Category: Advanced Strategy

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Games I Prefer

Generally, I’m going to play the game that returns the most — including slot club, promotions, and mailer. Sometimes, however, I have a choice between a few different games that return about the same amount.  Here is my approximate ranking — your mileage may vary.

Hundred Play > Fifty Play > Ten Play > Five Play > Triple Play > single line games. Assuming the same return, the more lines the better. This increases the fun and decreases the variance.

I prefer these over Double Super Times Pay and Super Times Pay. Keep in mind, though, that if it’s the same pay schedule, the DSTP version adds about 0.5% and the STP versions adds half that. These additions more than make up for the fact that these aren’t my favorite games. The reason for my lack of excitement on these games is the speed. Whenever you get a multiplier, it takes five seconds or so for the exact multiplier to be “squeezed” out and made visible. I’d prefer to have that five seconds to play another hand.

Quick Quads > Ultimate X. Since neither game regularly comes in good pay schedules (other than at the South Point), the choice is moot for most people who seriously value winning. Quick Quads has a different strategy — but not a greatly different one. The sound Quick Quads makes when you get a Quick Quads (namely three of a kind where the ranks of the other two cards add up to the rank of the trips) strikes the right level of excitement and non-annoyingness. Ultimate X is a game with a sky-high variance and the strategy for the game is quite a bit different than regular video poker games. You have to be in the mood to play and willing to lose a great amount today, even with a good pay schedule.

Spin Poker is okay, but not nearly as attractive to me as Ten Play.

I usually avoid Dream Card as I find the sound effects annoying.

Multi Strike is an interesting game, but it’s slow. Keeping four strategies straight requires some effort, although it’s not impossible. If I’m playing while tired, though, I’ll sometimes make mistakes on this game.

I prefer slant tops to uprights to bar tops. Bar-top machines, even with good pay schedules, have stickier than average buttons due to drinks being spilled on them. I can play longer on slant tops than I can on uprights.

I prefer adjustable seats to non-adjustable. I am taller than average and prefer a higher chair than average.

Each of these game-types come with several different games.  That is, you can find Double Double Bonus, Jacks or Better, Deuces Wild, etc., in most of these game types.

Deuces Wild is generally my favorite game. (It doesn’t exist in Quick Quads.) What makes it interesting to me is you never know what you will get. Start with two deuces and you can end up with anything from 3-of-a-kind to four deuces — meaning anywhere from five coins to 1,000 — per line.

Jacks or Better — This game is arguably the simplest and has the lowest variance. Some people get bored with the variance, but not me. Since I’m playing games where the slot club and other goodies give me an advantage, it’s plenty okay just to grind it out.

Double Double Bonus — This is the most popular video poker game in the country. I generally avoid it because it rarely returns more than 99%. When found in a better version, or with a GREAT promotion, this game is fun. Better have your seat belt on though. It has a lot of variance.

I will play other games, of course, if they happen to be the best game at a casino. Exactly which one it is doesn’t matter much to me. If I can learn the strategy, I can play it. If learning additional games doesn’t come easily to you, you might limit your selection to the games you already know.

There are games like Ultimate X Bonus Streak and others where the correct strategy is unknown — at least by me. I do not have the computer programming skills to work it out, and commercially available software does not contain these games. To get good at a game I need a computer to correct me when I make a mistake.

As I said at the beginning, the total return of the game is the most important thing to me. It matters to me not at all if your favorite games are different than mine.

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If Bob Dancer is Playing . . .

A few years ago, for several days in a row, I was hammering a $5 Five Play 9/6 Double Double Bonus game. This game returns 98.98% and it is very un-Dancer-like to play so much on a game that bad.

I received an email from somebody I didn’t know asking me why I was playing the game. While I generally respond to polite emails, this time I didn’t bother. I share a lot of information, but I’m not required to share everything. I had figured something out, I believed, and I wasn’t talking except to a very few players who also sometimes share juicy things with me.

After it was over, one of our guests on the Gambling with an Edge podcast, Sam, who I hadn’t known previously, told me he was approached by somebody who saw me playing and figured that if it was good for me, it was probably good for others as well. The person asking didn’t have the bankroll to do it himself, which is why he approached Sam. Sam asked me if it would have been a good idea for him to bankroll the other player.

I knew the incident Sam was talking about. I’m still not talking about the details because parts of it are still alive and friends are still playing it on occasion.

I told Sam that in general, just seeing me there wasn’t sufficient to have an edge.

