Poker and Philosophy
Page 11
Players with acute loss aversion also tend to buy into the popular poker myth that “you should quit while you’re ahead.” Why should you? If you’re ahead, it’s because you’re either lucky or good. If you’re lucky, there’s no reason to think your luck’s “bound to change” (see our discussion of the gambler’s fallacy below). And if you’re good, chances are you’ll win some more. So if the poker’s good, you’re feeling sharp, and there’s still beer in the fridge, feed the pot ’til you drop.
Superstitious Thinking
I don’t believe in superstitions. They’re bad luck.
—BOBBY VALENTINE
“Hey Joe, let’s go to the casino tonight.” “No way, can’t do it.” “Why not?” “It’s Friday the Thirteenth, too much bad karma.” Let’s hope this dialogue isn’t a reflection of how you decide when or how to play poker. Superstitious thinking is commonplace in our society. It cuts across all types of behavior. Hall of Fame baseball player Wade Boggs was widely known to eat chicken before every game. Keep in mind his career lasted eighteen years and approximately 2,400 games. That’s a lot of chicken. Baseball players are renowned for their superstitious behaviors. One baseball player was known to wear the same jockstrap for four years in a row because he thought it brought him good luck.11 You also may be familiar with stories of professional athletes who must have a certain jersey number to play, or with craps players who must blow on the dice before the roll, or supervisors who must wear their “lucky” tie before giving any big presentation at work. From the time we’re kids we’re bombarded with old wives’ tales and superstitions that get passed on from generation to generation. Step on a crack and you’ll break your mother’s back. Break a mirror and you’ll have seven years of bad luck. This is the Cubs’ year.
Superstitious thinking occurs when a person forms an irrational belief resulting from ignorance, fear, or belief in magical causes. “I can’t believe I was the big winner at cards last night. I never beat these guys. It must be this lucky shirt I was wearing. From now on I’m always going to wear it when I play cards.” Games in which chance can play a significant role, like poker, tend to produce more superstitious thinking than other challenges that are based primarily on one’s skills and motivation, such as driving a car or trying to open a beer bottle without showing your cards. Gamblers in general are known for various types of superstitions, such as lucky numbers or wearing a certain article of clothing. The seasoned poker player understands the role that luck can play in poker rather than looking for causes of good or bad fortune.
Doyle Brunson tells a funny story that illustrates the dangers of superstitious thinking. He describes a young poker player from Canada named Alexander who came to Vegas with $200,000. He got upset when anyone called him “Alex” because he thought it brought him bad luck. He wore a shirt that “had pockets everywhere: little pockets, giant pockets, pockets made out of felt and pockets made out of paper!” (Brunson, p. 66). Every time he saw a poker hand he liked (whether it was his or another player at the table) he would rip off a pocket. He believed that if he ripped off a pocket, those hands would come back to him sooner or later. Not surprisingly, he left Vegas a lot poorer than he came. So please, next time you play poker, leave your lucky underwear (or jock strap) at home, and play smart.
The Gambler’s Fallacy
A single death is a tragedy; a million deaths is a statistic.
—JOSEF STALIN
Let’s say you take a quarter out of your pocket and flip it. It comes up heads. You flip it three more times, and each time it comes up heads. Before you flip it a fifth time you ask your friend to predict the next flip. What do you think he’ll say? What would you say? Most people will predict tails. When you ask people why tails, the typical response is that tails is “due” to come up. “After four heads in a row, the odds are way in favor of a tails coming up.” This answer is an example of the gambler’s fallacy. People incorrectly believe that the odds change because of the previous events. In flipping a coin, previous flips have no effect on the next flip. The odds remain at 50-50 (assuming the coin is fair). Gamblers too often allow prior independent events to affect their betting on future events, which is why this cognitive error was named the gambler’s fallacy.
The gambler’s fallacy extends to other arenas as well. For example, in basketball imagine a player who is a career seventy-percent free throw shooter and has gone 5 for 5 from the line so far. He goes to the line again. You might hear the TV commentator say he is due to miss this one, which implies that he is more likely to miss his next free throw rather than make it. Wrong! The odds say he will probably make it (seventy percent chance he will make the shot). Another example of this error occurs in baseball, particularly when a batter is struggling in a game. A .300 hitter who is 0 for 4 for the day comes to the plate in the ninth inning. You may hear people say that the manager shouldn’t pinch-hit for him because he is due for a hit. In reality, the odds of him getting a hit haven’t changed because of his 0 for 4 performance so far.
In terms of poker, if you’re holding a pair after the flop, what are your odds of getting three of a kind on the turn or the river? Experienced poker players may know that the answer is below ten percent. Knowing this statistic should be helpful in playing this game. However, knowing this percentage can also lead to committing the gambler’s fallacy. You’ve been playing all night with your buddies. For the last several hands you’ve been dealt a pair but so far you haven’t been able to land trips after the flop. On the next deal you get a pair of 10’s. You decide that you are long overdue for the trips, so before the turn you bet high. You have just committed the gambler’s fallacy and most likely you won’t get the third 10 that you are desperately hoping for. In playing poker knowing the odds of various poker hands can be a strategic advantage over your opponents. However, if you believe these odds change over the course of the night, then you’re setting yourself up for disappointment.
