Thursday, September 20, 2012

20 thoughts on skill vs. chance in poker, part 14: Does rate of showdown matter?

<-- Part 13: On control and equal challenges

A simple, popular outcome-based approach to predominance considers how often real-world hands of a particular poker variant end in a showdown. Intuitively, the argument here is that, when a hand ends in a showdown, the cards held by the players have "controlled" the outcome, and when a hand instead ends in all but one player folding, since the cards were never shown, the "cards didn't matter" and thus the players' decisions to fold are what "controlled" the outcome.

This idea was most famously formalized in a 2009 study by security firm Cigital which computed showdown rates using a 100 million hand database of real Holdem hands, supplied by PokerStars. The study itself is a short read with a simple approach. It immediately discloses in its summary that it doesn't attempt to quantify the effect of chance, merely to provide "compelling statistics about the way that the outcomes of games are largely determined by players' decisions rather than chance", which is a terrific self-awareness. So how compelling are its arguments?

The primary finding of the Cigital analysis is that, 75.7% of the time, in a real-world Holdem hand there's no showdown. A secondary finding is that, of the remaining 24.3% of hands that do go to showdown, only about half of them are won by the hand that, had no players have folded, would have gone on to be the best hand. Therefore the random deal of the cards only controls the outcome about 12% of the time. This echoes the ideas of the toy game "Luck Holdem", where players place bets on their hands prior to the deal and then run out the cards and see who wins, as described by Howard Lederer in a rather solid short essay on skill and chance in poker (written many years ago, when he was still a respected member of our community).

Showdowns, however, do not directly correlate with either skill or chance. Once again, I can't put it better than Ike Haxton already has:
The notion that skill is limited if you can't fold and unlimited if you can is hand-wavy nonsense that is superficially compelling only because it coincidentally aligns well with our intuitions about which games are more or less skillful out of the class of commonly played gambling games. There's no folding in bridge or gin but they are obviously highly skillful games. Heads up limit holdem with no folding allowed would be another. One can conceive of poker variants that allow folding but have essentially no room for skill (NLHE with face up hands for instance).
Indeed, poker without folding is still a game which fits a broader definition of poker, as long as checking and betting are still allowed. Heads-Up Limit Holdem without folding, as Ike mentions, still has plenty of skill, though it is probably less skill than regular poker. To that extent, it's reasonable to say that adding the option of folding back into a poker game should generally serve to increase the depth of skill of the game — but introducing any new strategically-nontrivial move to a game would increase the strategic space of the game.

The ability to fold is only one of various strategic options, not necessarily of any greater worth than any other. It is possible that there might someday be a type of poker game which doesn't allow folding but which nonetheless involves more skill than the forms of poker that we play today. Chance would probably be higher as well, but with enough strategic depth, the skill could be increased moreso than the chance was under any desired measure. An approach such as that of the Cigital study would not capture the role of skill in this type of poker game. Similarly, this sort of approach is also dependent on the underlying population and thus could change over time if player tendencies shift due to development of the game strategy. It doesn't seem likely for multiplayer NL or Limit Holdem, but it's theoretically possible that, someday, they might be played using strategies that led to more showdowns and that these strategies, unknown to us currently, turn out to be better strategies exhibiting a deeper probing into the skill of the game. More realistically, the Cigital study may have yielded different results if play-money or micro-stakes games were observed.

Another study, published by sociologist Kyle Siler, explored the relationship between player strategies and payoffs using real hands of poker. The study contains some interesting observations on the relationship between social psychology and players' strategies at poker, but the most memorable "finding" of the study, thanks to the media attention this point received, was one relating to showdown rates. Siler found that players who won pots more often were more likely to be losing players, unsurprising to any experienced poker player but generally misinterpreted in the media. Naturally, overly-loose strategies will lead to winning more pots, but will lose money overall. Siler suggests the idea that inexperienced or poor players may conflate the ideas of winning pots and winning chips, causing them to skew their strategic decisions towards trying to win hands, which is an interesting behavioral hypothesis.

While I don't think that Siler meant for this conclusion about losing players winning more pots to be taken as a statement on the role of skill and chance in poker, to do so properly would nonetheless illustrate that players' strategies control the outcome, whether one is considering the outcome as the winner of the hand or as the magnitude of the amounts won and lost by the players in the hand. A player can choose a loose strategy and will win more pots by doing so, which shows that a player's strategic choices exhibit control over how often they win hands. Similarly, if the player who chooses a loose strategy ends up losing more money by doing so, this shows that the player's strategic choices also exhibit control over how many chips they win — which is, of course, the object of poker, rather than trying to win every pot. The various mainstream treatments of Siler's study seemed to generally miss this distinction, instead drawing unwarranted and illogical conclusions like "in gambling, quit while you're ahead".

Returning to the core idea of the Cigital study, there is some potential philosophical trouble with the role that the random components play in guiding player decisions. If we are to say that the players and their decisions have fully controlled the outcome within a hand that did not go to showdown, are we ignoring the fact that the cards dealt to the players played a role in their decisions? Has the random deal of the cards "controlled" the decisions of the players, thus transitively controlling the outcome of the hand? The key distinction here may be that compelling, suggesting, or guiding the players' decisions is not the same as controlling them; the players are endowed with free will and can choose to call that river bet with their nut-low missed flush draw if they want to. The random elements can guide strategic choices in a way that is occasionally forced... but it's only forced if the player wants to play well. If the player were truly controlled by the cards, there would be no strategic option available. That bad moves exist within a game is emblematic of the existence of diverse strategies within that game.

For either consideration of what an outcome is in poker, despite the fact that folding and bluffing aren't necessary conditions for skill to exist in a card game, they certainly serve well as the most obvious and salient ways in which players can control outcomes. In a context where we are forced to defend poker on the basis of the winner of a hand being the outcome, with no consideration given to the fact that superior players will win bigger pots and lose smaller ones, arguments such as that of the Cigital study play an important role. It's at least a little intellectually dishonest, as it's in some sense only a coincidence that the most popular forms of real-life poker happen to involve enough folding for showdowns to occur less than half of the time, but, given the ambiguity and indeterminacy of the question of predominance, some degree of hand-waving is often necessary.

Part 15: Does rake matter? -->

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