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Poker Showdown Between Luck and Skill

Carl Bialik writes a column called "The Numbers Guy" for the Wall Street Journal and keeps his columns here.

Bialick 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.

We have discussed this problem in previus issues of Chance news here and here

Texas Holdem like other poker games starts with the the players being delt a number of cards. Then the players put must put 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 or if their are ties the money is shared. You can read the rules for playing Texas Holdem here

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. 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.