  1. This might have been an invited guest situation where some players have an offer that others don’t. If Sam didn’t know why I was playing, he didn’t get the offer.
  2. There could have been point multipliers available to players who get regular mailers and would not be available to Sam, who wasn’t an established player there. Even players who do get multipliers don’t always get the same multiplier.
  3. Maybe I had to play a certain amount quickly in order to be eligible for something juicy.
  4. Possibly there was a loss rebate promotion going on.
  5. There could have been one or more drawings included in the EV, some of which Sam didn’t know about and/or for which he wasn’t eligible. As an example, Sam wouldn’t qualify for a senior drawing, but I would. Or even if he did know about and was eligible for a drawing, possibly he would have had something else to do on the night(s) of the must-be-there-to-win drawing(s).
  6. There could be annual tier levels to which I aspired, but Sam didn’t care about. Several casinos, for example, offer cruises if you reach their highest tier level. Bonnie and I enjoy these. I know several players who are bored out of their minds on a cruise and playing extra to earn one isn’t something they would consider.
  7. I might have been playing extra to earn additional comps for some reason.
  8. There was more than one seemingly identical machine at this casino. I might have known one of them was superior for some reason.
  9. There were higher-EV machines available at this casino, but knowing what I knew, I believed they were actually lower-EV when you considered everything. If Sam played a higher-EV machine so he could “improve” on the way I was playing the game, his results would have been worse.
  10. I could possibly have had a deal with the casino that if I played $1 million on this game, I would get a $5,000 rebate — or something. That’s a half-percent in equity. That could easily change a “not playable” game into being playable. Perhaps it was a deal I negotiated individually. Perhaps it was one open to all players who played $1 million coin-in a month.
  11. It’s possible I screwed up and this play wasn’t as good as I thought it was. This doesn’t happen a whole lot for me, but I am 72 years old and it happens more than it used to. Sam couldn’t know if it was happening “this time.”
  12. There are bankroll issues on plays. Five-dollar five play 9/6 DDB takes more bankroll than most players are used to. Let’s say it went bad this time and the player (either me or Sam) lost $30,000. I understand the swings and am used to that. I wouldn’t be delighted by that result, but it really isn’t a big deal. It’s part of my world. How would Sam feel about that?

Did all of these things happen? No, of course not. Not on that one occasion, but they all have happened at least once to me. Were some of them in effect this time? Absolutely.
Seeing me (or another knowledgeable player) at a casino definitely provides some useful information for you. And sometimes you are also a regular at that casino and you know what promotions are going on — and can easily figure out why that game is being played today.

But if it’s not obvious to you why I’m playing, it’s probably not a good game for you. There are so many possible reasons why I might be playing, and without knowing which reasons are in effect at this time, it could very well be that it’s not a good play for you at all.

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Chasing a Progressive

There are hundreds of video poker progressives in greater Las Vegas. As a general rule, I avoid these games. Progressives are not my bread and butter. Still, I occasionally do sit down at a progressive that catches my eye, and recently there was such a case.

A $2 9/5 DDB progressive at the South Point was at more than $16,000 for the royal, with additional progressives for aces with a kicker and 2s, 3s, and 4s with a kicker. Putting all the numbers into computer software showed the game was currently worth about 100.80%, plus a 0.30% slot club. Additionally, in general the more coin-in you have, the better your mailers are. So, I sat down.

I had enough cash on hand, I thought, including the availability of markers. I was used to DDB itself, which has a variance of a bit more than 40. Doubling the royal jacks up the variance to around 100. Although I have the tools to figure out bankroll for this, I wasn’t near my computer and I had to wing it. I figured I was up to playing for four or five hours. If the royal hadn’t been hit by then, I’d reevaluate whether or not I wanted to continue.

There are 20 machines connected to this progressive and perhaps a third of the seats were taken when I got there at 10 p.m. on a Saturday evening. At midnight, half of the machines were taken, and the progressive was more than $18,000. The 2s, 3s, and 4s, with a kicker progressive had been hit a few times. It started out at $1,600 and was usually hit by $1,700. The difference between this jackpot at $1,600 and the same jackpot at $1,700 is 0.14%. Not chopped liver, but it’s not the primary prize.

Aces with a kicker were worth more than $5,000. That added more than 0.6%, but even without that, the royal progressive was high enough that the game was worth playing. When the aces were knocked off, the royal progressive was more than $19,000, which is worth about 101% even without the lesser jackpots.

At about 2 a.m., the royal reached $20,000. About 2/3 of the seats were full and at that point, somebody hit the royal. Time to go home.

I had run $40,000 coin-in through the machine. I failed to hit any W2G (regular aces are worth $1,600, in addition to the other jackpots already discussed.) My score was $7,100 in the soup. No fun. But not really a big deal. DDB is a heaven-or-hell game, and special quads and the royals add a lot to the EV. Blanking on those is expensive in the short run.

Generally speaking, when playing a progressive, the person hitting the royal comes out way ahead and the others lose. In this case, the guy who knocked off the aces with a kicker was also probably ahead, but most of the rest of us lost. Such is the nature of playing DDB progressives. Play the game enough and you’ll get your share.

I recognized more than half of the players when the royal was finally hit. Some I hadn’t seen for several years. I assume most of them knew who I was, as I’m well-known in the Las Vegas video poker community, although not in the video poker progressive-playing community. I don’t know this for a fact, but it wouldn’t surprise me if a few phone calls had been made in the nature of, “You better come down here. It is so juicy even Bob Dancer is playing it.”

Am I going to do this again soon? Doubtful. But maybe. It’s a positive play, albeit one with large swings. Between casinos restricting players and the general tightening of machines, it’s hard to find good video poker opportunities in Las Vegas these days. This is one avenue to stay in the game, although it’s not my first choice.

