Poker mathematics

As its known, poker as a card game is a combination of mathematics and psychology. