dead hands than a grave robber, and I’ve also seen a blackjack dealer lose so many hands that the floorman actually switched the game from two decks to one deck in an effort to change the casino’s luck (it didn’t work).

I played with plastic cards. I played a game in which a player’s two hands were dealt one face up and the other face down (don’t ask). I saw a man deal the first half of the shoe, walk to the other side of the table, and play the rest of the shoe himself.

Sometimes I was barred for card counting, including one telephone ejection at 1 a.m.. Golly, didn’t that casino manager’s mother ever tell him it was impolite to call after 9 p.m.? A card counter once told me that if you’ve never been barred, you’re doing something wrong. I guess I did something right four times.

A few tips if you’re going to make a similar trip: Bring money. Have reliable transportation. And don’t blow into town at 8 a.m., you little Carlsonite, because the blackjack game isn’t open until 4 p.m. and what are you going to do all day when there’s absolutely nothing to do?

Don’t bother showing up at 10 p.m., either, because that means you will have traveled on a two-lane Nevada blacktop at night on roads so dark that if some animal decides to cross the road in front of your vehicle, you’ll never see it until it’s draped over your hood, which is bad for your paint job.

It’s a long way from Nowheresville to South Nowheresville in Nevada, as you will soon learn. This is not a trip from Las Vegas to Henderson we’re talking about.

Let’s say, for instance, that you decide to travel to Montgomery Pass to play blackjack. Try finding it on a map. Better yet, try calling information. Chances are you’ll have no luck either way. Hint: The place is actually called the Montgomery Pass Lodge and Casino, but it’s also called Soper’s Cafe, and there’s no town anywhere nearby. If you do manage to find it, you’ll enjoy the $2 chips and the aformentioned plastic cards that the casino employees wash rather than replace. There will also be a sign advising you not to drop your cigarettes into the urinal, always a sign of a first-class establishment.

Along the way, amazing things happened to me, as they no doubt will to you should you take on this assignment. In Beatty, for instance, I realized every card counter’s dream. I won so much money at the Burro Inn — well not all that much, but pretty big for Beatty as my blackjack profits crept into the mid three-figures — that the game actually had to come to halt because if I won the next hand, there would not be enough chips to pay me. Yes, all action actually stopped as we waited for one of the bartenders to step into the casino cage to chip-run another rack of reds for my gambling pleasure.

Good thing, too, because my next hand was a blackjack.

I found an Indian casino outside of Laughlin, though I actually found quite a few more Indians near the Say When Casino in McDermitt, and I wound up helping some of them herd horses across the state highway. Found some cowboys in Mesquite, too. And highway patrolmen in more than one place, although why they found 132 miles per hour objectionable is something I’ll never quite understand — heck, there weren’t any other cars for miles and miles, for Breedlove’s sake.

I met cattle who looked meaner than Mike Tyson after a three-day drunk, and pit bosses who looked meaner still. Then again, I ran into gorgeous blackjack dealers, who made me sad that I was already engaged, although there is no evidence that any of these women would have had the slightest interest in me anyway.

Can You Win Counting Cards in Winnemucca?

Now to the important question: Can you actually win counting cards in these towns? Yes and no. You can’t win thousands of dollars, because some of these towns don’t have thousands of dollars. In Wells, the highest limit blackjack game is $25.

Forget about black chips — in plenty of places you’ll never even see green chips. If you visit the Bird Farm in Fallon, the highest amount you can play at blackjack is $5 per hand, though by brilliantly spreading from one hand of $2 to two hands of $5 I was able to carve out a $26 profit.

Nor can you blithely spread from $1 to $100 with impunity, Mr. Uston, because even the smallest places have heard of card counters, although in some places I doubt they’ve ever actually seen many of them. At Sturgeon’s in Lovelock, not only did they cut off two of the four decks, but they burned a card after every round. The blackjack game wasn’t much more attractive in Topaz Lake, or in Gardnerville, or in Jean. And I couldn’t even find the blackjack game in Amargosa Valley, which turned out to be open only on weekends.

Then again, there was Yerington. I lost there — no big news; I lost in a lot of places — but I did find one intriguing practice at Casino West. The blackjack game was four decks, with the cut card placed halfway up. When the cut card appeared, the dealer would ask the players if they wanted her to shuffle; if they said no, she’d keep dealing until only a few cards remained. Does that mean you could have gotten negative shoes shuffled away while asking the dealer to keep going on the positive shoes? Apparently so. Hmmmmm.