We’ll see.

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A Matter of Perspective

I had a trip to take not related to gambling. There was a casino nearby. I knew that if I gave them some action, I could get a comped room and possibly a meal or two. I figured if they had at least 8/5 Bonus (99.166%), I was money ahead by staying at the casino.

I looked at www.vpfree2.com. This is a site that tries to list the loosest games in most casinos around the country. It is run by volunteers, and it is not always completely accurate. It is usually accurate, and sometimes you need to make decisions based on the best information available.

This website said 8/5 Aces & Faces was the best game. This is a 99.255% game. It is the same as 8/5 Bonus, except that you get the 40-for-1 quads on kings, queens, and jacks rather than twos, threes, and fours. It certainly qualified as being “at least” 8/5 Bonus, so I booked the room.

When I got there, I found the game as advertised. They also had 8/5 Ace$ Bonus at 99.407%. This game has “sequential” aces, meaning that if you got the aces in alphabetical order in either positions 1-4 or 2-5, you get paid 4,000 coins rather than 400.

It is clearly superior to 8/5 Bonus, except the sequential aces bonus feature kicks in approximately every 250,000 hands. Assuming you don’t hit the sequential aces, it’s worse than 8/5 Bonus because you make some plays “going for it.” The most common such play is that when you’re dealt aces full with the three existing aces in sequential position, you toss the pair and go for the fourth ace, hopefully in the correct position.

I was only going to be playing a few thousand hands. Which is the better play?

Assuming variance isn’t an issue financially or psychologically, it’s clear that going for the game with the highest EV is the better choice. And that’s what I chose. I didn’t hit the bonus hand and there was not dealt an appropriate aces full hand.

I did not torture myself by taking special note of how many of which quads I hit so I could afterwards decide whether the Aces & Faces version would have been better. Some folks do this, but you need to make your decisions beforehand and whatever happens this particular time is pretty unimportant.

But for many people, discounting variance shouldn’t be done so cavalierly.

If you live and die with today’s score, the Aces & Faces game is a better choice. If you’re playing for stakes that are a bit higher than your comfort zone, the same answer applies.

We will never know why the Ace$ Bonus game wasn’t included on the www.vpfree2.com listing. It could have been the monitor didn’t see it, didn’t know how much it was worth, or was afraid of the game because of the variance. There could be other reasons as well. It is, after all, a site where you don’t know who does the work behind-the-scenes and you never find out their motives or abilities.

Even though the information I sought was incorrect on the site, I’m glad the site exists. It’s generally correct and when you’re going to a location where you haven’t scouted recently, it’s a major time saver. I wouldn’t depend on it for a frequently visited casino where I play a lot, but for “just popping through” for a few days, it’s satisfactory enough.

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A Look at the Blackjack Apprenticeship Boot Camp

Colin Jones is a former leader of the “Holy Rollers” blackjack team and has founded blackjackapprenticeship.com as a way of helping players learn to play. He’s been a guest on GWAE a number of times.

Several times a year, Blackjack Apprenticeship runs a two-day “boot camp” in Las Vegas. This is a $3,000 intensive training over two days. Players come out of there with the knowledge to count cards profitably. They are supposed to know perfect basic strategy when they arrive. Most do. Some don’t.

I thought it would be interesting to check this out. I last played blackjack professionally some 26 years ago and I am not interested in becoming a working blackjack professional again. But I was interested in seeing how good players can become in one weekend.

On a personal basis, I used the Uston APC count way back when — a poor choice in retrospect — and they use the HiLo count at the bootcamp. I know the HiLo count in general (2-6 each count as +1, 7-9 count as 0, and tens and aces count as -1), but I’ve never played it and never have memorized the indices for strategy deviations.

Day One of the bootcamp (a Saturday) was about becoming as profitable of a blackjack player as possible. They discussed ways to maximize EV, comps/cover/travel, and bankroll management. I skipped this. I was not interested in becoming proficient myself, but rather seeing how others progressed through the training.

On Sunday, which I attended, were checkouts, advanced stuff, and celebrity speakers. (Tommy Hyland, who has been leader of a blackjack team for 40 years, told his stories. Andy Bloch, former MIT blackjack player and WSOP bracelet-winner poker player told his. And I spent some time talking about whether it makes sense for blackjack players to also play video poker.)

There were levels of checkout. At a minimum, the players were tested as to whether they could keep the count and move their bets accordingly. That is, when the count moves up, could they increase their bet appropriately. This skill requires paying attention to the cards and being able to figure out how many cards are left. For some players, this is as far along as they got.

The next step is to use the index number deviations. That is, when you have 16 versus a dealer ten card, it’s a close play whether to stand or hit. Many other plays have index numbers as well. Mastering all of them is more difficult, but some players were up there.

A third level of checkout included all the above, plus somebody asking you questions, such as: “Where are you from?”; “Have you seen the show here?”; “Have you tried our steak house?”  These questions weren’t mean or unusual. They were merely to see if you could walk and chew gum at the same time. You will certainly face this in a casino, and competent players need to be able to handle this kind of thing. A few players had the game down at this level.

