Bayes Theorem and Poker
Bayes Theorem is used in almost every scenario that involves the probabilities of an action dependent of that of another. The same case can be made for utilizing Bayes Theorem in poker, particularly the aspect of deciding whether or not to fold or call.
The article opens the case for using Bayes theorem by positing a scenario in which your poker opponent in which he bluffs 40% of the time and bets his true value 60% of the time. The probability for ensuring that it is a value bet is much more difficult to discern do to the 60-40 distribution of the probabilities. Luckily, the opponent has a tell such that when he puts away an Oreo, the opponent is bluffing 80% of the time. Given these probabilities, is it in your best interest to fold or call? We can use Bayes Theorem to answer this.
What we are trying to solve in this scenario is “what is the probability that he is bluffing, given the information from his betting pattern and from the tell?”
To understand this it is necessary to further examine the scenario given the article’s information of the trials in determining these probabilities as illustrated by the table below:
| Bets true value | Bluff | Total | |
| Eats cookie | 48 | 8 | 56 |
| Puts cookie away | 12 | 32 | 44 |
| Total | 60 | 40 | 100 |
The p(bluff) when he puts the cookie away is 32/44, which is 33% higher than the total probability for a bluff. Thus, it would be prudent to call instead of fold and by extension we can conclude that by utilizing Bayes theorem and its consequent dependencies we can asses each scenario in poker and whether or not to call or fold.
The article illustrates quite well the mathematical implications of poker to demonstrate that the game is not purely based on behavioral patterns. Moreover, it illuminates the central role that statistical science and probabilities have on luck-based games such as poker. This can be helpful to act as a set of guidelines that allows for a more structured approach when playing.
While it may seem poker is a specialized exemplification of Bayes theorem, the application of the theorem can extend in many aspects of everyday life from equities speculation to deciding which jar the cookie is in. In fact the theorem was so integral to statistical sciences it was even used to attempt to prove the existence of god. Whether it be merely a game of poker, or proving the cosmological composition of the universe, Bayes theorem remains an integral part probabilistic science.