Unit 3: Luck Vs Skill in Poker - Game theory

Poker & Game Theory - 'Know when to fold em'!

IN THE New York Times on October 9th, Chad Hills, a gambling analyst for Focus on the Family—a position roughly comparable to monitoring Satanic churches for the Vatican—was quoted disparaging the argument that poker is a game of skill rather than chance, because nobody “can tell you what the next card flipped over is going to be”. The outcome of a single poker game can indeed be determined by the flip of a card—just like the outcome of a single baseball game can be determined by a bad hop, the results of a horse race (legal to wager on in the United States, thanks to a generous legal carve-out) by the condition of the track, or indeed the price of a company’s shares by adverse weather, say, striking a manufacturing plant. Time and chance happeneth to them all, as the preacher said.


But poker players do not play just one game. A good player knows how to minimise his losses during a bad streak and maximise his winnings during a good one. Skilled poker players, to use David Sklansky’s memorable phrase, are “at war with luck”. The relevant question is not whether luck has any role at all, but whether poker itself is principally a game of luck or skill. Common-sense would seem to settle that question: there are numerous professional poker players, and they make a living because they are better at the game than the average weekend kitchen-table player (I am a pretty good kitchen-table player; every time I have sat down with professionals I have been skinned alive, swiftly and mercilessly). I know of no professional roulette or slots players, for instance, and about the pamphlets at my corner bodega that purport to reveal “secrets of the lottery” the less said the better. But why rely just on common sense?

Here, for instance, is a paper from Steven Levitt and Thomas Miles, that analysed play during the 2010 World Series of Poker and found that skilled players made an average return on investment of over 30%, compared with -15% for others (profits that most investors would kill for, especially today). Cigital, a software consultancy, analysed 103m hands of Texas Hold ’Em played at Pokerstars.com, and found that 76% of them ended before a showdown: that is, before opposing players reveal their cards and the strength of their openly compared hands determines the winner. Victory, in other words, was determined not by Mr Hills’s feared flip of a card, but by players’ in-game decisions. It further found that in a showdown only slightly more than half the hands were won by the table’s best possible five-card hand. In 49.7% of the cases the player who could have made the best possible hand folded before the showdown: another outcome determined not by chance but by player decisions. Finally, consider losing rather than winning. Can you deliberately lose a hand of poker if you tried? Of course: bet badly, fold with winning cards, and so on. Can you deliberately lose a game of baccarat or roulette? No: to play you have to bet on an outcome that might happen, regardless of what you do.