During the checkout, you could see which players had practiced hard in preparation for the boot camp, and which ones hadn’t. Several of the students came out ready to play. Others needed a lot more work. You simply must put in the work (before, during, and after the boot camp) before you’re ready. The students were pretty unanimous that they got their money’s worth and came away inspired to keep working.

There were some students who flunked the checkouts — even the most basic one. Some of these students will conclude that this is not for them. It simply requires too much work to become good at this game. Others will use this as a wake-up call and apply themselves. There is another bootcamp in a few months, and some of these people will be back (at a reduced price, I assume) to see how much they’ve improved and if they are any closer to success.

You certainly don’t need a certificate to play. Any player of age can go to any casino and bet away. But if you can’t pass checkouts, you probably don’t have the skills to succeed. Blackjack is a pretty cut and dried game mathematically.

I was asked several times if returning to blackjack is something I’m considering. The short answer is “No”. My traveling days are largely over, and my face is too well known by casino employees. Getting good again is within my capabilities, I believe, but it’s not how I want to spend the rest of my life.

I was also asked if I wanted to create a video poker weekend boot camp — and right now my answer is “No.”

Video poker is way too difficult to master in one weekend. In blackjack, once you learn basic counting skills, the adjustments for different rules and deck sizes are relatively minor. In video poker, you play Deuces Wild considerably differently than you play Double Double Bonus. And one pay schedule in Deuces Wild is played considerably differently than other pay schedules. Players are certainly capable of learning one game (or maybe two) in a weekend, but with more than that, they would be overwhelmed.

Also, the best game differs from casino to casino. The best game in one place is often not the same as the best game elsewhere. Starting out with 9/6 Jacks or Better might be good for players in some areas, but many parts of the country don’t have that game.

Finally, a major part of the video poker game is learning to deal with slot clubs and promotions. That’s a several-hour course in and of itself. And while I’m generally familiar with the casinos in Las Vegas, if someone lives in St. Louis, Tunica, Pennsylvania, etc., I just don’t have the depth of knowledge to explain how the casinos in each of those areas differ from each other.

Colin Jones joked that he was going to reserve the web address www.videopokerapprenticeship.com. If he does, I’ll be happy to work with him and help him on the course. But I don’t predict a lot of success for it.

If you’re interested in becoming a competent blackjack player, www.blackjackapprenticeship.com is a good place to start.

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It’s All About the Quads

In February, I was playing 25¢ Five Play Multi-Strike 9/6 Jacks or Better at the South Point. This is a 99.79% game, played for 100 coins ($25) at a time. With the normal 0.30% slot club, the knowledgeable player has a small advantage all of the time.

In February, however, there were always two casino-wide progressives going on which added some small amount of EV. The bigger progressive must hit between $10,000 and $25,000, and was currently at about $22,000. Assuming there were 1,000 players playing, each of us had a 1/1,000 chance of hitting the progressive — but if we were in the other 999/1000 when it went off, we’d each receive $25 in free play.

It was not a huge amount of equity, but I needed to get some play done to keep the mailers coming, so this was the time I would be playing.

There are four such machines at the casino, and frequently the other three of them are empty. This time, however, there were two guys playing the 9/6 Double Double Bonus version of the same game. I had never seen them before, but they were discussing hands like they knew what they were talking about.

Although I hadn’t checked recently, I was pretty sure that the Jacks or Better game returned quite a bit more than the Double Double Bonus game. Still, here were two obviously knowledgeable players, so I decided to check next time I was at my computer.

When I got home that night, I discovered that the 9/6 DDB Multi-Strike game returned 99.18%. While I didn’t have this number at my fingertips, it was consistent with about what I thought it was. The base game starts out with JoB worth 0.56% more than DDB and I thought the Multi-Strike aspect to the game would add approximately the same amount to each game. It turned out that it added 0.25% to JoB and 0.20% to DDB.

Two days later I stopped by and the progressive was more than $20,000 again, so I sat down to play. One of the players from two days before was there and he asked me if I was Bob Dancer. He told me he had purchased the Video Poker for Winners software years before and that taught him how to play the game. He comes to Vegas five times a year for a four-day trip and always played DDB Multi-Strike. He boasts that he was taught by Bob Dancer.

I asked him why he played DDB rather than JoB? He said the results were all about the quads and it was a lot more exciting for him.

I told him I understood. Four aces return $200 or $500 (depending on whether they have a kicker) and on the 2x, 4x, or 8x line it can turn into a taxable. Four 2s, 3s, and 4s pay $100 or $200 depending on the kicker and the other quads pay $62.50. These numbers are quite a bit larger than the $31.25 that all quads pay in JoB. Excitement is fun!

At the same time, I told him the game he played returned 0.6% less than the JoB version. Since he played about $150,000 each time he came to Vegas, on average that’s $900 per trip or $4,500 per year. Was it that much more exciting?

Even JoB is plenty volatile in the Multi-Strike version. DDB is quite a bit more so. Yes, there will be trips he goes home a winner, but there will also be trips he loses quite a bit. He agreed, saying he was down $8,000 so far this trip.

