Author: Bob Dancer

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A Silly Mistake

This silly mistake happened in July while playing at the M Resort. It has been more than 10 years since I have made a similar mistake — – and I’m fortunate that this mistake was relatively small — – but let me tell you what happened and what I did about it.

I had some free play to pick up — – $130 — – and I was also playing through an additional $850 to earn a “free” lunch buffet. They have some $1 NSU machines and I was using those to pick this up.

I downloaded the $130 and played — – and ended up with $75 in credits, meaning this time I had lost $55 in the process of playing off my free play and earning the free buffet. Not a great result by any means, but that’s gambling and the daily score didn’t bother me at all. I recorded my result and went off to enjoy my lunch while reading a book that I had brought along.

Afterwards, I decided to cash out my $75 ticket between the buffet and the parking garage — and couldn’t find it. I searched my wallet and all possible pockets. I also thumbed through my book in case I had put the ticket there as a bookmark of sorts. Nothing.

I stopped by the machine “in case,” but nobody was playing the machine and the last ticket cashed out wasn’t for $75.

I was late to an appointment so I left the casino. I was going to be back the next day for a drawing, so I figured that I would then check with the slot department in case the ticket was turned in. It wasn’t likely, but I thought it wouldn’t hurt to check. Maybe a slot attendant saw the credits, cashed the ticket, and turned it in. Maybe the next person who sat down there was the sort of person who would turn it in. Who knew?

I don’t know how likely either one of these scenarios was, perhaps 10% – 20% total — – that’s a wild-assed guess — -but if I didn’t ask, there was probably no chance I’d see any part of that $75. And a 10% – 20% chance was better than no chance at all.

So, I got there the following day and asked to see Kevin. I don’t know his exact title — – he’s some sort of slot supervisor or maybe the slot shift boss — – but I’ve known him from playing there for three or four years. Our relationship is friendly and I don’t have a reputation there of being an angle-shooter. I figured he’d believe my story and would help me if he could.

He asked questions about what time of day it was and what machine. I told him and in about two minutes he found a record that showed much of what happened. The slot record he looked at (he didn’t let me see it) indeed showed I had played about 10 minutes with my card in and left without cashing out. The record he was looking at didn’t show the number of credits I had left behind and this wasn’t a big enough deal to warrant him pulling up the surveillance tapes. Perhaps I could have made it that big of a deal — – were I really stressed about this and insistent — – but I saw this as a “bump in the road” and figured the “finders keepers” rule would apply. If I need a big favor down the road, I don’t want to have used it up on something this small.

Eight minutes after I left, according to the slot record, a woman whose name I didn’t recognize (whether Keven knew or not, he didn’t say) inserted her players’ card and some money, played eight minutes, and cashed out for $40.

There was nothing suspicious here to Kevin’s eye, and the fact that she inserted some money and played some masked whatever really happened — – at least according to this particular slot record. Kevin said he was sorry that he couldn’t help me.

I was glad he checked for me. I figured it was a longshot anyway and it was my own fault, so why get upset? I’m 70 years of age now — – and I suspect these things will happen a little more frequently as I get older. That’s the nature of getting older.

In spite of no “good” result, I’m glad I checked. I could have gotten lucky, and checking improved my chances even though I didn’t cash on those chances this time.

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I’m Glad I Didn’t Hit It — Revisited

The Undoing Project is a recent book by Michael Lewis (author of Moneyball, Liar’s Poker, and The Blind Side, among others). It follows the careers of two Israeli psychologists, Daniel Kahneman and Amos Tversky, as they break new ground and basically invent the field of Behavioral Economics. I’ve written about these guys before and one man they greatly inspired — Dan Ariely.

Today I want to talk about the Undoing Project itself and the psychology of regret. Had I understood these concepts better many years ago, I would have never written a particular article that I now intend to revise.

