Author: Bob Dancer

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Dollars and Sense

This column is written primarily for beginners and low-intermediate players. Readers more advanced than that should give it a once-over as well. There’s a chart here you’ve likely never seen before.

You’re playing Double Double Bonus, receiving 45 for a full house. How much you get for the flush is irrelevant to this discussion. If you get only 40 for the full house in the game you typically play, you’re permitting yourself to play such a bad game that no amount of advice from me is going to help you be a winning player.

You’re dealt K♠ K♥ 6♣ 6♦ 5♠. You’re debating holding just the kings or holding the two pair. You’ve read from people like me that holding two pair is correct by a mile, but it’s counterintuitive to you. After all, you get the same “even money” for a pair of kings as you do for two pair and if you hold the kings you might get lucky and receive four kings. So why not go for it?

Let’s talk dollars and sense. Assume you’re playing dollar single line DDB, five coins at a time. Holding two pair, you have the following possibilities — and the value of those possibilities.

The frequency numbers from the chart may be found in Video Poker for Winners or other quality software. The dollar figures aren’t generally seen, although you do get the sum of them, shown in green. And notice I didn’t include columns for straights, flushes, straight flushes, or royal flushes simply because you can’t get one of those when you start out by holding a pair or two pair.

Let’s take the line corresponding to KK66. You have 47 possible draws, which is the normal number when you’re drawing one card from a 52-card pack and you’ve already looked at a five-card deal. You’ll end up with two pair 43 times and a full house four times. You can probably do this much in your head if you start with figuring how many full houses you can get. After all, the only time you’re going to get a full house is when you draw one of the two remaining kings or one of the two remaining sixes. In all other cases, you’re going to end up with the same two pair with which you started.

What’s new in this chart, shown in blue, is how much each of these hands is worth. The two-pair final hand contributes $4.57 to your total EV and the full house adds $3.83. Rather than give a definition for how I figured out those numbers, I’ll show you the calculations: $3.83 = (4 * $45 / 47). $4.57 = (43 * $5 / 47). The $45 and $5 in the formulas are the amounts you receive from a full house and two pair respectively in this game.

In the line corresponding to holding the kings, there are now 16,215 possible draws. For most of us, including me, there are way too many possibilities to figure this stuff out in our heads, or even with paper and pencil, with a high degree of confidence. Fortunately, software to do this for us is very fast, accurate, and inexpensive.
The number that really pops out at me on this line is the 69¢ that the chance at a 4-of-a-kind is worth. Yes, the quad is worth $250 when you get it, and that’s the number beginning players focus on, but you only get it a little less than one chance in 360. Multiply it out and it comes to 69¢.

Also, note that the chance for a full house is 47¢ when you hold a pair, compared to the $3.83 it’s worth when you hold two pair.

It’s easy to think of possibilities — like you COULD get a four-of-a-kind. It’s much harder to think of probabilities — which means how often does it happen percentage-wise. It’s even harder to multiply out the VALUE of the hands which means the probability multiplied by the pay schedule.

Players sometimes confuse this hand with A♠ A♥ 6♣ 6♦ 5♠. To put this into the above chart we need to add another column for four aces with a kicker. If we do that, we’ll find all the numbers in the chart stay the same, except the value of the four aces without a kicker is worth $1.63 and the value of four aces with a kicker is worth $1.48. Adding those together gives us $3.11 — compared to the 69¢ the kings were worth. This makes holding the aces worth more than holding two pair, aces up.

The strategy for this part of the game is AA > Two Pair > KK, QQ, JJ. If you can read the strategy and just follow it no-questions-asked, then you don’t need columns like this one. If you ever wonder “why,” and haven’t figured out the answer to this particular question, maybe this column will be useful to you.

As for me, I’m always wondering “why?” Once I figure that out (which I normally can do in video poker — not so much in certain other parts of life), it makes it much easier to keep strategies memorized.

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There’s More to EV than Just EV

“EV” stands for expected value, which is a type of weighted average. The exact definition I’ll leave to the probability and statistics textbooks. As cut and dried as the definition is in the math books, there’s plenty of wiggle room in the way it’s applied to video poker.

Before we discuss this wiggle room, let’s talk about how EV is most properly used. EV gives you a “best guess” of how a situation will turn out — on average — if you play it out zillions of times. It’s not a guarantee at all of how things will turn out this time. If you’re flipping a fair coin 100 times, the EV is for 50 heads to show up. But sometimes only 40 heads will appear, and equally often 60. In actuality, ending up with exactly 50 heads out of 100 trials is an underdog to happen. If you’re betting on heads, you may well be upset that the actual result this time didn’t match up with the EV.

The definition of EV is about “how many times something happens.” In video poker, we often turn this into a percentage. For example, 9/6 Jacks or Better has a well-known probability of returning 99.544% when played perfectly. That means if we play $100,000 through a 9/6 JoB machine, our average ending balance will be $99,544, meaning the casino keeps $456 from our play. This will be true whether we play for nickels, quarters, dollars, or larger stakes. This will be true whether we are playing single line, Triple Play . . . or Hundred Play.

It is common among video poker players, but not universal, to add the return on the game with the slot club return and call the result EV. That is, if you’re playing 9/6 JoB at the South Point on double point days, the EV is 99.544% +2(.300%) = 100.144%. Adding the slot club return is reasonably certain, as almost always you know what it’s going to be before you play.

Adding mailers is a bit iffier, if that’s a word. If you know you are going to get mailers worth $80 for $40,000 coin-in, you can go ahead and add another 0.20% to the EV. But we are rarely that certain — or rather, the ones who are certain are frequently mistaken. Slot clubs change their parameters for mailers all the time, and usually these parameters are unpublished. You can get a feel for what the rules are if you talk to enough players, but it’s normally the case that players don’t keep good enough records to be useful.