Even brilliant poker players can sometimes commit the gambler’s fallacy. In his generally excellent Winner’s Guide to Texas Hold’em Poker,12 Ken Warren suggests that there are alternations of bad luck and good luck. When you have a streak of good luck, which Warren calls “a rush,” you should become more aggressive until you lose a few hands in a row, when you know your rush is over, and you go back to your normal style of play.
Just in case we might have misinterpreted what Ken was saying, a page later he writes that there are periods when low cards win:
Cards can and do run in cycles. The theory of large numbers says so. If you experience a period when it seems like nothing but the low cards are winning the pots, then it is a perfectly legitimate strategy to start playing low cards.
Now it’s perfectly correct that probability theory says there will be bunching: wins and losses, wins with low cards and wins with high cards, will not be evenly spaced. But the theory does not say that the streaks or bunches will be of equal or predictable length. In short, if you’ve had more than your fair share of good hands in the last half-hour, your chances of having a good hand on the next deal are precisely what they would have been if you had experienced more than your fair share of lousy hands in the last half-hour. And your chances of seeing low cards win the next hand, following a spate of low-card wins, are precisely what they would be following a spate of high-card wins. Or put another way, if you (a) continue to play now, or (b) go to bed, and resume playing a week from tonight, your chances of maintaining a winning streak, or a losing streak, or of witnessing a continued succession of low-card wins, are precisely the same. (We’re talking here, of course, only about the aspect of pure chance as it applies to the way the cards come, not about possible changes in playing conditions or in how well you play.)
Better Poker through Better Psychology
Turn your eyes inward, look into your own depths, learn first to know yourself!
—VIENNA SIGGY FREUD
Good poker players know odds, strategy, and how to read faces. Great players know,
in addition, that they are human, and thus subject to all the frailties to which human flesh is heir. Among these frailties is the tendency to fall prey to the seven critical thinking errors discussed in this chapter. As research has shown, these errors are both pervasive and deeply rooted in basic human emotions, drives, and cognitive biases. Smart poker players need to understand and avoid these errors. And please, no wine coolers.
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1 Thomas Gilovich, How We Know What Isn’t So: The Fallibility of Human Reason in Everyday Life (New York: Free Press, 1991), p. 77.
2 Scott Plous, The Psychology of Judgment and Decision Making (New York: McGraw-Hill, 1993), p. 134.
3 Not us of course. To steal a line from Milton Berle, we’d gladly admit our faults if we had any.
4 Richard D. Harroch and Lou Krieger, Poker for Dummies (Forest City: IDG Books Worldwide, 2000), p. 30.
5 Doyle Brunson, Poker Wisdom of a Champion (Cooper Station: Cardoza Publishing, 2003), pp. 90–91.
6 Unless of course you’re reading this in bookstore and have no intention of buying it. In that case, use a No. 3 pencil.
7 For good discussions, see Plous, The Psychology of Judgment and Decision Making, pp. 174–188; David A. Levy, Tools of Critical Thinking: Metathoughts for Psychology (Needham Heights: Allyn and Bacon, 1997), pp. 83–89.
8 Plous, Psychology of Judgment and Decision Theory, p. 85. The expected value is obtained by multiplying the probability of each possible outcome against the payoff if that outcome were to occur. As our colleague Dan (“The Man”) Ghezzi, reminds us, however, Alternative A would be a rational choice for people who absolutely, positively need the million bucks (for example, someone who owes large gambling debts to a dude whose middle name is “The Fish”). Buttoned-down academics who study these sorts of things tend to overlook exceptions of this sort.
9 (Las Vegas: Creel, 2000), p. 19.
10 Taking care, however, not to play overly predictably.
11 Amanda Shank, “Superstitious Players Tend to Wear Same Undergarments for Long, Long Time,” USA Today (27th April, 2005). But inquiring minds want to know: Was he also lucky with the ladies?
12 New York: Cardoza, 2000 [1996], pp. 85–87.
8
Probability as a Guide to Poker
DON FALLIS
The goal of poker is to make money. In order to achieve this goal, you need to make plays that have the highest possible mathematical expectation.1 The mathematical expectation of a play is the average amount of money that you would expect to win if you made this same play over and over again. Even if you consistently make plays that have the highest possible mathematical expectation, it’s still possible for you to suffer a bad beat in any given situation. For example, the one card in the deck that can crack your Aces full of Kings might come on the river.2 But you can expect to make money in the long run.3
Imagine that you’re playing No-Limit Texas Hold’em at the final table of a World Poker Tour (WPT) event. Four players folded their hands before the flop. You are holding Big Slick (AK). The flop and turn are rags (no high cards and no flush or straight possibilities). There is one card left to come. Your one remaining opponent has now bet $20,000 into a $140,000 pot (so that there is now $160,000 in the pot). What to do?
There are several different plays that you can make. You can fold, you can call, or you can raise (and choose how much to raise). From all of these various possibilities, you want to identify the play with the highest possible mathematical expectation.