When somebody wants to “undo” something, they usually think about relatively easy ways it could be accomplished. For example, Andy is driving and reaches an intersection just at the point where it’s a very close call whether to speed up and go through the intersection when the signal is orange or slow to a stop and wait for the next green. Andy’s decision may be the same or different from yours, but all drivers have occasionally experienced this sort of thing.

Regardless of whether Andy sped up or slowed down, let’s assume that at the next intersection, his car was sideswiped by another car which caused considerable damage, although thankfully Andy came out okay.

If Andy wanted to think about how this could have been undone, his mind would naturally go back to the speed-up-or-slow-down decision he had just made and conclude that if he had done the opposite, he would never have been sideswiped. He would not, typically, think that if the other driver had been killed the week before in a drive by shooting, then Andy would have avoided the accident. People just don’t think that way — but frankly, either “solution” would have kept Andy’s car from being crumpled.

When I read about this, I thought back to an article I had written perhaps 20 years ago. Seems like I was playing $1 10-7 Double Bonus at the Orleans and a woman sitting nearby commented, “I’m glad I didn’t hit it.” She was playing only four coins and had been dealt A♠ K♠ Q♠ J♠ 7♦. She threw the 7 away and ended up with a worthless 6♥.

I commented that if she had hit the royal, it would have been worth $1,000 rather than the nothing she received. I thought she was basically an idiot for preferring $0 to $1,000.

The thing is, though, that if she had hit the royal, she would have felt terrible that she hadn’t been playing max coins at that time. She would have seen it as a $3,000 loss rather than a $1,000 gain. The pain of losing $3,000 (even though it’s all in her mind) was bigger than the pleasure of actually winning $1,000.

Since I had studied economics before Kahneman and Tversky came along, I “knew” that having $1,000 was better than having $0. There was just no other way to look at it insofar as I was concerned. This woman was being very foolish.

Now, I realize that this woman isn’t alone in her thought processes. When she wished to “undo” the results of a “mere” $1,000 jackpot, she normally would think that, “I should have been playing five coins.” She “knew better” and now was being punished for only playing four coins. The pain she would feel would be very real to her.

I, of course, would have recommended she play one coin or five — depending on bankroll considerations, but never four. Still, that ship had sailed and she bet four coins. Although I still feel betting four coins per hand was foolish, I have more empathy for her “I’m glad I didn’t hit it” statement.

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How Often Do Things Happen?

Today’s paper is on simple video poker mathematics. Let’s assume you are playing a game where, on average, you hit a quad (i.e., a 4-of-a-kind) every 400 hands. Further, let’s assume you play for a total of 1,200 hands. I’ll arbitrarily say that it takes you two hours to complete the 1,200 hands. How many quads can you expect to end up with over that number of hands?

It appears obvious that the answer should be three, but this is the wrong answer. To get the correct answer, we need to look at the binomial distribution, the results of which appear here:

 

0 5%
1 15%
2 22%
3 22%
4 17%
5 10%
6 5%
7 2%
8 or more 1%

 

What this says is that 5% of the time you won’t hit any quad; 17% of the time you’ll hit four; 2% of the time you’ll hit seven; etc. These numbers don’t tell you WHICH quad you’ll hit. Just how many.

These numbers are accurate, but not really precise. For example, the chance to get exactly three quads could more precisely be written as 22.4322%, but that is far more precision than we need for today’s discussion. It looks like they only add up to 99%, but that’s rounding error and also not important for today.

One of the interesting features of this distribution is that the number of quads that we think we “should” get, namely three, actually occurs less than one time in four. Another typical feature of the distribution is that the probability of getting one fewer quad than typical is virtually the same — actually 22.4135%, which is slightly less.

We could, I suppose, refer to getting either zero or one quad as “bad luck”, getting two, three, or four as “typical luck”, and getting five or more as “good luck”. It doesn’t change anything by assigning terms dealing with luck to the results. When somebody asks me, “How much skill and how much luck was involved?” in describing whatever happened yesterday, my answer is often, “I have no idea.”