And sometimes the blackjack games were downright good. I had a very nice 80% penetration shoe dealt to me at the Nugget in Searchlight, and the $415 I managed to drop there was simply my way of saying thank you. And the dealt-to-the-bottom blackjack game, discovered at the Station House Casino in Tonopah, proved more than pleasant until I was asked to please leave town as quickly as possible.

Not that you’re likely to find that game any more. Game conditions in these little towns change more often than Bill Clinton’s stories, although you can generally assume bad rules. When the best blackjack game in town is four decks, dealer hits soft 17, double on 10 or 11 only, with a $50 maximum, it’s safe to assume that high-powered card counting teams will be spending their evenings elsewhere. You can’t scout these games, either — it might look a tad suspicious for a stranger to loiter around a game all day without playing, and you can’t very well table-top because there is no other open table to hop to.

There is decent action in some of these out-of-the-way places, though.

Take Wendover, for example. It’s on the Utah border, and Utah is one of only two states (Hawaii is the other) where there is no legal gambling of any kind. Naturally the Mormons who populate the state occasionally like to get down a bet or two, and so there are a couple of very large casinos there as well as some smaller ones. At the State Line Casino, I saw a guy bet two hands of $500 apiece. A warning, though: the chips in Wendover are in the weirdest colors you’ve ever seen, so be careful what you’re betting because just when you think you’re betting $17 on a hand, you just might accidentally be betting $341.

Elko gets some play, too. The owner of the Red Lion Inn owns an airline and flies in players from all over the West. Not real big players, you understand — show up with $350 in front money and you’re in, no playing obligation required — but it’s eerie to visit this small northeastern Nevada town and see dozens of players sporting junket buttons.

Comps at Casinos in Small Town Nevada

The good news is that in some of these places, if you play for anything resembling quarters, you’ll probably get comped, or least score a casino room rate. At the Saddle West in Pahrump, I had only been playing about fifteen minutes for $35 or so per hand when I asked the floorman what I needed to do to qualify for a comp; he proudly displayed the comp slip that he had already written for me, and gave me a discounted room as well. At the Tahoe Biltmore in Crystal Bay, another eager pitster offered me a room before I even had a chance to ask about it, and I had only been there about ten minutes.

Tourists in these burgs are few and far between, the action mostly confined to locals and truckers. You probably won’t find Wayne Newton in the showroom, if you can find a showroom at all. The town’s gourmet restaurant might well be the casino coffee shop. Your room will have a bed and a thin bar of soap.

But hey, it’s blackjack. Just make sure you gas up the car, because between towns is the desert, and if you run out of a gas there’s no filling station for 50 miles. It’s also probably best not to try such a trip with a 15-year-old salvage vehicle, unless you have hefty towing insurance and don’t mind waiting a week for a part to come via UPS from Las Vegas.

Another reason to double-check your automobile is that it would be highly unfortunate to find yourself alone at night on a road next to an inoperable car that’s got $20,000 in cash stuffed in the trunk. It’s bad enough that some of these places don’t have safe-deposit boxes, and you’ve got to sleep with two chairs propped up against your motel door. The last thing you want to do is break down on some bandit-filled Nevada highway, where finding some abandoned mine in which to hide your bullet-riddled body would take the average criminal maybe ten minutes.

If you take up the road warrior’s life, you don’t have to worry much about running out of casinos, since Nevada is a pretty large state. If you’ve worn out your welcome in Minden, you’ll still be welcome in Verdi.

Many places, of course, are still more than happy to bar you if you play with any skill at all, no matter how big or small they might be. After powering my way to a hefty $40 profit at Harrah’s Tahoe, for instance, I was asked to take my action elswhere, preferably to the bottom of Lake Mead. Hey, Mr. Harrah — it wasn’t me who lost millions on your New Orleans project. Where’s your sense of humor?

It’s difficult to disguise your play much in the little towns, because there is usually only one cashier’s cage, only one or two shifts, and sometimes only one or two tables. If somehow the casino is short a thousand dollars, there are very few suspects, no matter how good your act. So you’re not going to be able to camp out for a week in Battle Mountain and bury the Owl Club and the Nevada Hotel for very long.