Someone can accurately tell you that their mailer is $25 a week. But if you want to know how much they won or lost each month over the last six months, including how much was played during promotions and on which machines, that information is tougher to come by. And, at some casinos, how many times did the player come into the casino? And what “discretionary” comps were issued to this player? Some or all of this information is used by at least some casinos to determine your mailer. And most casinos don’t publish the formula they use.

Still other players (including me) add an estimate for the value of the current promotion into the EV calculation. I wouldn’t be playing at all at any casinos if it wasn’t for their promotions. (Yes, I could play 100% games for low stakes in Las Vegas for less than $10 per hour. And there’s money to be made playing video poker progressives. If that’s your thing, welcome to it. For me, no thanks.)

I was playing $1 9/6 JoB Spin Poker on a recent double point day at the South Point, when there was another promotion going on as well. There are higher-EV games there, but only for lower stakes. With good enough promotions, playing $2 single line ($10 per hand) 99.728% NSU Deuces Wild sometimes just isn’t as good as the 99.544% ($45 per hand) game.

Another player was playing $1 9/5 White Hot Aces on the same Spin Poker machine. I asked him why he chose that game instead of JoB and he responded “Higher EV.” Really? Not in my book.

The WHA game returns 99.572% which is certainly a tad higher than the 99.544% you get from JoB. But every time you get dealt a quad, the Jacks or Better game returns  “only” $1,125 which, importantly, is less than W2G range. Getting two or more quad 2s, 3s, or 4s, or even one set of aces, generates additional W2Gs.

For professional players who get LOTS of W2Gs, these are not particularly terrible things. We have learned how to “write off” a high percentage of them. Still, at this casino, on a double point day, it takes more than five minutes per W2G for a slot attendant to arrive and reset the machine. On a promotion that is worth, say, $36 an hour, not playing for five minutes costs you $3. Are you planning on tipping when you get paid for your W2G? If you typically tip $5, that’s $8 out of every W2G. That more than eliminates the difference in EV from the game itself.

You pretty much get the same number of royals in the two games, but you get more straight flushes in WHA. Why? Two reasons. First of all, you get paid $400 per straight flush rather than $250 so it only takes three to get a W2G rather than five. Also, the strategy calls for you to go for straight flushes more in WHA. For example, from a hand like 3♠ 4♥ 5♥ 6♥ 7♥, you hold five cards in JoB and only four in WHA. When you do catch a straight flush on the draw, usually you get three of them — and hence a W2G.

Instead of EV, I use a form of “expected dollars per hour,” which includes how many hands per hour I can play and at what stakes. Are my calculations different from those of other players? Maybe. Part of the calculation includes an estimate for the current promotion, and personal estimates differ. But for figuring out whether I should be playing at Casino A or B, I find the calculation very useful.

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Was She Talking Like a Woman or Talking Like a Man?

Using stereotypes to say “women are this way and men are that way” in today’s political climate is a formula guaranteed to generate multiple negative comments. Rightfully so. There is very little interesting where you can say that every female (or every male) is a certain way. There are always exceptions.

With that said, there are also tendencies that appear to be there. A tendency doesn’t mean a certainty. For example, I can correctly say that in general men tend to be taller than women. And that’s true on average — but we recognize there are some taller and shorter examples of each sex.

What brings this up is something that happened to a friend of mine, Reuben, who is also a competent video poker professional. He was playing at a casino whose name he doesn’t want me to publish, and playing a game that is still around. He said that if I wrote about it, I could call it $5 Multi Strike — just to give it a name — but in fact it was a different game.

He was playing two machines at a time — which happened to be the only two $5 Multi Strike machines in the casino. He believed that the game plus the slot club plus whatever promotions were going on gave him enough of an advantage to justify him being there.

He rarely played two machines at a time. It often announces “I am a pro” to a casino which tends to reduce your longevity there. But in this particular casino, he had run unlucky and to date was a big loser — even though he had always played games with positive EV. Since he figured this casino wouldn’t make him as a pro, he could play more aggressively than he otherwise would.

After playing a while, a woman he had never seen before came up and asked if these were the only two high-denom Multi Strike machines in the casino. Instead of his usual “I don’t know,” which is generally the smart answer in cases like this, he told her that yes, he believed they were.

The woman then asked, “How long do you intend to play?” Reuben said he hadn’t really decided yet. It depended on how much he lost and how quickly. Which was nonsense, of course. Reuben was planning on playing until midnight, which was when the promotion ended. She looked at the machines longingly for a while and then left.

Reuben speculated that she was waiting for him to offer her a machine. After all, in Reuben’s experience, women tend to be more empathic and less direct in their requests. Had it been his wife instead of a stranger, his wife would have expected him to realize that she wanted a machine — and hence, given one to her because it was the polite thing to do.

Still, keeping both machines was the desired goal and if this lady wanted a machine, she was, at a minimum, going to have to explicitly ask for one. Whether Reuben would have said yes or no wasn’t a certainty. He would have made a decision when necessary — but not before. There are often extenuating circumstances one way or the other.

Reuben considered the possibility that the woman would go to the slot shift boss and complain that she couldn’t get a machine and one guy was hogging both of them. He didn’t want that to happen, although it was largely out of his control. He preferred to be a “low maintenance” player. It doesn’t take too many incidents for some casino employees to conclude this player is “always” causing trouble. If he developed that unwanted reputation, close calls down the road (such as whether to pay him in a sticky button situation — or whether to allow him to remain even after he starts winning) might not go his way.

