Game Theory’s Application to Poker
https://www.wsj.com/articles/how-game-theory-changed-poker-11642087507
I decided to review Oliver Roeder’s Wall Street Journal article titled “How Game Theory Changed Poker.” In the article, game theory was utilized by computer algorithms to create poker strategies. Specifically, the dynamics inherent to a mixed strategy equilibrium were seen in a practical situation. In this situation, many programmers are hired to analyze professional poker players’ gameplay, in order to find mistakes in their play. The algorithms attempt to make players’ gameplay less predictable and therefore harder to combat. The article cites an example of the game rock paper scissors; if one plays each move at random, it is impossible for one’s opponent to discern a pattern. Similarly in poker, if one reduces discernible betting patterns it can be advantageous. For example, the article cites that if other players know that an individual player will only raise $100 if they have a pair of pocket aces, than other players can exploit that. Therefore, the article recommends that one should create ranges of bets, and raise money with pairs of kings and queens, and not just aces. Further, the article notes that one shouldn’t place the same bet amounts with the same range of hands. Instead, players should employ mixed strategies and randomize. For instance, two-thirds of the time that one has a pair of aces they should raise, and a third of the time they should call. The article further notes that some players use a wristwatch to determine their randomization. For example, to determine whether to call or raise, one looks at the second hand on their watch; in the first 40 seconds of the minute they raise and in the last 20 seconds they call. This playing style is called Game-Theory optimal since it enables players to ignore their opponents and focus on their own betting strategies. Therefore, players hire programmers to evaluate the chosen bundles and percentages of betting in order to find room for improvement.
As I considered the article, I realized that there were many similarities between this strategy and a mixed-strategy, multi-round Nash equilibrium solution to the prisoner’s dilemma. In both cases, one should not choose a single “dominant” strategy and instead should employ a mixed strategy. Interestingly, when applied to Poker, this strategy replaces traditional thought. Instead of trying to read into an opponent’s tells (such as their eye movements, betting patterns or other indicative ‘ticks’), this strategy mathematically assigns a betting strategy based on the likelihood of one’s cards winning against an average hand. Further, it closely mimics the strategy of a multi-round game; since there are many rounds, players must ensure their opponents do not catch onto their playing strategies and that their cards and/or likelihood of winning remain difficult to ascertain. For instance, if one only raises with a hand of a full house or above, their opponents are likely to catch on and change their strategies. Therefore, the mixed strategy equilibrium ensures a measure of confidentiality. Based on the similarities noted above, the parallels between the prisoner’s dilemma and this poker strategy enable similar lines of reasoning to be applied to both cases.
Though poker is significantly more complicated than a prisoner’s dilemma 2-by-2 matrix, programmers have developed algorithms to mimic this strategy that are designed to exploit the natural odds inherent to poker games by applying strategies from game theory. When playing poker against top human players, it wins 58% of the time (with a margin of error of plus or minus 5%.) Using game theory to analyze poker results in better play, reduced variance, and ultimately, higher payoffs.