Poker and Philosophy

by Bronson, Eric

  Begin by understanding that in game theory an optimal strategy is just the best possible strategy given that everyone else is playing optimal strategies too. Thus in principle the only stable outcome—the only situation in which no one improves his chances by changing strategy—is when everyone is simultaneously playing optimal strategies. (This is known as a “Nash equilibrium.”) Say, for the sake of argument, that in the case of poker this optimal strategy turned out to be some complicated function of your own cards, other players’ bets, and the overall chip situation. Call all the players following this strategy Poker Philosophers. But let’s suppose now that one obstinate player, let’s call him Stupidus, is not playing the prescribed optimal strategy. Suppose for instance that instead Stupidus insists on always initially raising the maximum, regardless of his cards, but then folding if he is ever called. I think we have all played against characters like Stupidus at one time or another.

  Notice two important points. First, it is unlikely that the optimal strategy played by the Poker Philosophers is any longer optimal once pitted against Stupidus. A much better play against Stupidus would be always to call him, thereby winning his maximum raises every time without a fight. Second, the Poker Philosophers might (depending on the exact parameters) actually be losing to Stupidus. For, most of the time, Poker Philosophers would fold meekly against Stupidus’s initial aggression, and when with good cards they finally did make a game of it then Stupidus would just drop out immediately rather than incur big losses. An optimal strategy is only optimal against other optimal strategies. In general, it cannot even guarantee winning, let alone winning optimally. So who is Stupidus now?

  A truly optimal strategy needs to recognize players such as Stupidus and adjust play accordingly. But given that there are literally an infinite number of possible strategies to sift through, this complicates the mathematical task enormously—a task, remember, that is already intractable. There would also now be the problem of just how you would recognize exactly which strategy an opponent is playing. For instance, it would take many rounds to get a sense of what Stupidus was up to. Technically, it seems unlikely the task could be completed for sure in a finite time. And this doesn’t even take into account the possibility of Stupidus varying his strategy through the game.

  So even granting the fantasy of discovering an optimal strategy for real-life versions of poker, we still remain a long way from knowing how to win in actual games against actual players. It seems therefore that in the end, game theory offers no real replacement for those grizzled rules of thumb and salty poker wisdoms after all. We’ll all just have to keep on thinking about the usual suspects: seating order relative to active and passive players, tells, poker probabilities, avoiding going on tilt, and so on. Ultimately, for better for worse, and indeed for richer for poorer, not even game theory science can furnish us with that can’t-lose strategy.

  What Has Philosophy Ever Done for Us?

  While poker may equip you nicely for introductory courses in philosophy of science or in metaphysics, unfortunately it seems philosophy cannot really return the favor. In particular, it cannot tell you how to win—I’m sorry about that. Maybe it can tell you why to beware of hucksters pitching miracle perfect systems. There’s no such thing as a single objectively perfect strategy that will win for everyone against anyone at any time. Maybe some strategies are more useful than others, but you should also make room too for individual variation and special circumstance. And don’t forget, there is no way anybody can guarantee the truth of the counterfactual that if you were to follow the perfect plan then you really would win. Perhaps in a way this is all good news really for it suggests that never will poker be reduced to a game for robots.

  ________

  1 A hypothetical omniscient creature to whom nothing would be uncertain is sometimes called “Laplace’s demon,” named for the French philosopher and mathematician Pierre Laplace who put forward this metaphor for determinism almost two hundred years ago. Not coincidentally, Laplace was also a pioneer of the subjective interpretation of probability.

  2 Even if we do not assume determinism, still there may be no room for free will. This point has been strongly argued by the American philosopher Daniel Dennett among others.

  3 Note though that it would not address the worries concerning counterfactuals and objective probabilities. Note also that many game theorists are of course aware of the further difficulties about to be pointed out in this section.

  4 Already in these games it proved optimal to bluff some of the time.

  10

  “I Should Have Known It!” Gilbert Ryle and Poker Knowledge

  KENNETH G. LUCEY

  You’re in a Texas Hold’em game with four A’s, and prior to the showdown you suspect that you’re on the losing end of a “bad beat,” making you the potential winner of fifty percent of this casino’s “bad beat” jackpot,1 that currently stands at $180,000. You’re holding pocket aces as your hole cards, and the board is A, 9, 8, with a 7 of diamonds on the turn, and an A on the river. The way the betting has gone you think you’re up against two flushes, and you hope against hope that only one of them is a straight flush, putting you on the losing end of the “bad beat.”

  As it turns out, your four A’s were worthless. Each of your two opponents has a straight flush. One is holding J-10, which makes him the winner. The other is holding 6-5, which makes him the “bad beat” loser, and thus the recipient of half the jackpot. At this casino the other players at the table share ten percent of the jackpot, so your consolation prize is $2,250, which is not much in relation to what you thought you were going to win, but it nevertheless puts you ahead for the day.

