McCulloch used an alternative method to explore skill and chance in poker, also based on real games. Together with Paco Hope of the software consultancy Cigital of Washington DC, he looked at 103 million hands of Texas hold 'em played at the PokerStars online site and calculated how many were won as the result of a "showdown" - in which players win thanks to their cards beating their opponents' cards - versus those that were won because all the other players folded.
They argue that the latter hands must be pure skill, because no one shows their cards. Their analysis, released on 27 March, revealed that 76 per cent of games did not end in a showdown, suggesting that skill is the dominant factor.
John Pappas of the Poker Players Alliance (PPA) in Washington DC says both studies are badly needed to help properly define the law. In many US states, judges and juries use a so-called "predominance test" to gauge skill and chance, based on the opinions of expert witnesses.
Although courts in Pennsylvania, Colorado and South Carolina have all ruled this year that poker is a game of skill, not all courts do. "It would not be wise for any of us to rest on our laurels," Pappas says. The PPA expects the Cigital study will now be used as evidence to fight appeals against court rulings that decided poker is a skill game.
However, Preston Oade of law firm Holme Roberts and Owen in Denver, Colorado, who worked on a separate poker case in Colorado, cautions that the studies still may not persuade juries, as this is a "moral, political and social issue", as well as a mathematical one.
Pappas hopes the studies will help to persuade the US Congress to grant poker an exemption from the Unlawful Internet Gambling Enforcement Act, due to come into force in December 2009. The act will make it illegal in some states for banks to process transactions from gambling websites.