If the slot shift boss came over and asked for a machine for the woman, Reuben’s answer would have been an immediate, “Of course.” He likely would have added, “All she needed to do was to ask me, but she never did.” The last four words were absolutely true. The first nine — maybe. But the slot shift boss couldn’t know that.

It’s possible the woman believed she shouldn’t have to ask. She possibly believed even a guy should have been able to understand she wanted a machine. It could seem to her to be common courtesy that should prompt Reuben to give up a machine. That definitely was Reuben’s best guess as to what his wife would believe were she the one wanting a machine.

One thing that Reuben felt was a bit of a safety cushion this time was that the slot shift boss was a man. Right or wrong, he believed a male shift boss would be more sympathetic to “she never actually asked” than a woman shift boss would. Reuben’s actions would likely have been the same with any boss, but he would expect the aftermath to be gentler on him when the boss was a male.

Could Reuben’s stereotypes and assumptions based on them have been way off? Of course. No player or boss acts exactly like you expect him or her to.

Is he smart to use such stereotypes and assumptions in his decisions? Absolutely. You are frequently called on to make decisions based on incomplete information, and sometimes stereotypes give you some extra information that is useful.

Would Reuben be called prejudiced or sexist if he verbalized his thought processes? That too. You can’t please everybody, and people will use whatever ammunition against you that you give them. Often, it’s better to make your decisions quietly and not discuss why you made them.

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Whom Do You Trust?

I’m showing my age, but I remember the “Who Do You Trust?” television show hosted by Johnny Carson before he got the Tonight Show gig. He always said later that the first word should have been “Whom” rather than “Who,” and if you can’t trust Johnny Carson, whom can you trust?

Many of the people who attend my classes are quarter or dollar players. It’s no secret that I play for higher stakes, at least some of the time. Usually once or twice a semester, someone says something like, “Although I would never play for the stakes you do, I’m really curious as to what games you play and where. Will you tell me?”

My standard answer is that I write about the places I play that I don’t mind you knowing about, and don’t write about the ones I would rather keep secret. So, if they don’t already know about one of my plays, I’m not going to tell them.

The reason for this is simple. Many plays can only support one or two competent players. Telling the world about such a play would be the kiss of death to the play. No thanks.

One player followed up with, “But I promise I won’t tell anybody, and I certainly won’t be playing those stakes myself. Don’t you trust me?”

Well, I’m not sure. I’d rather not put it to the test. If I trust 20 people and 19 of them never told a soul, the secret is still out. Is this guy one of the 19, or the one who says, “It won’t hurt anything if I mention this to my brother-in-law?” I don’t know beforehand, so it’s better that I keep quiet.

I’m not a proponent of the “Two can keep a secret only if one of them is dead” philosophy. If Richard Munchkin wants to know the where and why on any of my plays, I’m going to tell him. I trust him — even though he has the bankroll along with family members and close friends who could burn out any play I told him about. Among top gamblers, their word is their bond. If I told him, “I’ll tell you about it but you can’t play because of xxxxx,” I believe he’d honor that.

On the radio show, we’ve had blackjack team captains describe teams they were on where one of the team members ripped off the others. This is rare — but it happens — and it’s always a shock when it does. You can protect yourself from this by never telling anybody anything, but that’s going to be a lonely life you lead.

Trusting somebody has similarities with marriage. Although it ends badly some of the time (and I’ve experienced my share of that), overall, I’m convinced my life works better being married than being single.

I’d actually be more comfortable telling Richard about a play than I would be telling Bonnie! Bonnie is not a player at all and although she’s definitely on my side, if I tell her I’m going to be playing at the (pick a casino), it’s possible that she would inadvertently tell her sister, daughter, or a girlfriend where I’m playing. If I tell her over and over again, “This is a secret — you can tell no one,” she’ll honor my wishes. But she has no good gambling sense about what is a secret and what isn’t and she’s not really practiced in keeping secrets. It’s better not to tell her.

If I took her to a comped meal at the Wicked Spoon buffet at the Cosmopolitan, she would figure out that there was some play (now gone) that I had there, but she isn’t really capable of understanding why the play there was better or worse than playing at some other casino. She’s willing to listen and nod her head if I tell her, “The game pays xxx% off the top, with yyy% from the slot club, and zzz% from the mailers.  This other promotion they’re having now adds another vvv%, and there’s a pretty good chance I can talk them into www% worth of comps.”  These are just numbers to her and it’s all kind of gobbledygook.

Richard, however, would understand each of these things and if he didn’t, he’d ask me to explain further. And he could put the numbers into context of other plays he knew about. That is, a 100.5% play is pretty good if the best you can find otherwise is 100.3%. But if you can find a 101% play for the same stakes, a 100.5% isn’t such a good deal.

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You’re Not Ready Yet

Immediately after one of my classes at the South Point, a man, “Joe,” came up to me and asked if I would mentor him in becoming a professional video poker player. He told me he had plenty of bankroll and wanted to turbocharge his learning process. He had heard that I would do private consulting for $250 an hour with a two-hour minimum and that did not present a problem for him.

I had another engagement after class, so we scheduled a lunch date for the near future. Although I have food comps at casinos, I preferred having the conversation at a local Applebee’s where the chances of being overheard by other players was far less. I don’t pay retail for food in Vegas very often, but this was one of those times.