It should be noted that there are actually at least three reasons why you might not want to make the play with the highest possible mathematical expectation in some circumstances. First, you will sometimes want to be especially cautious. (You are short-stacked and you want to give some other player a chance to be eliminated from the tournament. In fact, it may even be correct to fold A’s before the flop in this case.4) Second, you will sometimes want to take extra risks. (You’re only going to be satisfied with winning the tournament and you want to build your chip stack quickly. In fact, this is the explicit strategy of a number of top players, such as two-time WPT Champion, Erick Lindgren.5) Third, you will sometimes just want to be “intentionally inconsistent” to keep your opponents from getting a read on you (Sklansky, p. 222). (This is arguably the secret of three-time WPT Champion, Gus Hansen’s success.6) But let’s ignore these complications here.
Raising is often the best play. But for the sake of simplicity, let’s focus on whether calling or folding has a higher mathematical expectation in this example. If you call the $20,000 bet, you are getting eight-to-one odds on your money. As a result, if the probability of your ending up with the winning hand is greater than a threshold of 11.1 percent, calling the bet has a higher mathematical expectation than folding.7 However, if the probability is less than 11.1 percent, folding has a higher mathematical expectation. Thus, what you should do comes down to what the probability is that you will end up with the winning hand when the river card is dealt.
There are a couple of things to be noted here. First, since there will be one more round of betting after the river card is dealt (at least if no one is already all-in), you should also take into account the money that you might make by betting on the river if you improve your hand. In other words, the implied pot odds (which we won’t discuss here) rather than the actual pot odds should be used to calculate the mathematical expectation of the various plays (Sklansky, pp. 47–48). Second, making plays that have the highest possible mathematical expectation does not just mean betting or raising when you have the nuts. As this example indicates, it sometimes means calling even when it is very unlikely that you will end up with the winning hand. You are probably going to lose the hand, but you are still getting the best of it.
Probability as a Guide to Life
It is often said that poker is a game of skill. But it is also a game of chance. After all, as Phil Hellmuth famously quipped, “I guess if luck weren’t involved, I’d win every hand.” But a big part of the skill is knowing what these chances (or probabilities) are.
The same applies to life in general. As Bishop Butler once said, “probability is the very guide of life.”8 In other words, what we should do typically depends on how likely certain things are to happen. For example, whether you should invest in stocks or in bonds depends on how likely it is that the market will go up. Also, whether you should major in business depends (at least partly) on how likely it is that you will get a good job. Drawing on work in philosophy, we will see that probability can be a useful guide to poker as well as life.
As with most things, the devil is in the details, and so a number of philosophers have tried to say exactly how probability should guide one’s life.9 The most famous proposal comes from Princeton University philosopher, David Lewis. Lewis (1941–2001) was one of the most influential philosophers of the late twentieth century, publishing in almost every area of philosophy. In probability theory, he proposed his famous “Principal Principle,”10 which essentially says that we should calculate mathematical expectations using objective chances. For example, you should call the $20,000 bet rather than fold if the objective chance that you will end up with the winning hand is greater than 11.1 percent.
Recently, the British philosophers Helen Beebee and David Papineau have criticized Lewis’s proposal. They point out that it is only correct to use objective chances to calculate mathematical expectations if we know what the objective chances are. And, since we don’t always know what the objective chances are, this is a serious limitation. Their alternative proposal is that we should calculate mathematical expectations using what they call relative probabilities. The relative probability of an outcome (such as ending up with the winning hand) is the “objective probability of that outcome relative to the features of the situation which the agent knows about” (Beebee and Papineau, p. 218). Beebee and Papineau argue that it is always correct to use relative probabilities.
Of course, it’s not just philosophers who have vi
ews about how probability should guide one’s life. Poker experts (most notably, David Sklansky) also have views on this topic. Let’s use my hold’em example to discuss four main proposals for how probability should guide one’s life at the poker table. As we will see, the proposals of the poker experts have the same sort of limitation as Lewis’s proposal.
Objective Chances
Philosophers are interested in whether the universe is stochastic or deterministic. (In other words, does God play dice with the universe?) In a deterministic universe, every event is completely determined by a) the current positions of all the particles in the universe and b) all the laws of physics. In particular, whether you will end up with the winning hand is completely determined. You will definitely end up with the winning hand or there is absolutely no chance. In other words, the objective probability of your ending up with the winning hand is either 100 percent or zero percent. (By contrast, the subjective probability that you assign to your hand winning will probably be somewhere in between.)
In a stochastic universe, however, there are true chance events. For example, even if we knew the current positions of all the particles and all the laws of physics, we still could not predict whether a particular uranium atom would decay in the next five minutes. But even if the universe is stochastic, the last card left to come in a game of hold’em is not a true chance event. Your cards, your opponent’s cards, and four of the community cards have already been dealt. The river card is already sitting there in the deck (right under the burn card). It is either going to give you the winning hand (if it’s the A, say) or it is not (if it’s the 9, say). Thus, the objective probability of your ending up with the winning hand is still either 100 percent or zero.