This guy taught himself how to play, thanks to the software. But there’s a lot more to playing successfully than just knowing how to play the hands.

If this guy has the money and this is how he wants to spend it, great. Everybody gets to make their own choices.

Still, it bothered me that someone who loses so much regularly tells people that I was his teacher!

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An “Advantage Play” I Detest

What is an advantage play? While I have never heard a precise definition, generally it is when you use your intelligence, knowledge, or guile to gain an advantage over some other person or group. The term is most often used in discussions about beating a casino.

Counting cards at blackjack is a common advantage play. Using video poker knowledge to choose which machines to play and to play every hand correctly, combined with an understanding of slot clubs and promotions, is the type of advantage play in which I regularly indulge. Betting sports, where you have computed that the line should be -3 and the books have them at -7, is still another. As is seeking dealers who expose the bottom card or make incorrect payouts. Here we are extracting extra money from a casino – which is the entire point of intelligent gambling.

Outside the casino, clipping coupons could be considered an advantage play – especially if sometimes you get the stuff for free. Doing all your shopping during sales and never paying full retail is another. Standing in the “10 items or less line when you actually have 11 items is another.  The list is endless.

In normal use of the term, advantage play includes legal actions and excludes illegal actions. With this definition, using a computer strapped to your thigh to help you figure out how to play blackjack accurately in Nevada is not an advantage play. It is an illegal one.

The problem with this definition is that often what is legal or illegal is a gray area and must be determined by the courts — where it helps to hire good lawyers. While I strongly believe the edge sorting that Phil Ivey and Kelly Sun did at Borgata, Crockfords, and other casinos should be a 100% legal advantage play, the courts have disagreed. Sometimes you just don’t know what is legal or what is not, although there is not doubt about the most egregious cases such as using a gun to rob a bank.

Let me get to what bugs me so much.

My wife, Bonnie, fell hard recently and hit on her buttocks/hip area. Nothing was broken, fortunately, but she’s 75 years old and the fall debilitated her. Although she may be walking without assistance when you next see her, for several weeks she used a walker, or a cane, or sometimes even a wheel chair. She asked her orthopedist to sign the form for a temporary “Disability Placard” to enable her to park close to places she needed to go. The doctor agreed and we went into the DMV to get the placard.

While we were in the DMV, where we had no problem, on the next chair over was a woman writhing in pain. She could barely even sit down, and she was constantly moaning. Clearly, she was in agony.   It was uncomfortable to see. We didn’t know her and couldn’t really help her, but someone hurting that much made our hearts go out to her.

We finished before she did, and I left Bonnie by the front door of the DMV while I went to retrieve our car and pick her up. When I got there to pick up Bonnie and was helping her in the front seat, we saw the woman who was in so much pain exit the DMV, immediately straighten up, and begin to jog towards her car!

Although there may be another side to this story, to us it looked like she got the disability placards merely so she can park up close to wherever she’s going. This was clearly an advantage play.

You might consider this smart until you consider that there are only a limited number of handicapped parking spots at many places, and the spot she’ll be taking should be left available to someone who really needs it.

When she signed up, Bonnie received two placards. One she placed in her own car, of course, and the other she gave to me. When she’s with me, I park in a handicapped space. When she’s not with me, I don’t.

On one occasion, the temptation to use the placard when she wasn’t with me was strong. I resisted. But I might someday not resist.

In order to help me “practice what I preach,” I offer you the following promise: If you ever see me use a handicapped space inappropriately (i.e. when Bonnie’s not around or when I don’t qualify for one myself, which I don’t currently but I’m 72 years old and who knows what the future holds?), mention it and I will give you $100. If there are three of you in the group, I will give all three of you $100 each.

Parting with a few Benjamins won’t break me, but I don’t throw money around. It would irritate me (at my own short-coming) should I ever have to pay money for something I shouldn’t be doing anyway. I’m not really famous, but I’ve taught enough classes that tens of thousands of people in Las Vegas recognize me. Knowing that I might have to fork over some money if I “cheat” will assist me in walking the walk.

Forgive the pun please, but we all need crutches, and this is one that will help me.

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Two Cards or Four? When Does It Matter?  

Consider the following two hands in games where you get your money back for a pair of jacks or better:  A♠ K♠ Q♥ T♦ 5♣ and A♠ K♠ Q♥ T♦ 5♠. There are games where the correct play in both hands is AK; games where the correct play is always AKQT; and games where in the first hand you hold AK and in the second you hold AKQT. Today we’re going to look at which games fall into which category, and why.

First, I’ll provide the “executive summary” for when each condition holds. That’s all some of my readers wish to know. Afterwards, I’ll provide some more detail as to the “why.”

     A. In games where two pair returns 2-for-1, always hold AK.

     B. In games where two pair returns 1-for-1 and straights return 4-for-1, hold AK in the first hand and AKQT in the second.