In the time before I met with Joe, I tried to figure out what kind of person I would be willing to mentor. Assuming he had the bankroll, I figured the main criteria were:

a. His personality was acceptable to me. This isn’t a particularly high bar to cross, but there are a few people I just don’t enjoy hanging out with. I didn’t want a long-term relationship with somebody like that.

b. He was smart enough. Video poker is applied math. Not everybody is capable of learning it at a high level.

c. He had some history of success at the game and could study on his own. When I’m consulting with somebody two hours at a time, I don’t really care how good they are when they come to me. I’ll spend the two hours doing my best to improve their skill and knowledge level. But a mentoring relationship is a longer-term affair and spending dozens of hours while moving somebody from beginner to intermediate isn’t how I want to spend my time.

Okay. After Joe and I ordered lunch, I asked him where he lived and how he got his bankroll. I had spoken to Joe a few times previously and he passed the personality test, such as it is. He had sent me a number of emails over the past few years with questions and/or suggestions for the Gambling with an Edge radio show. These emails led me to believe he was smart enough to succeed at this.

Joe told me he was 49 years old, lived on the East Coast, and had recently inherited more than $2 million. He planned to retire from the Air Force Reserve in a few months and was looking at how he wanted to spend the rest of his life.

Joe had listened to a number of the radio shows and it really sounded like I enjoyed my life more than he enjoyed his. Plus, he had read my Million Dollar Video Poker autobiography and was fascinated with the life of a gambler. He decided he wanted to invest a portion of his inheritance, maybe $200,000, to see if he had the aptitude to maybe be the next Bob Dancer.

I asked him how many of the Winner’s Guides he had closely studied. He told me he had purchased a set but had yet to open them up. I asked him how much time he had spent with a computer program such as Video Poker for Winners. He told me he hadn’t purchased a copy of that yet but it was next on his list.

I told him he wasn’t ready for mentoring yet. In the next six months, I suggested he learn two games at the professional level — perhaps Jacks or Better and NSU Deuces Wild. Using the Winner’s Guides and the software, this wasn’t such a formidable task. But neither was it a trivial one.

Then, I wanted him to spend at least two weeks straight in Las Vegas or another casino city gambling 30 hours a week. At the end of that, if he still wanted me to mentor him, he knew how to get in touch with me. I would give him a test on the two games, and if he knew the games at a high level, we could revisit the mentoring idea.

Joe was in love with the idea of being a gambler, but he hadn’t had any actual experience. It’s hard work to get to the professional level at one game — let alone two. Playing 60 hours will turn out to be a boring experience for many people.

Video poker is a grind-it-out affair. It’s one thing to be fascinated by what appears to be a glamorous life. It’s another thing entirely to go through the process of getting good at some games and then successfully playing those games for 60 hours without going totally bonkers.

Can Joe do this?

I don’t know. If he can’t, he was never going to be a success at gambling anyway. If he can master two games and still be interested in being mentored after some real-life experience, then at least he will be going into this with his eyes wide open rather than looking through the rose-colored glasses he seems to be wearing today.

On one of our radio shows, Richard Munchkin told us that he periodically gets these kinds of requests from people wishing to learn blackjack. Richard tells them to learn basic strategy completely for four different games — i.e. with or without standing on soft 17 and with or without the ability to double after splitting. Once they know all four of these basic strategies, come back and see him again.

Richard tells me he’s never had somebody come back to him with these four strategies memorized.

I guess Richard’s experience influenced how I dealt with Joe. The task I gave Joe is more difficult than learning four basic strategies — each of which is more than 90% identical with the others. Jacks or Better and Deuces Wild are games very different from each other.

Still, if Joe passes this test, he’ll be a worthy student and I won’t mind at all working with him.

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Is it Wrong?

I’m glad my articles are now posted on the GamblingWithAnEdge.com website. That provides a forum and often people take the time to respond to what I’ve said — or to comment on other responses.

A while ago somebody posted there, “Is it wrong to see someone drop money and you don’t tell them?” I want to tackle that one today.

My answer today is probably different than it was twenty-four years ago. Twenty-four years ago, I was brand new to Las Vegas and had moved to town with $6,000 in cash. My car was in decent repair. I wasn’t broke — but I was one or two unfortunate incidents away from being broke. I was playing blackjack with a girlfriend-partner, and that $6,000 had to cover bankroll AND living expenses.

At that time, I would probably have kept my mouth shut, waited until the person who dropped the money had stepped away, picked up the money, and left the area. This exact scenario didn’t happen to me, but similar-enough situations occurred that I’m pretty sure that’s what I would have done. I REALLY was in survival mode. Not literally, but psychologically. Since I hadn’t caused the person to drop the money, I wouldn’t have felt I was stealing the money. I could have slept at night.

Today I’m in a different situation in life. When I see people drop something, I normally speak up — basically by reflex. It’s usually not money which is dropped, of course, but sometimes it is. Today, the pleasure I get from an “extra” $100 is usually less than the grief felt by the person who lost it.

Even when I was barely getting by, there would be situations where I would speak up. Such as:  If a mother was struggling with three young children and one of the kids caused her to drop some money — even if I was in a survival mode, I would have spoken up. Whatever her financial status, a mother with three young kids is having a difficult time and I wouldn’t want to make it any more difficult. Keeping the money would forever have me worrying about, “What if she was getting medicine for one of the kids and that was the only money she had?” Best to play it straight and not have those worries.

Picking up money that has been inadvertently left behind has lots of analogs in a casino. You see credits left on machines. You see multipliers left on Ultimate X machines. You see players leave “must hit by $500” machines when the meter is at $498. Sometimes you know who left these things and sometimes you don’t. Collecting credits left on the machine may be against the law in some jurisdictions (usually you won’t be caught), but often there’s no law telling you what you must do. Often, you’re free to make your own judgments and decisions.

Is there a moral difference to what my actions should be based on whether I was poor or I was rich? Probably not, but the world sure looks different depending on whether things are going your way or not.

