RGS Academic Journal 2022 - 2023

036 037 The Maths Behind Poker Dhiren Wadhva Poker is one of the most popular card games due to its simplicity. Anyone can learn the rules of poker very quickly and all you need to play is a pack of cards and some poker chips for betting. Whilst poker is classified as a sport, there are still people who believe that it is a game of luck and that there is no way to keep winning repeatedly. In fairness, this is true in the short run, but in the long run poker is solely based on strategy and skill. Maths has become vitally important, and it factors into so many aspects of poker. For those who are unfamiliar with poker, there are a couple of variations; however, this article will focus on the maths behind the most popular version of poker, widely known as Texas hold ’em. Here is a link to the rules of poker: https://www.pokernews.com/poker-rules/texas-holdem.htm Probability is a branch of maths looking at the chances of an event occurring. This has many applications in poker such as working out the probability of receiving a certain hand, the likelihood of completing a flush and using this information to call, raise or fold, or the chances another player has a certain hand from whether they are raising and by how much. The probability of receiving a pair of queens So, there are 52 cards in total and only 4 are queens. This means the probability of your first card being a queen is 1/13. This leaves 3 queens available from 51 possible cards so the probability of the second card being a queen is 1/17. This is a dependent event because the chance of the second being a queen is impacted by the first card. So, to work out the probability you must multiply the chances of the first event by the chances of the second event given that the first event has already occurred. In probability notation, this would look like the following: 1. P(A) = 1/13 2. P(B|A) = 1/17 3. P(A ∩ B) = P(A)*P(B|A) = 1/221