     C. In games where two pair returns 1-for-1 and straights return 5-for-1, always hold AKQT.

 

Now let’s go a little deeper. In Category A, we basically have Jacks or Better and Bonus Poker. The pay schedule matters not at all for the value of AKQT, so long as it has the standard return for straights, two pair, and high pairs. The value of AKQT is always going to be $2.66 for the five-coin dollar player.

The value of AK, however, is also affected by the value you get for full houses and flushes — but not much. Holding AK in 9/6 Jacks or Better is worth $2.87 and $2.79 and in 8/5 Bonus Poker these values drop to $2.82 and $2.75 — which are still well above the $2.66 benchmark for holding AKQT. A key fact that will come in later in the article is that in the Jacks or Better case, when the low card is unsuited with the AK, then AK is worth 21¢ more than AKQT, and when the low card is suited with the AK, then AK is worth 13¢ more than AKQT.

You do get a full house holding AK one time in 900 and flushes one time in 99 when the fifth card is unsuited with the AK and one time in 136 when the fifth card IS of the same suit as the AK. These are not big numbers. The pay schedules matter, but unless you get into a Bonus Poker game that is so bad that two pair only returns 1-for-1, you always prefer AK.

How much you get for two pair doesn’t affect the value of AKQT because the only hands you can get when you hold those five cards are a straight or a high pair. From AK, however, you end up with two pair every 22.8 times. Since that means an extra $5 every 22.8 times when you get one unit more, changing the value of two pair from 2-for-1 to 1-for-1 is worth 22¢.

Close readers might remember that in 9/6 Jacks or Better when the low card was unsuited, AK was only worth 21¢ more than AKQT, so why wouldn’t changing the value of two pair change the play? The answer is that in the games where two pair receives 1-for-1, the value of 4-of-a-kinds (especially aces) is much higher than the $125 you get in Jacks or Better. Even though you only only have a 1-in-16,215 chance to get four aces holding AK and drawing three cards, the difference in the payout from $125 to $800 is worth about 4¢.

In 9/6 Double Double Bonus, for example, holding AK is better in the first hand by 4¢ and AKQT is better in the second hand by about 4.5¢. To me, these numbers are plenty big enough that I’m going to pay attention to the suit of the small card in these hands. Whether they are big enough for you to reach the same conclusion is a decision you’re going to have to make for yourself.

The third category where two pair returns 1-for-1 and straights return 5-for-1 is really just the best versions of Double Bonus Poker. Since the straights pay 25% more than they do in most otherwise similar video poker games, it should be no surprise that you hold AKQT on both hands.

There are a few games that will not fit these rules exactly, and variations on games like Ultimate X, but in general these rules apply widely.

I picked AK in this case. I could easily have chosen AQ or AJ with exactly the same results. All three combinations are equal.

The rules for KQ, KJ, and QJ are different than the ones given here. Perhaps I’ll discuss them in another blog someday.

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Ed Thorp’s Wife

Ed Thorp is one of the fathers of blackjack card counting. Recently he made a nice donation to the Blackjack Ball, which ensures the continuance of the ball even after it’s founder, Max Rubin, passes away. As a partial thank you, Max told Thorp that he could invite his entire family to this year’s Blackjack Ball if he wanted, totally complimentary.

This year, Thorp brought his wife, three children, one son-in-law, and two grandchildren. Slightly before the dinner started, I sat down at a random table. One of my goals at the ball was to find guests for the podcast. Before dinner I was writing up notes before I forgot who the people on my list were and what made them interesting.

It turned out that the table where I had sat down was the one that the Thorps were planning on reserving for themselves. As there are only eight chairs at the table, I told them I would move. They graciously said that wasn’t necessary and they’d just go find another chair, which they did. So, I ended up sitting between his granddaughter, who had just graduated from Dartmouth College, and his wife, Catherine.

While I conversed with both ladies, as well as others at the table, I had the longest conversation with Catherine. She had married Ed Thorp, who is now in his mid-80s and still quite sharp, about seven years ago. Since I married Bonnie five years ago, there were certain similarities.

Catherine said Ed chose her mathematically! He had some mathematical model that told him that she was the one! I found that fascinating. I’m happy with my choice of Bonnie, but certainly did not use any mathematical formula to pick her out. So, I decided to ask Ed to tell me more about his methodology.

He smiled and said it’s not original with him and Wikipedia addresses this as the “Secretary Problem.” My explanation below is going to be highly simplified, but you can look it up in Wikipedia should you like.

The Secretary Problem was originally derived in the context of determining how many potential secretaries you should interview before deciding on which one to hire. The problem requires that you know the number of interviewees in the pool, n, and that you are able to rank each secretary relative to the others.

The key number for the optimal number of secretaries (or candidates for marriage) turns out to be n / e, where e is a mathematical constant whose value is approximately 2.718.

That is, when Ed was looking for a wife, if he thought he would have five years to find one and would meet eight potential mates a year, that would be 40 candidates. Doing the math, we have 40 / 2.718 = 14.7. This means that with the first 14 women Ed meets, no matter how desirable they are, he does not propose. He merely ranks each one relative to the others.

