How Can Maths and Probability Inform your Poker Game?

Coin Flip

In the cutthroat world of poker, where there are experts lurking in every corner of the internet, players need to constantly update and refine their techniques and strategies in order to win. The game is constantly evolving and, with the internet age, players have had to draw upon a greater toolbox of skills to make it to the top. Maths and probability have become a major aspect of the game and being able to quickly work out the odds of winning a hand can put players at a significant advantage. Here, we examine what probability is, look at different poker hands’ odds, and discuss how to incorporate probability in your poker strategy. This is essential information for anyone who wants to increase their chances of winning a greater number of poker games.

What is Probability?

Probability isn’t simply a term confined to poker discussion, and you will have heard it before if you ever studied maths at school. It can be used to describe the likelihood of any number of events, such as the chances of winning the lottery or someone’s life expectancy depending on their lifestyle. Someone looking to improve their poker game should not just look at probability at the poker table but conduct wider research into the topic itself.

Probability is quantified as a value between 0 and 1, where 0 is equal to impossibility and 1 means something is a certainty. It can be written as a fraction or a percentage but those who are familiar with televised poker will know that, in those circumstances, a player’s chances of winning are always listed as a percentage. A simple way to explain probability is with the flip of a coin. A regular coin only has two possible outcomes; heads or tails. For that reason, you can say that the probability of it landing on heads is 50 per cent. The probability of it landing on either heads or tails is 100 per cent and the probability of it landing on neither heads nor tails is 0 per cent – excluding the statistically insignificant chance of it landing on its side.

Things obviously get a lot more complicated when other factors and variables come into play and poker players who want to work out their probability of winning need to have supreme maths skills that they can quickly deploy in the game. The concept is probability theory and it is a commonly-used form of risk assessment in many things in life, not just gambling.

The Probability of Different Hands and What This Means

In poker, probability gets a lot more complicated than the result of a coin flip. For this discussion, Texas Hold’em probability will be analysed, as this is the most commonly played form of the popular card game. In the game, players need to take into account the number of players at the table who each receive 2 cards, along with the five community cards in the middle. They also need to consider the number of cards that weren’t dealt. So, on a table with eight players, there will be 21 live cards and 31 unused. Any player could have any combination of cards, while the only information available to the individual player is what they are holding and the community cards in the middle.

Players need to use probability to work out when they should bet and when they should fold. The most important time to consider probability is pre-flop, and there are certain starting hands that just shouldn’t be played because they have such a low chance of producing a strong hand. 7-2 is a prime example of a hand that should never be played unless you’ve already put in a big blind. In poker tournaments, the professionals will look to only play high pairs and high connectors most of the time. Obviously, they will adapt their strategies depending on the other players at the table and how loose or tight they are.

Different hands in poker have varying probabilities of occurring. A straight flush is the least likely hand with a probability of 0.00139 per cent or odds of 72,192: 1. This is why it is the most valuable hand in the game. Another high-value hand is the Full House, which has a pre-flop probability of 0.14 per cent. The probability of getting a pair, which is the lowest value hand, is 49.9 per cent. In the middle region, three of a kind is 2.87 per cent, while a straight is 0.76 per cent. Players can look at these probabilities and assume that, around every five hands, they should have three of a kind or stronger and, therefore, they should be throwing away weaker hands and waiting for a better position at the table.

How Should Probability Affect your Strategy?

As noted above, the probability should have a strong influence on which hands you decide to play and which ones you muck. If you have stuck in a big blind and nobody raises, you can play anything. Otherwise, you should be sticking to top pairs, top connectors, or suited connectors. These cards will give you the best chance of hitting something on the flop.

Probability also guides poker players when they are deciding whether to call a bet or fold. In situations where players are waiting for a card on the turn or the river to complete their hands, they need to work out how many “outs” they have. For instance, if you were waiting for one more card to make a flush, you need to understand that there are only nine other cards that can save you. These are your outs. Some of these cards could have already been dealt to other players so the chances of hitting the card you need are fairly slim. You need to weigh up the risk in relation to the bet size and how deep your stack is.

Probability has always been a key component of poker but a knowledge of it has become even more important in the world of online poker. Players need to use well-reasoned strategy in situations where they can’t get by on bluffing skill alone, and calculating probability can be the best way to minimise risk.

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