If you want to play reds for awhile and maintain a moderate spread, chances are nothing too terrible will befall you, though your chances of getting rich are none too great, either.

Sure, the Venetian has beautiful suites and the Desert Inn has a lovely golf course, but can you stay in a historic hotel for $19.95 on a Saturday night as I did in Ely, or play a nine-hole golf course that’s only slightly more challenging than Mel’s Mini-Putt as I did in Hawthorne? OK, there are no Bellagios in Indian Springs, but exactly how many floral cornucopias do you need to see, anyway? ♠

A Parable About Winners’ Testimonials

by Arnold Snyder
(From Blackjack Forum March 1983)
© Blackjack Forum 1983

Swami Pastrami, the Great Guru of Gambling, had a dream one night that thousands of croupiers were being strangled by their bow ties while drowning in 100-gallon vats of tomato soup. The following morning he sent an epistle to his one million followers: “I have had a vision! Send me just $10 and I shall share with you the secret of acquiring unlimited wealth!”

All one million of the Swami’s followers sent him the money he’d requested, making the Swami a very rich holy man. The Swami sent each of his disciples his interpretation of his strange dream: “Find a croupier with a crooked bow tie and bet one hundred dollars on red. Parlay your winnings until you are rich!”

Unbeknownst to Swami Pastrami and his followers, the Swami had misinterpreted his dream, which was not, as the Swami had presumed, of divine origin, but had actually resulted from the Swami’s over-indulgence in jalapeno peppers at dinner the previous evening.

Within the next month, all one million of the Swami’s followers had found croupiers with crooked bow ties and placed $100 bets on red. Since the chance of winning this bet is only 18 out of 38, it came to pass that 526,316 players lost their $100, while 473,684 players won. Those who had lost left dejectedly, but those who had won praised the Swami and soon all the winners had placed $200 bets on red.

As expected, 249,307 lost their money and left the tables. But 224,377 players won, and now excitedly bet $400 on the red square. This time 118,093 lost, while 106,284 won. These players, with $800 each, were now firm believers in the Swami’s systems, and so were the casinos! Since the Swami’s followers had begun playing, the casinos had already won a combined total of almost $15 million just from the Swami’s disciples! Word spread from casino to casino, and soon there was a standing rule that any follower of Swami Pastrami would be covered for any bet of any size at the roulette tables. There wasn’t a croupier in Las Vegas with a straight bow tie.

The 106,284 remaining followers each placed $800 bets on red. In no time at all, the Swami’s followers were reduced to 50,345, each with $1600. After another bet, the remaining players were cut to 23,848, each with $3,200. Then they became 11,296 players, each with $6,400. One bet later, there were only 5,351 players left, with $12,800 each.

After yet another parlay, there remained 2,535 players, each with $25,600. These players were now worshipping the Swami publicly. One bet later, however, their numbers were reduced to 1201 followers, each with $51,200. The casino had now profited more than $38 million from the Swami’s followers.

The Swami, meanwhile, had a new ad campaign going, which was based on honest facts: “More than 400,000 of my followers doubled their money the first day!” More than 1200 of these dedicated disciples have watched their $100 bankrolls grow to more than $50,000!”

There is a moral to this story.

Remember that literally millions of gambling systems and books on how to win have been sold over the years. The fact that an individual has made money using some inexplicable system is not proof that the system is valid. Beware of system sellers who use “testimonials” from successful players in their advertising. You’ll find this form of advertising popular for craps, roulette, baccarat, keno and some blackjack systems. Although the testimonials may be real, the short run experiences of individual players are meaningless.

Incidentally, if you are wondering what ultimately happened to the Swami’s 1201 successful disciples, who had $51,200 each, eight parlays later only three followers were left, each with more than $13 million. By this time, the casinos had profited more than $60 million from the ex-disciples.

Noting the continually-shrinking ranks of the Swami’s original followers, the three remaining disciples wised up and decided not to place any more bets on the wheel. Instead, each disciple paid Swami Pastrami $1 million for the honor of opening a Pastrami Roulette Franchise in his own neighborhood. They all made their second $13 million twice as fast as their first. ♠