Starting with the 15th woman, he should propose to the first one he meets who exceeds the others in ranking. Assuming she accepts, that’s the one he should marry. If none of the last 26 women outrank the best one in the first 14, he should simply marry the last one.

(Presumably in the real world, if the 40th one was totally inappropriate, he would continue until he found one that’s reasonably appropriate.)

So, I told Catherine that I might forget her name before next year, but I was probably going to remember that she was Ms. 15, because she couldn’t have been in the first 14! She and Ed were both fine with that!

This was a pleasant chat and “intellectual” discussion with two charming people, but I have my doubts that this was actually the method Ed Thorp used to select his wife. Why? Because it’s extremely difficult to rank people.

Let’s say he’s met Karen, Linda, and Mary and assume they are all “reasonably” acceptable. One will be prettier, one will be smarter, one will make better lasagna, one will be more responsible financially (a definite consideration because Thorp is, I believe, a billionaire or close to it), one will be more compatible on religious and political issues, one will be better liked by his family members, etc.

How can you possibly give a unique ranking for these three women — let alone 14?  It’s virtually impossible that one woman could be superior in every aspect to the others. So, you’re going to have to make some kind of formula that tells you which attribute is most important. And these are real live women, who each come with lots and lots of attributes, each of whom have good days and bad days. This is not a catalog where you can pick and choose.

So, this strikes me as an apocryphal story that Ed and Catherine like to tell but was not actually used in real life. However he actually chose her, he did well. She appears to be quite charming and they are clearly very fond of one another.

The Secretary Problem, however, is an interesting theoretical concept about when to stop your searching. I’m glad I was introduced to it.

Author’s note:  After I wrote the above, I sent it to Dr. Thorp to get his feedback before I published. It’s possible I misrepresented the problem, and I was, after all, suggesting that he wasn’t being entirely truthful in saying he used this technique to find Catherine. He is one of my heroes and I didn’t want to insult him.  He responded:

Hi Bob,

 

We enjoyed your company.  Yes, a math model like this is fun to think about but the real world is so much more complex in this instance that one shouldn’t, and we didn’t, follow it.  

Best,

Ed

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The Twenty-Third Annual Blackjack Ball

The Blackjack Ball is an annual institution where about 100 of the world’s best gamblers meet up, socialize, drink too much, and compete against each other. The 2019 version occurred a few weeks ago.

The first order of business after two hours of drinking and socializing was to vote for the newest member of the Blackjack Hall of Fame. Six worthy candidates were nominated, and each professional player got one vote — with Hall of Fame members votes counting triple.

This year’s winner was Rob Reitzen. This is the way Rob was listed on the ballot.

There are few, if any, players that have won more money in the history of Blackjack than Rob Reitzen. From simple card counting to shuffle tracking/sequencing to bottom steering to advanced computer play, Rob has beaten games in more innovative ways than most professional blackjack players even know to exist.

The founding partner of CORE, which went on to become the largest and most profitable player-banking operation in history, Rob was featured in an Esquire Magazine article in which thereporter followed him and watched him beat Caesars Palace in Las Vegas out of more than $500,000 while using a sequencing technique he dubbed “The Hammer” on a single weekend!

Rob’s acceptance speech was somewhat lengthy. Host Max Rubin quipped afterwards that Rob must have thought he had a chance to win so he wrote “War and Peace” to read just in case.

The highlight of the ball is the test of 21 Questions. The five top scores get invited into the skills contest. Of these five, one player is eliminated quickly.

There were three people there who were ineligible to play: James Grosjean, Richard Munchkin, and myself — albeit it for different reasons. James and Richard have each won three times and have been determined to be “too good.” The first-place winner gets the Grosjean trophy, and the second-place winner gets the Munchkin cup.

The winner also gets an engraved Nebuchadnezzar (15 liters) of Luc Belaire Champagne, donated by Hall of Fame member Don Johnson who is an ambassador for that company.

I got included on this list for an entirely different reason as my blackjack career was short and uneventful. Although I did get to the final table at the Blackjack Ball once, I blew out immediately and didn’t end up in the money.

My contribution is that I submit a LOT of test questions. I submitted about 30 questions this year and they actually used seven or eight of my questions, depending on how you count. Since host Max Rubin has been a bit under the weather, he doesn’t have the time and energy to create as many questions as he used to and he’s grateful to me for supplying some. And, since taking a test where I had submitted a third of the questions would hardly be fair to the others, I’m not eligible to play. That’s cool. I get a kick out of composing questions that stump some of the smartest gamblers in the world — while other such gamblers get the questions correct.

Before the competition, we have a Calcutta auction. Host Max Rubin is a very charming auctioneer. He groups each of the 100 or so contestants into about 20 categories and we bid on who is going to win. Max teases, cajoles, insults, and praises various people in the audience in order to get them to bid. About $20,000 is raised and this goes to whomever owns the players who end up in the top four positions. Each player is allowed to buy up to 50% of himself back after the Calcutta and before the test is given.

The test is difficult — and questions can be about anything and everything. Some of the more interesting ones were:

  1. You are betting $100 on the pass line and place maximum odds at the Bellagio where 3-4-5 odds are allowed. On winning bets, what is the typical payout for the combination of pass line bet plus the odds?   