  Still, it’s understandable that you’re disappointed. You couldn’t possibly have assumed that you’d be up against two straight flushes. Or should you have known it? What can you claim to know in such a situation? Is it possible to have a kind of “poker knowledge” of the possibilities, of a sort that would have tempered your hopes in this case?

  To answer our questions about “poker knowledge,” we first need to talk about the various sorts of knowledge in general. The British philosopher Gilbert Ryle (1900–1976) emphasized the philosophical distinction between “knowing that” and “knowing how.” He writes, “Philosophers have not done justice to the distinction which is quite familiar to all of us between knowing that something is the case and knowing how to do something.”2 The former involves knowing the truth of some proposition where the latter involves a learned skill—like riding a bike or playing the piano.

  Poker knowledge involves both knowing how and knowing that. Any thoughtful poker player could benefit by being clear about Ryle’s distinction between knowing something is true, and then knowing how to follow through on it.

  Knowledge “That” and Knowledge “How”

  To begin with, any poker player must understand the fundamental concepts that constitute the game (in Ryle’s lingo, the “knowing that” something is true). In other words, one kind of poker knowledge simply consists of correctly understanding the vocabulary of poker: flop, board, turn, river, showdown, and so on. The next step is knowing the various hand rankings: high card, pair, two pair, three of a kind, straight, flush, four of a kind, straight flush, royal flush. In the jargon of the philosophers such knowledge is a priori knowledge in the sense that once the concepts have been acquired, the statement is necessarily true (for example, that a flush beats a straight).

  Without having to think about it, an experienced poker player knows that any flush beats any simple straight, and that any full house beats any simple flush. Likewise, any four of a kind beats any full house. The knowledgeable player just looks at his hole cards, and after the flop can tell what the best possible winning hand can be, and how many possible ways there are that he can be beat. For example, suppose I am holding those pocket rockets as my hole cards, and the flop comes 7, 8, 9. The skilled poker player knows that there are nine possible combination of cards that are beating him at
this point, plus a “diamond flush peril” if another diamond appears on the turn or the river.

  The single most important kind of poker knowledge is this kind of trained perception. It is something that the poker novice hardly notices at all, and something that the experienced poker player on occasion forgets about at his or her financial peril. Properly done it becomes, with experience, almost automatic. In a phrase, it is knowing the best possible hand given the flop, the turn, or the river. This sort of poker knowledge helps one look at the community cards and at a glance be able to say what the best possible winning hand could be. It requires the internalization of some simple principles, such as the following five:

  (1) If there is a pair on the board, then the winning hand could be either four of a kind, or a full house.

  (2) If there are three cards of the same suit, and no pair on the board the winning hand could be a straight flush or a simple flush.

  (3) If there are three cards within a five card span and no pair on the board, and no three cards of the same suit, then the winning hand could be a simple straight. A simple test here is that unless there is a 5, or a 10, either in your hand or on the board, then there is no way you could have a straight. For example, employing this sort of poker knowledge the experienced poker player looks at a board of 3-8-9-A-J and just knows that the winning hole cards could consist of a 7-10. Many a poker player caught up in the infatuation with his hole cards of A-J and his respectable two pair, has fallen victim to the overlooked possibility of a winning straight.

  (4) If there is not a pair on the board, and not three cards of the same suit, and not three cards within a five card span, then the winning hand could be either trips (assuming that some player has a pocket pair in the hole), or two pair, one of which matches the highest card on the board, or some lower two pair built from the under cards on the board.

  (5) If there is no full house, no flush, no straight, no set, and no two pair, then the winning hand is either the highest single pair, or at worst, the highest card of all of the hands still in the pot.

  The internalization of these conditionals allows the experienced poker player to simply know where his cards place him in relation to the various ways he or she can be beat. Such a player doesn’t have to think through the possibilities, any more than the experienced golfer has to think through the mechanics of her golf swing while teeing off. For example, on the flop the experienced poker player automatically notes if there are two cards of the same suit (say diamonds), and registers the “diamond threat,” for if another diamond appears on the turn or the river, a flush is a distinct possibility threatening any straight, three of kind, or one or two pairs that the player has in his own hand. On the other hand, suppose the player already has two diamonds as his own hole cards. In this case the player is hoping for that third diamond to appear on the turn or on the river. Yet the player also knows that the approximate odds are seventy-five percent against a diamond appearing on the turn and the same percentage against on the river. In other words the odds are distinctly against the player completing her flush. And, of course, even if she does complete her flush, she knows that unless she has the nuts someone else may have a yet higher flush.

  But just because you know that a flush can beat a pair of A’s, doesn’t mean you should suddenly save up ten thousand dollars and head off to Vegas for the World Series of Poker tournament. The most difficult thing to learn is the “knowledge how” to play particular hands given what you know. This is what separates the Phil Iveys from the Joe Blows. For example, if you’re on the river with two pair, and you can see that the board allows for two possible straights, as well as a possible flush, you should know that raising is not prudent given all the possible ways in which you can be beat. Knowing how to bet (as well as how to check and how to fold) in the appropriate circumstances is a crucial kind of “knowledge how,” that presupposes a considerable amount of “knowledge that.”

