As an expert on poker, I submitted two recent statistical studies. (I was paid to research the evidence and confer with the defense before the hearing.) The first paper was “Economics of Poker: The Effect of Systemic Chance” (2012) by Robert Hannum, a professor of risk analysis and gaming at the University of Denver. His study of more than a billion hands of online Texas Hold’em found that 85.2 percent of the hands were decided without a show of cards. In other words, players’ betting decisions were of overwhelming importance in determining the outcome. Of the remaining 14.8 percent, almost half were won by a player who didn’t hold the best hand but instead had induced the player with the best hand to fold before the showdown.
Hannum concluded: “Clearly the driving force behind the economic outcome of Texas Hold’em is skill rather than chance.”
The second study was “The Role of Skill Versus Luck in Poker: Evidence From the World Series of Poker” (2011) by Thomas Miles and Steven Levitt of the University of Chicago. During the 2010 World Series of Poker, 720 players identified beforehand as high-skilled earned an average return on investment of 30.5 percent, an average profit of more than $1,200 per player per event. The average return of all other players was minus 15.6 percent, a loss of more than $400 per event. Miles and Levitt noted that the divergent returns on investment were “highly statistically significant and far larger in magnitude than those observed in financial markets, where fees charged by money managers viewed as being the most talented can run as high as three percent of assets under management and thirty percent of annual returns.”