Let’s assume that on this particular day in question, we don’t hit any 4-of-a-kind. Definitely worse-than-average luck, but it happens about one day in twenty. Slightly rare, but not extraordinarily so. Now the question is, since you’ve just gone through worse-than-average luck, what will be the distribution of quads for your two-hour session tomorrow? For this, the following distribution will hold:

0 5%
1 15%
2 22%
3 22%
4 17%
5 10%
6 5%
7 2%
8 or more 1%

 

The distribution, of course, is the same as first given. Just because we had a bad day says absolutely nothing about what our score will be the next day. There is no tendency to either, “Once you start running bad you keep running bad because you’re an unlucky player,” or “You’ll get more quads the next day to make up for the shortfall.”

Let’s assume we change machines halfway through. Now the distribution of the quads expected over the 1,200 hands is:

0 5%
1 15%
2 22%
3 22%
4 17%
5 10%
6 5%
7 2%
8 or more 1%

 

Is this distribution beginning to look familiar? It should. Changing machines has nothing to do with changing the distribution.

In this discussion so far, we’ve said nothing about skill. We are assuming players are playing perfectly. If players play imperfectly, the distribution will change. For example, on a hand like K♥ K♠ 4♦ 4♣ 5♦, it is correct in almost every game to hold KK44, although many seat-of-the-pants players playing games where two pair only return even money incorrectly hold just the pair of kings. Making this kind of mistake systematically will IMPROVE your chances for hitting quads, but COST you overall. The increased number of quads you get by holding only one pair rarely compensates for the reduced number of full houses.

The numbers are for three “cycles.” If full houses normally come around every 90 hands on average, the numbers above apply to how many full houses you hit in 270 hands. If royals come about every 40,000 hands, the numbers above apply to how many royals you hit in 120,000 hands. In games where the royal cycle is 45,000 hands, the numbers apply to how many royals you hit in 135,000 hands.

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Gardena Poker Clubs: A High-Stakes History by Max Votolato

I was raised in Gardena, California, which is about 15 miles south of downtown Los Angeles. We lived just north and west of Vermont and 135th Street. The nearest card clubs were five blocks south, at Vermont and 140th. I was born in 1947, and the clubs were “always there” when I was a kid.

Richard Munchkin and I were sent copies of the Gardena Poker Clubs book by the author, presumably hoping for an interview on our podcast. I read the book with interest, having already known a bit about the subject. Whether or not we eventually discuss the book on the podcast hasn’t been decided at this point. But the book is certainly worth discussing here.

For a significant period of time, Gardena had the only legal card games in greater Los Angeles. This book chronicles the rise of Gardena poker in the 1930s and the demise of the game beginning in the late 1980s because of bigger clubs being built relatively nearby. The newer clubs, The Bicycle Club and The Commerce Club among others, offered fancier premises, higher stakes, alcohol, and better security. Today, only two poker clubs remain in Gardena, both owned by Larry Flynt.

The decades of poker in Gardena were never without opposition. I remember as a boy in the 1950s being instructed in Sunday school on the evils of allowing poker clubs, and to make sure our parents voted against them in the next election. (Our home was two doors north of 135th Street, which was the boundary at that time for voting in the Gardena elections. Regardless of whether my folks were for or against the card clubs, they didn’t have a vote. I suspect they would have voted in favor, because the card clubs sold inexpensive food in their restaurants, so our family ate at them fairly frequently.)

Sometime after I turned 21, I tried my fortunes at the clubs — with no success. Although I had read every book in the libraries on how to succeed at poker, I was not a net winner. I learned early on that I couldn’t make it as a poker player. Players dealt the cards at these games, and there was probably cheating at the games I played, but I wasn’t savvy enough to detect it and/or protect myself against it.

The book traces the political battles for the clubs and the various compromises and deals made along the way.  The book represents a major piece of scholarship in running this all down.

One of the movers and shakers of Gardena poker was Ernie Primm — the same guy who would eventually build Whiskey Pete’s along the Nevada-California border. Ernie was born in 1901, and it was his son Gary who expanded on his father’s dream in what is now called Primm.