I like living in a world where random acts of kindness are not all that unusual. And to have that world exist requires that I do my share. So, I do.

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Why Did You Print the Wrong Information?

I received an email from a player who told me that he found an error in Dream Card. I was definitely interested. If I verified that it was an error, I would send the information along to the folks at IGT (who manufacture the game), videopoker.com (who invented the game), and the player community. Whether IGT and videopoker.com chose to “fix” the problem in their next release would be up to them, but even if they did, older versions might still be out there and players should be warned about it.

Please note that this falls into the realm of “hearsay.” I didn’t see the error, and the man who told me about it said it happened to his son. There’s plenty of room in there for some misunderstanding to have taken place. Still, the situation is interesting on a couple of different levels which makes it worth talking about.

Curiously, I came away concluding that yes, there may have been an error with Dream Card in this situation, but it wasn’t the error I got the email about!

Here’s the situation. The player was playing 9/6 Jacks or Better Dream Card. Dream Card moves a 99.54% game to 99.56% — with a much bigger variance.

The dealt hand was A♠ K♠ Q♠ Q♦ DC, where DC indicates a Dream Card which is supposed to be the best possible card given the first four. The machine chose the T♠, giving the player a 4-card royal flush. The player wanted the Dream Card to be another queen, giving him 3-of-a-kind.

I told him that a 4-card royal was much superior to a 3-of-a-kind. I suggested he enter the hand A♠ K♠ Q♠ Q♦ T♠ on Video Poker for Winners and see that the 4-card royal is worth 92.34 coins. Then if he entered the hand A♠ K♠ Q♠ Q♦ Q♣, he would see the value of the trip queens is 21.51. If the reader hasn’t gone through the exercise of checking the value of combinations using VPW or other quality software, it’s an educational process to go through. It’s not difficult and it is eye-opening.

“So,” I asked, “why on earth would you prefer 3-of-a-kind to a 4-card royal flush? It’s not close!”

“Well, my son uses the Dancer-Daily strategy card and that card says 3-of-a-kind is better. If it isn’t better, why did you print the wrong information?”

Hmm, this could be embarrassing. I do have a good explanation for that but I can see where the confusion arose. The first two lines in both the Basic Strategy and the Advanced Strategy for that game are as follows:

 

RF5; SF5; 4-OF-A-KIND; FULL HOUSE; 3-OF-A-KIND; TWO PAIR

RF4 > FL5 and ST5 > any SF4

 

The top line of the strategy lists all hands in that game that are always held when dealt — with no exceptions. This list of hands is not the same for all games. There are games where from AAA44 or AA339 you just hold the aces, but Jacks or Better isn’t one of those games.

The second line lists those cases where a 4-card royal flush or a 4-card straight flush is in the same five cards as a dealt flush or a dealt straight. That is, from A♦ K♦ Q♦ J♦ T♣ you hold just the diamonds, but from Q♦ J♦ T♦ 9♦ 8♣ you hold all five cards.

A key underlying assumption for the strategy cards is that the combinations listed on the first line of the card are mutually exclusive with the combinations listed on the second line of the card. That is, you can’t have 3-of-a-kind and a 4-card royal in the same five cards. It takes at least seven cards to have both combinations.

I suppose technically you could argue the hand A♥ K♥ Q♥ J♥ T♥ is on the first line of the card, and any four cards from that combination are also on the second line of the card — hence the lines are not completely mutually exclusive.  But anyone who has trouble figuring how to play a dealt royal has no chance to understand my writings anyway.

If combinations are mutually exclusive, it doesn’t matter which order you list them in. Liam W. Daily and I recognized that using this underlying assumption allowed us to give completely accurate strategies with fewer rules. And we saw that as a good thing.

When you introduce the concept of Dream Card and you’re considering among alternative fifth cards, we can no longer hold with the assumption of mutual exclusivity while playing that version.

Simply put, the Dancer-Daily strategy card was designed for the “regular” version of Jacks or Better, not the Dream Card version. Since the machine almost always selects the correct Dream Card, you can continue to use the strategy card for the hands where Dream Card is not in effect.

With all that said, while the T♠ would be a much better choice than the Q♣ given the first four cards, the J♠ would be better still, simply because a jack presents three extra chances to end up with a high pair (namely the other three jacks) and a ten gives you no such chances.

Possibly the machine actually gave the correct card and there was a mix-up in the way the situation was presented to me. I assume IGT and videopoker.com can check on that easily enough. But whether there was or wasn’t an error, a discussion on an underlying assumption of the strategy card made this a conversation worth having.

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Twenty-First Annual Blackjack Ball

Recently, at some mysterious location in greater Las Vegas, almost 100 of the world’s best blackjack players and other gaming professionals, along with dates for some of the guests, met for the Twenty-First Annual Blackjack Ball. I’m always grateful that host Max Rubin allows one video poker pro to attend, and this year Bonnie was allowed to be there as well.

In addition to being invited and accepting the invitation early enough to get one of the coveted seats, guests are required to bring one bottle of premium champagne — preferably comped. This year getting two comped bottles wasn’t possible for me, so I went to Lee’s Discount Liquor Store and forked over $340 for two bottles of Dom. More than I usually spend for an evening out, but I was NOT going to miss the ball, especially the 21st.

There is pretty tight security surrounding the event — both because there is a significant amount of money in the pockets of the attendees, but also because there are only so many seats. If extra people get admitted, somebody is going to have to stand up. Some guy named Phil Ivey and his date crashed the party. Seems this guy plays a little poker. These gate-crashers were allowed to stay and, in fact, found seats right up front.

