A new study conducted by Cigital, Inc., a company specializing in software security and development, was released on Friday that its authors argue "provides compelling statistics" that in Texas hold'em "the outcomes of games are largely determined by players' decisions rather than chance."
After analyzing over 100 million hands of hold'em dealt at PokerStars during a one month period, it was discovered that less than one fourth of those hands ever reached showdown, meaning players' hole cards were never revealed to one another. Furthermore, of the hands that did reach showdown, only slightly over half of those hands were won by the player who had been dealt what would have proven to be the best five-card hand had the player not folded prior to showdown.
The study's authors, Paco Hope (of Cigital) and Dr. Sean McCulloch of the Department of Mathematics and Computer Science at Ohio Wesleyan University, note that while their findings cannot be used "to quantify the effect luck has on Texas hold'em," they do provide strong support for the argument that "the majority of games [of hold'em] are determined by something other than the value of cards." In other words, it is how the players play their cards — not the cards themselves — that much more often than not determines who wins and who loses.
Citigal acquired data from Rational Entertainment Enterprises Limited (or REEL, parent company of PokerStars) related to hands played on PokerStars from December 1, 2008 to January 2, 2009. A total of 103,273,484 hand histories were analyzed, all from cash games (no play money). Also, because researchers believed "microlimit" games (with blinds under $1) "are considered too much like play money games," only a small number of the hands analyzed came from those limits, with the majority coming from higher stakes games. Hands were drawn from no-limit, pot-limit, and limit hold'em tables, either six-handed or full ring (i.e., no hands from heads-up tables were considered).
In the study, researchers state their assumption that December 2008 was "a representative month of normal play on PokerStars," thus ensuring there was nothing especially unusual about the hands selected to be analyzed. Also, to ensure the data collected was accurate, some independent corroboration was conducted whereby Cigital asked a select number of players to submit hand histories which were then matched against the ones acquired from REEL.
Of the 103 million-plus hands analyzed, the outcome was determined without a showdown in 75.7% of the hands, meaning no player at the table was able to see anything other than his or her own hole cards and whatever community cards had been dealt. Of the remaining 24.3% of hands that went to showdown, only 50.3% of those hands were ultimately won by the player who had been dealt the best five-card hand. In other words, in only about 12% of the hands analyzed did the player who had been dealt the best five-card hand actually go to showdown and win.
In situations where two players would have tied for the pot, but one folded prior to showdown, the researchers counted the hand as an example of one in which the best hand did not win. For example, Player A and Player B are each dealt 9-8, the final board reads 5-J-7-K-6, but Player A folded preflop while Player B took his hand to showdown and won with his straight. That situation was counted as an example of a hand in which a player dealt the best possible five-card hand did not win. Hands in which the five community cards constituted the best possible hand for all players (e.g., a board reading A-A-A-A-K) were also counted as hands in which a player holding the best possible hand did not win (if, that is, someone in the hand folded prior to showdown). According to Cigital, to have considered these special cases differently "would have [had] only a small impact on the final result as such hands are relatively rare."
Although the Cigital study does not address the nature of PokerStars' shuffling software, some may find it relevant to note that at PokerStars the randomizing program is run prior to the hand being dealt, but not afterwards. That is to say, once randomized, the order of the "deck" (or "virtual stub") is not changed throughout the rest of a hand. Thus conclusions drawn by researchers about what would have happened had a given player not folded his or her hand are valid, since — like in a brick-and-mortar poker room — the cards that were subsequently dealt were the same whether that player had stayed in or not. Such could not have been concluded quite as confidently on sites where the randomizing program continues to run throughout the hand, and certain variables — including player mouse movements and events timing — help form the vast compilation of data used to affect the randomizing process.
The entire study is available for download at the Cigital website (cigital.com).