The latest political wars around Gardena poker surround Larry Flynt, publisher of Hustler magazine. The churches who were against poker in general on moral grounds were even more opposed when there was a pornographer in the discussion. But money talks in Gardena, so Flynt was able to prevail.

Today, there are more poker games in greater Los Angeles than anywhere else in the world. Gardena remains a part of it, but no longer the main part.

If you wish to know more about the history of poker clubs in Gardena, this is definitely the book for you.

Image result for Gardena Poker Clubs

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When You Get the Run Around

There was a small drawing at Hooters Casino in Las Vegas on a Friday night ten years ago, but it could have happened anywhere. I read the rules and they stated that you could earn tickets starting at 12:01 Friday morning up until 6 p.m. for the 7 p.m. drawing. It was a too-small-to-be-interesting drawing, but I already had dinner reservations with a friend at the casino. If we’re going to be there anyway, why not enter the drawing?

I arrived at the casino at about 1 a.m. and started playing a $5 machine that was attractive for more reasons than just the drawing. I played until around 3:30 a.m. and figured I had earned approximately 140 tickets, which meant I’d played around $42,000 through the machine. I wasn’t positive of the number, but it had to be pretty close.

I arrived at 5:45 for our 6:00 p.m. dinner date and went to the booth. I was given 25 tickets, implying I’d played $7,500. I knew this was wrong, so I asked to speak to the supervisor. “I AM the supervisor,” I was told.

I explained when I started and how much I’d played and I was assured that the computer system said 25 tickets. “Is your boss on property?” I asked. “Or the Director of Marketing? There is something wrong with the way you are calculating entries and I’d like to get it rectified before the drawing.”

“There’s nothing wrong with the way the system calculates entries,” I was told. She said the Marketing Director was in a meeting but that he’d come and find me in the restaurant if the meeting broke before 7 p.m.

“What about the slot director or the GM?” I asked. “Are either of them on property?” I was trying to be polite with my requests, but I was frustrated and becoming angry. I sincerely believed that I was in the right and I kept being told that I must be confused about when I played. She knew I was Bob Dancer and, hence, probably experienced at this sort of thing, but she was sticking by her position.

It happened that the slot director was walking by. We knew each other and I explained the situation. I asked him if the “official casino day” started at 3 a.m., and if so, perhaps most of my play showed up on the computer on the day before. But there should be a time-stamp on my play, and the rules clearly said you could start at 12:01 a.m.

The slot director confirmed that the casino day started at 3 a.m. and he took the club supervisor into the back room to look at the record. After about five minutes he came out and told me that I was correct and the booth would be giving me more tickets shortly. Somehow the slot club personnel were confused on the difference in “actual day” and “casino day.” In about three minutes, another slot club employee came out and handed me 134 tickets and told me I was mistaken when I asked for 140. That was fine. 140 was an estimate only and 134 was close enough — and certainly better than 25.

It didn’t have to end this way. It was possible that nobody knowledgeable would have shown up and I would have been out of luck. So, what do you do?

For me personally, making a huge scene was out of the question. My personal experience is that upper management tends to take the side of their underlings and if I make a big commotion it’s a convenient excuse to ask me not to play there anymore. Certain other players have no compunctions about loudly sticking up for their rights when they feel they’ve been wronged. But while I wasn’t going to make a big scene, I WAS willing to persistently keep asking to speak to any higher-level employee who would take the time to look at the computer screen.

I could have threatened to “take it to Gaming,” I suppose, but this would end up being way too much effort for way too little gain. I was about to ask to see the computer screen myself figuring that I would be more adept at understanding what was there than the boothlings were. It didn’t go that far and I don’t know if I would have been allowed to do this or not.