Guest speaker was Professor Edward O. Thorp, whose seminal Beat the Dealer was the book that allowed the career of “blackjack professional” to exist and whose equally seminal Beat the Market basically created the profession of Wall Street quants. Each gambling professional at the ball received an autographed copy of A Man for All Markets, Thorp’s newly released autobiography. Professor Thorp referred to himself as a pebble thrown into a lake, whose ripples became a tidal wave. A video of Dr. Thorp’s speech was posted by Richard Munchkin on January 31 at gamblingwithanedge.com.

There was a musical duet by Megan Riordan, who happens to be Max Rubin’s daughter and starred in the Dublin production of Once: The Musical and Blackjack Hall of Fame member Darryl Purpose. I wasn’t familiar with the haunting and lovely Academy Award winning song, “Falling Slowly,” but Bonnie and I had worn dance shoes “in case” such a moment occurred. We had scoped out the best nearby dance floor (off to the side so it wouldn’t interfere with the performance) and we danced our quiet two step while Megan and Darryl did their rendition. It added to our night without subtracting from anybody else’s.

One feature of the Blackjack Ball each year is the induction of a new member into the Blackjack Hall of Fame. This year’s winner, Don Johnson, arguably the most famous blackjack player in the world after his well-publicized $15 million win in Atlantic City, is both highly qualified and very popular. It could be argued that he stacked the ballot box, so to speak. Both this year and last, Johnson donated HUGE bottles of champagne to the ball for the winners. This year’s winner of the blackjack ball competition, who I will keep secret for a few more paragraphs (but you have heard of him), says the bottle was the Nebuchadnezzar size, containing 15 liters of the bubbly.

The ball is primarily about like-minded folks who don’t get to see each other that often, getting together and partying. They have a skills competition, preceded by an “impossible” test to get the final table number of contestants down to five. I call it impossible, but there is significant correlation between who ends up at the final table every year. This year Anthony Curtis made it there for something like the seventh time out of the 21 balls and two guys who were on the MIT Blackjack team (John Chang and Andy Bloch) also made it back to the final table. I made it to the final five one year — kind of like a Slumdog Millionaire situation where I just happened to know the questions asked that year. This year it took 12 correct answers out of 21 and I only got nine correct. That might sound close, but there were probably 40 others in the competition with nine, 10, or 11 correct. I was definitely an also ran.

Although I have been known to submit questions to Max for the ball, and I was really proud of my question this year, Max decided not to run it. There was one video poker question submitted by somebody else. I’m glad I got it correct because it would be embarrassing for me to miss the only video poker question. Let’s see how you’d do:

At the Casino Snoqualmie, you are playing Double Double Bonus and are dealt 9TJQA, all of the same suit. Choose your best play from these five choices:

  1. Hold all five cards for a flush
  2. Throw the A away and draw to an open-ended straight flush
  3. Throw the 9 away and draw to a royal flush
  4. Throw all five cards away
  5. It doesn’t matter what you do. Your EV is the same whatever play you make.

I’m pretty sure all of my readers know the right play in Nevada would be “c.” Going for the royal is much the better play when the game is dealt fairly. But if you know that Snoqualmie is in the State of Washington and games there are rigged by the state, you have a chance to come up with the correct answer of “e.”

One of the rules of the quiz was that you had to take it in ink and if there were any double answers, blanks, or scratch-outs, you were automatically disqualified. I was grading the test sheet of someone whom I didn’t know before the ball, a young man who calls himself Loco. He got 12 correct, which would put him at the final table, but there was a scratch-out. The scratch-out, however, was at least contributed to by Max misreading the question.

Max had a question regarding who said, “Sentence first — verdict afterwards.” Was it Joseph Stalin, the Queen of Hearts, or Attorney General nominee Jeffrey Sessions in his confirmation hearing? Unfortunately, Max said Robert Sessions, not Jeffrey Sessions. Loco, who guessed it was Sessions (as did I — we were both wrong because the correct answer comes from Lewis Carroll’s Alice in Wonderland) wrote down “Robert Sessions” and then crossed out the “Robert” when Max corrected the question.

There was no debate that Loco missed that question — but should he be disqualified for Max’s unintentional misreading? Other than briefly meeting Loco an hour previously, I didn’t know him from Adam and had not bet on any player winning. Still, I thought that applying the “no scratch out” rule in this case wasn’t fair and took it up front for Max and his assistants to make an official ruling. It was decided to not penalize Loco for this scratch out and he was in the final five, along with the three players I’ve already named and a player named David Spence. I had seen David at an earlier ball but had never met him.

There were four questions at the final table, each question eliminating one player. The first player out doesn’t get any of the prize pool, but the approximately $14,400 pool is shared among the other four, as $7,200, $3,600, $2,160, and $1,440. That prize pool was generated by everybody anteing $20 at the door and then bidding on who they thought was going to win. My apologies to Munchkin, who has “owned” me for a couple of balls and has yet to receive any return on his investment.

The first and last questions were both, “How fast can you count cards accurately?” For the first test, each player was given a well-shuffled single deck and was asked what counting system he used. If he used the Hi-Lo system, the cards 2, 3, 4, 5, and 6 are considered low; cards 7, 8, and 9 are considered neutral; and T, J, Q, K, A are considered high. Some players used this, some didn’t, but whatever count you used had to be announced up front. Max then removed one card from each deck and set it face down on the felt in front of the deck.

Players were told to turn the deck over and start counting — slamming the deck down on the table when they were finished. When asked in order from slowest to fastest, the player needed to tell whether the card removed by Max was high, low, or neutral. First guy wrong was out. If everybody got it correct, the slowest guy was out. From fastest to slowest, the order of finish was John Chang, Anthony Curtis, David Spence, Andy Bloch, and Loco. All players correctly identified the missing card, so Loco was eliminated.

