poker hand winning probability calculator

His work from 1550, titled Liber de Ludo Aleae, discussed the concepts of probability and how they were directly related to gambling. Motivated by Paccioli's work, Girolamo Cardano (1501-1576) made further developments in probability theory. In 1494, Fra Luca Paccioli released his work Summa de arithmetica, geometria, proportioni e proportionalita which was the first written text on probability. The development of probability theory in the late 1400s was attributed to gambling when playing a game with high stakes, players wanted to know what the chance of winning would be. Probability and gambling have been ideas since long before the invention of poker.

By pushing all-in with AK you give your opponent the opportunity to fold for fear of an overpair, which will improve your expectation in the long run.In poker, the probability of each type of 5-card hand can be computed by calculating the proportion of hands of that type among all possible hands. This means that it is always better to be pushing all-in rather than calling an all-in with AK if necessary, because to call with AK against an under pair is a losing play in the long run. The table shows that although the odds are fairly even, the under-pair will usually have the slight advantage. Therefore you should be careful not to become overly excited when cards like these are turned over in an all-in situation, because your opponent is not always as far behind as you think.Īnother interesting all-in match up is the very common AK versus an under pair. For example, if you have another player dominated with a hand like A J against J T, your opponent will win the pot 1 time in 4. All in match up odds evaluation.Īs you can see from the table, some of the match-ups are closer than you might expect them to be. The is due to other factors such as the increased probability that two overpairs will appear on the board creating a higher two-pair with a better kicker for the player holding A K. The table can be used to estimate your chances of winning in common all-in situations, however, the table does not highlight the exact probabilities for the certain match-ups in general.įor example: in the pair v overcards match-up, 2 2 would be a 53% favorite against A K instead of being a slightly stronger favorite like T T with a 57% chance of winning. How to use the all in match-ups odds chart. The table also assumes that there are no other players in the hand, although the results should be very similar. The percentage chance of winning assumes that both players are all-in and that all 5 community cards will be dealt to determine a winner. The table below shows the odds of each hand winning in typical all-in match ups in Texas Holdem.

Poker hand winning probability calculator