Generally speaking, the proper strategy is to not give up when you think you are right. There comes a time when going forward is clearly fruitless, and then you have to decide whether to pursue remedies after the fact. Had I not been able to reach a satisfactory solution before the drawing took place, many casinos would have “taken care of me” after the fact should they finally agree that their boothlings were in error. If I won the drawing anyway there would be no extra compensation, but if I came in second or third, a case could be made that I would probably have done better with an additional 100+ tickets so they might offer me some extra money. They won’t do this, however, unless you are persistent about it.

Players who take a “it’s the principle of the thing and I’ll take it all the way to the Supreme Court!” attitude are being very short-sighted, in my opinion. It’s a long war you’re fighting, not a single battle. I had maybe $200 in EV in this drawing when given the appropriate number of tickets. Losing out on this much EV would be a relatively minor bump in the road. Losing my welcome at this casino (and maybe others because some of these employees will eventually work elsewhere and may well remember if you treated them like dirt way back when) would be much costlier than $200.

Although most promotions have a “management reserves all rights” statement in there, most casinos will try to do the right thing — if they can be persuaded that they were in the wrong.

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A Matter of Perspective

If you’re a computer programmer working on a video poker game, the hand A♠ Q♥ T♥ 8♠ 3♥ is equivalent to A♦ Q♣ T♣ 8♦ 3♣, but both of those are different from A♣ Q♥ T♥ 8♠ 3♥. Can you see why?

The ranks of the cards are the same and in all three hands QT3 is suited. In the first two hands, the ace and eight are suited with each other. In the third hand, the ace and eight are unsuited.

To 99% of all players, 99% of the time, that distinction is irrelevant. It could possibly be important, for example, in a Double Bonus game where there is a progressive on four aces. At reset, you hold QT on this hand. If the progressive on four aces is high enough, you just hold the ace. How high the progressive has to be will be different if there are 12 cards still in the pack unsuited with the ace than if there are “only” 11.

With that kind of thinking in mind, assuming you are playing 9/6 Jacks or Better, do you see any difference between A♦ Q♣ T♣ 8♦ 3♣ and A♠ Q♥ T♥ 7♠ 3♥?

For anyone who would hold just the ace on either of these hands, you’re a hopeless Jacks or Better player. Holding the ace can be correct in certain other games, but not Jacks or Better.

The Basic Strategy play on both hands is to hold the QT. It’s the second-best play in both cases, but AQ is better. The fact that AQ is better than QT in these two hands is because the 3 is suited with the QT. This is known as a flush penalty and is generally only of concern to advanced players. Many players have enough trouble just learning the basic plays without dwelling on the fine points. What makes the hands different is that in the first hand, the 5-coin dollar player is making a nickel mistake versus a 2-cent mistake in the second.

The difference in the size of the mistakes is due to the 8 interfering with the straight possibilities of QT and the 7 not doing so. Why is this important? Well, it’s not if you’re playing the game with a 4,000-coin royal.  But if you’re playing a progressive, holding QT is correct in the first hand when the royal is at 4,685 and above, while in the second hand, holding QT is correct at 4,365 and above.

So, for whom is this kind of analysis important? Frankly, only to a pretty small self-selected group. Some pros learn these things — many don’t. A few recreational players become competent in these distinctions — although it may never be cost-effective for them.

Some of us just plain like studying things. This has been one of my “secrets to success.” The more I know about how and why things work the way they do, the easier it is for me to learn and memorize strategies.

If you think my secret is worthless to you, that’s your right. But in general, the more people study these things, the better their results turn out to be. Whether it makes sense dollars-and-cents-wise if you put a value on your time is debatable. But if it gives you pleasure to gain insight into these games, why the heck not do it?

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Want to be a Co-Host on Gambling with an Edge?

There is a recent book from Huntington Press called Rock Vegas: Live Music Explodes in the Neon Desert, by Pat Christenson. It covers concerts in Las Vegas over the past 30 or so years.

 

It’s not about gambling, but it is about Vegas, many players here have attended and/or are interested in musical events, and Huntington Press has been a big supporter for our show. So we’re going to have an episode on GWAE about this book.

