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Poker Showdown Between Luck and Skill

The Numbers Guy
March 27, 2009

The Wall Street Journal has a number of Blogs, one of which is called "The Numbers Guy". It is managed by Carl Bialik who writes on the "way numbers are used, and abused". Many of his articles appear in his column on the Wall Street Journal.

In this article Bialik writes: Is Texas Hold'Em poker more a game of chance or of skill? That question has figured in several legal tests of playing the card game for money: Games of chance are considered gambling under U.S. law. Now a major poker Web site has sponsored a study it claims demonstrates that it takes skill to win — which would help the site’s legal standing. But several poker experts question that claim.

Texas Hold'Em like other poker games starts with the players being dealt a number of cards and the players putting a prescribed amount of money in the "pot". Then in a number of stages the players make bets which other players must match or drop out of the game. When there are no more bets there is a "showdown" among the players still in the game. The player with the best hand wins the money in the pot with the money shared if their are ties.

Bailick writes: "PokerStars paid Cigital, a software consulting firm, to analyze 103,273,484 hands played on the site last December, for real money — usually at least $1 blind bets. (for the uninitiated here's a guide to the rules) Three quarters of the hands analyzed ended without a showdown, meaning that the winner never had to show his or her cards — everyone else eventually folded during the rounds of betting. And half the time that hands did end in a showdown, a player who would have won had already folded.

Paco Hope, technical manager at Cigital and co-author of the study, argues that the paucity of showdowns shows poker is a game of skill: The winner could have won by making identical bets no matter which cards he or she had drawn. “Most people think, you get your cards, and the best hand wins,” Hope said. He added, “Whether or not you go to a showdown is determined by the decisions you make, which are determined entirely by your skill.”

Bailick writes: "Who folds is determined to a huge degree by the value of the cards! Peter Winkler, a Dartmouth College mathematician who has studied games of skill and chance, said in an email. The player who picks up AA [two aces] and stays in while the rest fold is the lucky one; the player who picks up 32 [a three and a two] and folds before the 332 [three, three, two] flop comes down is the unlucky one. That the AA player wins with an ultimately inferior hand does not prove poker is a game of skill. If anything, it shows the opposite: an unskillful player holding the 32 hole cards might have stayed in.

Hope counters that skill dominates luck in decision-making: “The same information is available to all players (the values of the cards), but it is skill in interpreting that information — not the presence of that information — that determines whether a player folds.

As for the failure to track individual players, Hope argues that it doesn’t matter whether skillful competitors are identified. “I don’t care who won or why they won,” he said. “What I care about is the decisions they made. The fact they decided to fold indicates it was decisions that determined the hand.

Like other Blogs, Bailick invites readers to comment on these arguments. Particularly interesting comments were made by Patrick Fleming who writes:

Your analysis of the Cigital study is much too simplistic. Mr. Hope is not saying that because the majority of poker hands are resolved without a showdown that ALONE means poker is a game of skill. What is shows is that the vast majority of poker hands are determined by the way people play the cards, not the actual deal of the cards. IF it is also true that the way people play the cards is an exercise of skill, THEN it follows that the exercise of skill is the predominant factor in determining the outcome of poker. First, Isn’t knowing that your AA hand is likely to be the winner in and of itself an application of knowledge and therefore a skill? But even if you want more than that to qualify as “skill,” there is more, indeed much more.

Your statement “For one thing, players’ decisions are determined by the cards they draw, which is entirely a matter of luck.” is patently false, and I am surprised you of all folks made it. I know from previous blogs that you are familiar with the rules of poker. A player’s decision is NEVER “determined” by the cards they hold (except for a few very minor points, like who makes the first mandatory bet in some version of stud poker). The cards a player holds may influence his decision, indeed sometimes they may be the biggest factor in his decision, but they never (except as noted above) DETERMINE his decision. A player in hold-em is just as free to raise with 3-2 as he is to fold 3-2. What he actually decides to do with that 3-2 will depend on a number of other factors. If he is a skilled player, he may realize that the other players are “scared” of him. He may raise knowing that they will think he has much better cards. If he does that and the other players fold, he wins. His actual cards had nothing to do with his win in that situation.

Likewise, the comment by Mr. Winkler that ““Who folds is determined to a huge degree by the value of the cards!” shows a lack of understanding of poker. I doubt Mr. Winkler has played much poker. A player who bases his decisions solely or “to a huge degree” on what cards they hold is at best a beginning player, and will not be a successful player until they start to consider other factors before making their decisions. What cards you hold, as any poker pro will tell you, is only the beginning of the thought process. As Kenny Rogers sang, every hands a winner, and every hands a loser. Most of the time which one your 2 cards will turn out to be depends on many, many other factors.

This comments section is not the place I want to begin a discussion of all of the factors that go into deciding how to play a poker hand, whole books have been written on the subject, so I will just list a view: your image as a player, your position at the table, the size of the bet, the size of your bankroll, the styles of the other players, physical tells of the other players, and mathematical probability. Analyzing and applying all of these and other concerns, plus the actual cards you hold, is a very complex thought process. It is a learned skill, and a skill that can be improved. And that proves the second half of the equation, and that’s why this study HELPS to prove that the results in poker are MOSTLY the product of player skill. And please note my use of the word “mostly,” No one denies that chance determines some results in poker. When you raise “all in” early with A-A and an opponent calls with 9-10 cause he mistakenly thinks you are bluffing, and 2 remaining 10s are dealt (with no ace), chance has determined that outcome for the most part.

But the question is not whether chance determines EVERY outcome in poker, nor whether skill determines EVERY outcome. The question is which is determining the MAJORITY of outcomes. Since in the majority of outcomes the cards, as shown by this study, are not even consulted, that is strong proof that the majority of outcomes fall into the skilled category. And that becomes conclusive proof when one looks at the actual decision making process required in MOST poker situations, and realizes that it involves complex analysis frequently unrelated to the actual cards held.

And one final point, to the expert who asserts a better test would be to show that skilled players win more often, has he ever heard of Doyle Brunson? 50 years of being a successful poker player must have more to do with skill than with Doyle just being the luckiest person on the planet, don’t you think? In sum, the Cigital study is only one piece of a larger analytic framework, but it is an important piece. And when all of the pieces are put together, the evidence that poker is a game of PREDOMINANTLY skill is, as the judge in South Carolina recently stated, “overwhelming.”

Thank you,
Patrick Fleming

Full disclosure - I am the Poker Players Alliance Litigation Support Director and helped craft the argument that has been presented in the courts


(1) Does all this convince you that poker is predominately a game of skill?

(2) Do you think that this study would convince a court that poker predominately a game of skill?

Submitted by Laurie Snell