The second test was that you were given 10 seconds to estimate and write down the number of cards in a discard tray. Max put out 135 cards. Anthony estimated 136. David 131, and both Andy and John 124. They basically cut cards to see who stayed on, but with a twist for blackjack professionals. Max let them examine a well-shuffled single deck for about 15 seconds. Max then lightly riffled the cards once and let them use a cut card to cut to, hopefully, a high card. John cut to a deuce, effectively eliminating himself. Although Andy could have also cut a deuce, ending up in a tie which would require a re-cut, Andy cut to a ten and John was out.

The third test was to cut exactly 22 cards from the bottom of a single deck in less than ten seconds. Anthony missed by one, David by two, and Andy by three. So, Andy was eliminated and we were down to two players, David Spence and Anthony Curtis. Since I’ve already told you that you’ve heard of the winner, and David is not that well known to my readers, the actual winner won’t be a big surprise. But there was some drama still to unfold.

The last test was similar to the first, except this time it was a double deck and also, it only mattered what the faster counter said. That is, if the faster guy answered correctly, he was the 2017 Grosjean Cup for the World’s Best Blackjack Player winner. If he answered incorrectly, the slower guy was in.

I was standing at Max’s right shoulder throughout the competition — taking notes for this column and an upcoming radio show. As David and Anthony raced through the double decks, it appeared to be very close. As they slammed down their cards at the end signifying they were through, for me it was actually too close to call. Instant replay would have been useful! Max wasn’t sure either so he asked the crowd. The consensus was that David was first. Anthony didn’t dispute this, so it became official that David was the faster one.

Unfortunately for David, he miscounted. He said it was a neutral card removed (7, 8, or 9) and it turned out to be low. So, Anthony Curtis was our winner! I told Anthony that it didn’t affect whether he won or not, and he wasn’t required to answer, but did he think the removed card was high, low, or neutral?

Anthony had the confidence to announce that the removed card was low. We turned it over. We’ll tell you whether he was correct or not on the February 9, 2017 podcast of Gambling with an Edge, which will be all about the Blackjack Ball. Richard and I will be joined by Max, Anthony, and newest Blackjack Hall of Fame member Don Johnson. Should be fun!

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Which is More Believable?

I recently read the book Fluke by Joseph Mazur. This book looks at some improbably real “coincidences” and helps us understand the math behind what happened.

Like somebody who writes that she hit a royal flush on the first hand she played two days in a row and wants to know, “What are the odds on that?” Mazur correctly points out that there’s a huge difference between looking at how often that happens to someone anywhere and how likely it was to happen to Mary Smith on December 12 and 13 in 2015? Hugely different problems and Mazur does well to explain that.

If you’ve ever been amazed by that day in 2004 when you ran into somebody you hadn’t seen in 30 years — and you and he both just happened to be in a small café in Turkey at the same time — then this book will help you understand that it wasn’t as flukish as you thought.

One case Mazur covers, however, is Joan Ginther, who won the Texas lottery at least four times over 18 years. Although I accept that Mazur’s mathematical talents in this area are far beyond mine, this is a situation that, in my opinion, Mazur misanalyzes.

Mazur goes through the probability of anybody picking a winning lottery number — and he focuses on the type where you pick six numbers. He goes through the math of winning several times, the number of people playing, the number of lotteries there are in the United States, and concludes that it’s not that unrealistic to expect someone winning four or more times.

He also duly notes that the actual winner, Joan Ginther, has a Ph.D. in mathematics from Stanford University and possibly figured out some way to boost the odds in her favor. He mentions this and then ignores it.

I think Ginther’s background and intelligence are the crux of the matter.

Without precisely ranking Stanford among the elite universities of the world, I’m going to posit without proof that it’s on that list somewhere and that Ph.D.s in mathematics from that university typically have genius-level intelligence with a great facility at numbers.

Further, according to reports in several publications, Ginther’s wins weren’t on lottery tickets where you pick six numbers. Ginther’s wins were on scratchers, which is totally different animal. On a scratcher, some numbers on a grid are already exposed when you buy the ticket. It’s very possible that Ginther used this pre-printed information to decide which lottery tickets to buy. If so, the odds against her were significantly different than what they would be for someone who picked the cards blindly.

This type of advantage was discussed by Mohan Srivastava in https://www.wired.com/2011/01/ff_lottery/.  When Srivastava was a guest on our Gambling with an Edge radio show, he said he didn’t know the details of Ginther’s wins, but based on the analysis by a journalist named Peter Mucha, Srivastava speculated that Ginther used methods related to ticket distribution to win. (Listen here) If you like that podcast, Srivastava was on our show earlier (found here) where he went more into the basics of beating the lottery, but only mentioned the Joan Ginther case in passing.

Mathematicians (and video poker players, for that matter) tend to be better than average at “pattern recognition.” I can’t quantify this, but it does seem to lend more credence to the possibility that perhaps Ginther noticed and exploited certain patterns. Srivastava’s personal success was certainly based on this.

So, who’s right? Ginther isn’t talking, although she is said to live in Las Vegas and we’d love to have her on the show.  Let’s look at some assumptions and do a sort of Occam’s Razor analysis:

Mazur:  Pick 6 lotteries are played in a lot of places and have been for a long time. Getting four big wins could happen once by chance to anyone, and it just happened to be Joan Ginther.

Srivastava:  The lotteries Ginther won were not Pick 6, but had other characteristics. It’s possible to analyze those characteristics to gain an edge — if you’re smart enough and dedicated enough. A Ph.D. in mathematics from Stanford University is likely smart enough and dedicated enough to succeed. Although Ginther’s success had a luck element to it, assuming she was a skilled gambler makes a lot more sense than assuming she just got lucky.