 

Richard Munchkin is not opposed to such an episode, but it’s outside of his interests and knowledge so he thinks it would be better if we found another co-host for that one show.

 

So, are you interested in co-hosting? You’d have to read the book (a free copy will be provided —autographed if you wish) and when we do the podcast you’ll need to join in the conversation. Possibly the podcast will be done in-studio in Las Vegas and possibly it will be via Skype.

 

It’s an unpaid gig, so if you’re thinking about doing this for the money, think again. We can use your real name or a pseudonym, your choice. The perfect candidate will have a familiarity with and an interest in live music concerts.

 

If you’re interested, please send an email to [email protected] and explain why you’d be a good choice. I’ll pick the best two or three and do 3-minute interviews over the telephone to make sure you can speak in a way that can be understood, and that’ll be it.

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Dealing with Anguish

I received the following email recently: “I have been playing a few years and consider myself a pretty good player. I consider myself Bob Dancer-trained and try to play accordingly. I have given up at least six royals going for the high pair. My question is how you overcome the mental anguish of missing the royal. It takes me days to get over it. I am retired, play 10 to 20 hours a week of 9/6 Jacks or Better or 8/5 Bonus Poker. Help me, please. Anguished in Ann Arbor.”

I did some calculation and my best guess is that this has happened to me between 600 and 700 times. But it’s a guess, because I have no recollection of it EVER happening. This guess is based on how many million hands I’ve actually played, on which types of games, and how many were on single line compared to Triple Play through Hundred Play.

We’re talking about a hand such as K♦ Q♦ J♦ 5♦ K♠, where the correct play depends on the game and pay schedule. If you’re playing Jacks or Better or Bonus Poker, like Mr. Anguished is prone to do, you hold the kings. If you’re playing Deuces Wild, you hold the suited KQJ. If you’re playing Double Bonus where flushes return 7 for 1, you hold all four diamonds.

If you hold the kings (whether it’s the correct play or not), once in 1,081 times the first two cards out will be A♦ T♦. Also, once in 1,081 times the first two cards out will be the 7♥ 3♣. As far as I am concerned, these two situations are equally relevant.

After I’ve held the kings and pressed the draw button, my “job” is over for this hand, and it’s time for me to start concentrating on the next hand. The best I can do is to play the hands perfectly. Going back and changing the past is not something I know how to do.

Although I prefer that I end up with four kings on this hand, I’m not too invested in that result. I know that I’ll get the 4-of-a-kind one time in 360 (more precisely three times in 1,081), full houses, 3-of-a-kinds, and two pair more frequently than that, but the hand will stay a single high pair more than seven times out of ten.

I have this type of draw numerous times every week. Sometimes I connect on the 4-of-a-kind and usually I don’t. Over the course of a year or two, it’ll average out pretty well, whether tonight is lucky or unlucky.

I suspect I’ve ended up with a 4-of-a-kind from this kind of position more tha 2000 times in my life. What this also means is that I’ve thrown away the royal more than 600 times from this same position. Drawing three cards to a high pair, you get any specific two cards (i.e. the cards that fill in the royal) one time out of 1,081 and you complete the 4-of-a-kind three times out of 1,081. Over the course of years, the numbers come out very close to this.

How many of this estimated 600 missed royals have I noticed? Exactly zero. Checking to see how the cards would play if I made an alternative, inferior, draw is a huge waste of time in my opinion. Doing this consistently would reduce my speed from 800 hands per hour to about 400. Why on earth would I want to waste that much time? Since I’m playing only when I have the advantage, this is slashing my dollars-per-hour win rate in half. It’s not only worthless information, but it’s expensive to gather. If you’re playing Fifty Play or Hundred Play, it could take several minutes at the end of each hand to work through all of this. Why bother?