 

Answer: $700 — $100 for the pass line and $600 for the odds

 

  1. Donald Trump is the 45th American president. Express the number forty-five in roman numerals.

 

Answer:  XLV — this is not trivial. Many will say VL, which is incorrect

 

  1. In a National Basketball Association game, with 0.2 seconds left, the ball is out-of-bounds in possession of the team trailing by 2 points. The inbounding player throws the ball directly at the basket — and the ball would indeed have gone in except one of the inbounder’s teammates gently touches the ball when it is directly above the basket, 12 inches from going in. The teammate guides the ball into the basket. What happens?

 

  1. The inbounding team scores three points and wins the game
  2. The inbounding team scores two points and sends the game into overtime
  3. The inbounding team is guilty of offensive goal-tending, which causes them to lose possession and the game
  4. 0.2 seconds is not enough time for any of this to happen, so time runs out before any points are scored or there’s a change in possession

 

(Answer b: offensive goal-tending only occurs when the shot originated within the field of play. Since this “shot” originated from out-of-bounds, offensive goal tending could not happen.

Although the play originally began beyond the 3-point-line, the fact that the ball was touched directly above the basket turns this into a 2-point play.

The clock doesn’t start until the ball is touched by a player within the field of play — which in this case happened when the ball was one foot above the basket headed downward. 0.2 seconds is plenty of time for the basket to be made before the clock runs out.)

Those questions were three of the ones submitted by me, so naturally I think they are some of the most interesting. Here is one submitted by James Grosjean.

  1.   Playing six deck blackjack where the dealer stands on soft 17, which of the following starting positions has the highest EV.
  1. You have a hard 20 against a dealer ace before he checks for blackjack.
  2. You have an 11 versus a dealer 5
  3. You have a pair of aces against a dealer 4.
  4. You have a ten and a nine against a dealer 8

(Answer:  the exact numbers were given at the Ball, but the correct answer is a.)

One of the professional players only got four out of 21 questions correct. He was invited forward to receive a small “World’s Worst Blackjack Player.” The teasing was good natured, but he definitely got razzed.

The player with the most correct, 14, was Andy Bloch, former member of the MIT blackjack team and also an accomplished poker professional. Two players got 13 correct: Gemlo and Big Player. Since they want to be identified by their pseudonyms, I won’t identify them any further.

Coming in at 12 correct were four players: Arnold Snyder, John Brahms, Tony S, and attorney Bob Nersesian. Since only five players advance to the final game, we had to eliminate two of these four players. The way this was done was each of these four people had to name a casino that was formerly in Clark County but is here no more. Giving an incorrect answer, or a duplicate, eliminated you. There were probably fifty casinos named (e.g. Stardust, Riviera, Dunes, Landmark, Las Vegas Club, etc., etc. and finally Arnold Snyder and John Brahms gave incorrect answers and were eliminated.

On to the skills competition, which is held at a blackjack table. There was a stack of cards in the discard tray. Each of the five contestants needed to estimate the number of cards there. Worst guesser was eliminated — which happened to be Big Player. We were then down to four players.

Next test was a card-cutting competition. The 6♣ was placed at the bottom of the deck. Each player got to cut the cards. Munchkin then burned a card and dealt any number of hands that player named (from 1 to 7), with the object being to place the 6♣ face down in the dealer’s hand, e.g. as the dealer’s hole card.

The players all chose to deal six hands. Unfortunately, Andy Bloch cut the card four spaces away and was eliminated.

The third test was very unusual and was designed by James Grosjean. JG cut approximately one-inch squares out of the center of all twelve picture cards. Players had 90 seconds to figure out the rank and suits of each of the squares. Positive points were awarded for being accurate. Negative scores were awarded for inaccuracy. The mean score was negative! Gemlo did the worst and was eliminated.

It was now down to Tony S and Bob Nersesian and the contest was counting down a double deck. Richard Munchkin, who was running the final contest, removed three cards from each of the two deck stacks. The players had to determine what those cards were, using any card counting system they wanted.

Unfortunately, Bob Nersesian has never counted cards, whereas Tony S was a highly skilled professional for a number of years. Bob’s only chance was a wild guess. As soon as the clock started, he should have slammed his cards down and predicted his three cards would have a count of zero in HiLo.  He would win if there were three neutral cards, or one high, one low, and one neutral. He had a reasonable chance for success, whereas if he actually tried to count the double deck, he had basically no chance. There are actually better counts to use if you’re just going to guess, but Bob wouldn’t know about this.

Bob chose the wrong way to go about it. He tried to count the cards and ended up almost a minute behind Tony. Tony was accurate in his count, of course, and it was over. Although it didn’t matter, we asked Bob what he thought the count was in his deck. He said +6, which is an impossible number with only three cards using HiLo. Bob is a hell of an attorney but has never counted cards.

Congratulations to all our winners. We hope to have Rob Reitzen, Tony S, and Max Rubin on our podcast soon celebrating the twenty-third Blackjack Ball.