In my opinion, Srivastava’s argument makes more sense. What do you believe?

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Not What I Thought I Knew

I enjoy reading. I read both fiction and non-fiction — on a wide variety of subjects. Periodically I look at “Best Books of xxxx” lists to see if anything looks interesting. One such list included the novel Mata Hari’s Last Dance by Michelle Moran.

I vaguely remembered learning decades ago that Mata Hari was a seductress and a spy in World War I — but I didn’t know anything else about her. So, I ordered a copy from the library, figuring that if I couldn’t get into it in a few chapters, I didn’t have to finish it.

Mata Hari, the stage name of a Dutch woman named Margaretha Zelle MacLeod, was a dancer who, beginning in 1905, didn’t mind baring herself at a time when others didn’t do that. She also took several lovers over the years. To keep the mystique going, she regularly fabricated tales — especially to the press. Any novelist trying to get to the truth — and trusting contemporary accounts — was going to have to make some educated guesses as to the actual facts. In the end, nobody can be sure what the whole truth is — simply because there will always be conflicting accounts.

By the time the war started, Mata Hari was nearing 40 years of age and her career was eclipsed by imitators who were younger and better dancers. She made some mistakes and the French believed (probably erroneously) that she was a German spy.  They executed her in late 1917. Whatever spying she did was amateurish at best. The novel presents her circumstances as tragic — although it was clear that she was unwittingly her own worst enemy at times.

Plus, since that’s the only book I’ve read about Mata Hari, most of my “knowledge” comes from that particular book and that author’s point of view. I’m assuming the book was fairly accurate (as historical fiction goes), but I don’t have a depth of knowledge to know for sure.

Although I enjoyed the novel and reading about an era I didn’t know much about, let’s bring this discussion to gambling.

Many video poker players only “know” either what they’ve heard from somebody else or they “know” things about which they’ve made some semi-educated guesses and stuck with. While it may be intuitively “obvious” to some that from K♠ K♥ 7♣ 7♦ 3♠ you hold the kings and not two pair, that play is usually incorrect. From K♥ T♥ 3♥ 7♣ 4♦, it may seem trivial that the best play is to hold exactly two cards (and it is sometimes), but there are games where holding no cards is better, other games where holding one card is the best, and still others where three cards is superior number to hold.

I am somebody who accepts that for most players most of the time, choosing the play with maximum expected value is the way to go. Virtually all long-term successful players use these strategies. There are theoreticians who devise special strategies which have different goals than max-EV, but I’ve never used such a strategy and do not intend to.

How do you figure out what the best max-EV strategy is? Simple. Use a computer program that provides you that information instantly. I sell such a program (Video Poker for Winners) but there are others on the market as well.

The computer program will tell you how to play one hand at a time. That’s fine, but there are 2.6 million different hands — or slightly more than 130,000 if you treat all suits as being equal. That is, if you consider 7♣ 7♦ A♦ 9♦ 4♦ to be “essentially identical” to 7♥ 7♠ A♠ 9♠ 4♠, then you’ve cut the possible number of hands to learn by a factor of about 20. Surprisingly to most novices, 7♥ 7♠ A♠ 9♠ 3♠ is considered to be a totally separate hand than the previous ones.

Exactly how to simplify these things into a usable strategy is a discussion we’ll leave for another day. Modern software products do this for you — some better than others. Various authors have done the heavy lifting for you and present usable strategies — and again, some better than others.

I teach classes for those who prefer to learn by listening rather than figuring things out by themselves. (Author’s note: The next semester of free video poker classes at the South Point will begin at noon Wednesday, January 25, at the South Point in the Silverado Lounge. See bobdancer.com for the complete class schedule.)

Back to the question of “how do I know this is the right way to go?” Short answer is: (drum roll please) I don’t!

I do, however, believe I’m going about this the right way. And I’m betting many tens of millions of dollars a year on this belief. So, the question is:  Why am I so confident?

  1. I’ve been doing this for more than 20 years with a great deal of success. That isn’t a guarantee that I’m right. Luck plays a part in all results. Still, long term success tends to build your confidence.
  2. A lot of really smart players do it the same way. Bob Nersesian regularly says that the smartest people he knows are professional gamblers. I agree. And most smart, successful video poker players I know are using techniques similar to those I use.
  3. I have many contacts among casino executives, game manufacturers, gaming lawyers, game designers, mathematicians, and whole bunches of successful gamblers in other disciplines. I’m a sponge for new knowledge. I’m always tweaking what I do. You don’t get good in a vacuum. The more you talk to people in other somewhat related disciplines, the better you understand how things work.
  4. Other smart gamblers accept me as an expert in video poker. If I was way off base, someone knowledgeable would have probably said why. And I probably would have listened. I do read authors I disagree with. I can often gain something from what they say. Nobody has a monopoly on intelligent strategy and it pays to keep an open mind.
  5. Going through the process of putting your thoughts into words and letting any and everybody challenge them has a way of making you a lot sharper. People do find errors in my writing sometimes. I am far more grateful that I get to learn something new than I am embarrassed at being found imperfect. I accepted decades ago that I can’t walk on water.
  6. I’ve been reading and studying gaming strategies for many decades. Bright people tend to get good at what they spend their time doing.

Put this all together and I’m confident in what I say about video poker. I am far less confident in what really happened to Mata Hari, although I know more about her situation than I did a month ago. I likely won’t read another biography of her ever — but who knows? While I enjoyed the novel, becoming a history-professor type of expert on her is not in my plans.