Mr. Anguish seems to have the core belief that a missed royal is a tragic thing. He ignores the fact that trying for the royal every time (so that he can be assured of getting it when the cards are just right) would have cost him an extra 6,000 coins for every extra 4,000-coin royal received. He berates himself for not being clairvoyant enough to see the unforeseeable future.

The only reason Mr. Anguish takes the time to do this is to check whether he should feel really, really awful this time. One time in 1,081 he discovers that yes, indeed, feeling really, really awful this time is appropriate. The relief he feels the other 1,080 times is likely minimal.

To me, ignoring the specifics of a “what if” draw comes naturally. Perhaps Mr. Anguish is compelled to do this and can’t help himself. I don’t know. Offering useful advice on how you should deal with your compulsions is something I’m not good at. If this is something Mr. Anguish can learn NOT TO DO, I believe his life will work better.

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Does This Make Sense?

This is a column for “low intermediate” players and it involves 4-card inside straights in games where you get your money back for a pair of jacks or better, same payout for two pair, and 4-for-1 for straights. It also involves a paradox of sorts.

There are a lot of these games — Double Double Bonus, White Hot Aces, Triple Double Bonus, Triple Bonus Poker Plus, Super Aces Bonus, and others. What I’m talking about today does not work for games where you get double money for two pair (i.e. Jacks or Better or Bonus Poker), nor does it work for games where you receive 4-to-1 for straights (i.e. the best versions of Double Bonus.)

That last sentence should have caused many of you to do a double take. I said 4-to-1 rather than the more common 5-for-1. They are equivalent, but often players are a bit loose with their terminology. When a pay schedule lists numbers, the returns are always “for 1.”

Here’s the paradox:  Holding 4-card inside straights with no high cards (e.g. 4578 of mixed suits) is eligible to be held in these games.  (“Eligible” means better than throwing everything away. There may or not be higher paying options in the hand.) Assuming you’re playing dollar 9-6 Double Double Bonus, five coins at a time, holding this inside straight is worth $1.70. Holding 4-card inside straights with one high card (e.g. QT98 of mixed suits), worth $2.02 in the same game, is never held.

Both inside straight draws have four cards to fill them in. When there’s a high card involved, there are also three chances to pair up that high card. Of the 47 possible draws, three extra chances to get $5 (the payout in this game for a high pair), add 3 * $5 / 47 = 32¢, which is the difference between $2.02 and $1.70.

I call it a paradox because the greater of the two hands is never held and the lesser of the two hands is held sometimes (depending on the fifth card). So, what gives?

If you haven’t seen or heard this paradox before, I strongly urge you to see if you can figure it out for yourself before you read on. I’ll wait. No matter how many video poker paradoxes I write about, there are hundreds more that I will never get to. If you’re going to become a decent player, you’re going to have to learn to think for yourself.

The key to the paradox is using absolute values to deflect attention from relative values. The $1.70 and $2.02 numbers are absolute values — that is, what the position is worth on average if you play it out zillions of times.

What is important in video poker, however, are relative numbers. In the hand 4♠ 5♥ 7♣ 8♦ 2♠, we’ve already said the value of holding 4578 is $1.70. The important thing is that the value of throwing everything away is $1.62. Those are the best two choices, and the better of these two is to hold the 4-card inside straight.

From Q♥ T♥ 9♣ 8♦ 3♠, we’ve said the value of holding the 4-card inside straight is $2.02, but the value of holding the queen by itself is $2.12, and the value of holding the suited QT is $2.23. Relatively speaking, the value of $2.02 is less than the value of holding either the single high card or the high card with a suited ten.

Every time there is a 4-card inside straight with one high card, there is necessarily a high card by itself in the same hand — and sometimes a high card with a suited ten. So, we’re never going to hold this inside straight.

The fact that holding this inside straight is better than throwing everything away is interesting, perhaps, but irrelevant. We’re looking for the play with the highest EV, and throwing everything away isn’t going to qualify when there’s a high card in the hand.

Once you realize that we’re comparing one inside straight to throwing everything away, and the other inside straight to something else entirely, the paradox disappears.