  Getting “Ryled Up”

  Although Ryle worked hard to discriminate between different kinds of knowledge, he was also quick to counteract the intel-lectualist prejudice of such theories. Certain states of mind, Ryle argued, can best be understood dispositionally. For example, the mental state of believing is not best understood as a conscious entertaining of specific thoughts or propositions. It is better understood as being disposed to say or do various things (including entertaining thoughts). In a similar fashion I would like to emphasize that inescapable role of dispositions in the enlightened conduct of the Texas Hold’em player.

  For example, in a low-limit game with, say, a three-six betting structure, some people will stay to see the flop with any hole cards no matter how bad. Suppose your hole cards are a 2-9 (affectionately known as a “Montana banana,” on the grounds that anyone lucky enough to win with those cards could grow bananas in Montana). If anyone stays to see the flop with 2-9 enough times, in the very long run, a flop will come 9-9-2, thereby giving you a very strong full house. Here is where the “knowledge that” versus “knowledge how” distinction comes into play. The “knowledge that” in question is knowing that there is a very low percentage chance of your 2-9 hole cards winning. This “knowledge that” is worthless to you unless it is accompanied by a corresponding “knowledge how” to play those cards. And such “knowledge how” consists in part in an ongoing disposition to discard those cards and not pay to see the flop with them.

  Poker knowledge plays very different roles in low limit game and no-limit games. For example, in a low limit game a pair of pocket A’s may be of marginal value because so many players are staying to the river on every hand. By contrast, in a no-limit game the same pocket A’s may generate an “all-in” bet which instantly cuts the competition down to one caller—if that. So, the moral of this story is that poker knowledge is highly contextual in that the knowledge of the value of different combinations remarkably varies the appropriate betting. One’s dispositions must be developed accordingly.

  The poker player who knows how to play her 2-9 hole cards, exhibits that knowledge by her regular disposition not to waste her money by hanging around to see the flop. We all know she’ll be bitterly disappointed at not having stayed on the rare occasion when the flop makes those cards worthwhile. This finally brings us to the role of luck in poker knowledge.

  It is conventional wisdom that knowledge is power. In the case of Texas Hold’em it’s absolutely true that poker knowledge is a form of poker power. Poker power is not the same thing as poker success. Success at poker essentially involves the element of luck. With a little bit of bad luck, excellent hole cards lose to low hole cards due to low cards on the flop. Anyone who has had his A-K lose to an A-2 knows the role of luck in poker. Nobody likes to go bust by getting bad cards and then playing them badly. This is where poker knowledge enters the scene. Poker knowledge, in the sense of the dispositions that constitute “knowledge how,” permits one to avoid playing badly and experiencing the misery that attends knowing that one has done so. The game of poker has an amazing capacity to prove wrong anyone who thinks in advance of a flop that they know which cards are worth playing. We may think we know that rags aren’t worth staying with, but nothing stings quite like discarding hole cards which turn out to be exactly what is needed for a set, or a full house, or a lucky win. The phenomenon of luck sets serious limits to the scope of poker knowledge. Nevertheless, it is the combination of poker “knowledge that” and the set of dispositions that constitute the “knowledge how” to exercise that knowledge, that ultimately distinguishes the expert player from the beginner.

  So What?

  The critical reader who has followed my discussion of knowing how and knowing that may find himself asking “So what?” at this point of the essay. Such a reader might say: “All the author is saying is that you have to know the rules and how to apply them. How is this supposed to make me think differently about poker?” The quick answer is that corresponding to the dispositional activity that constitutes knowing how there is a proced
ural process of learning to. In order to know how to play poker one has to learn how, which is a matter of acquiring the more or less complex skills and techniques which are the behavioral underpinning of knowing how. This brings me to my final point about the distinction between these two kinds of knowledge. Knowing that is in a certain sense a horizontal activity, in that once a proposition is known to be true, that’s all there is to it, although one can explore what further propositions entail or are entailed by the known proposition. By contrast, what is important about the skills and techniques that enter into “knowing how” are a vertical activity.

  Philosopher Israel Scheffler has put the matter this way: “Knowing how to do something is one thing, knowing how to do it well is, in general, another, and doing it brilliantly is still a third, which lies beyond the scope of knowing how altogether. . .”3 The idea here is that knowing how forms a vertical spectrum of evaluation, some points of which are competence, proficiency, and mastery. Standards of achievement with regard to knowing how to play poker are, fundamentally open-ended in the case of such an advanced skill. The advanced poker player doesn’t just know the rules of the game and the various strategies of play. What he has in addition is an intelligence and sophistication in the application of those rules, which is capable of continuous refinement. Just as there is no maximum skill level in knowing how to play the piano, it is likewise the case that “know how” in poker play is likewise capable of endless refinement. Perhaps that’s why poker is so addictive. And so frustrating.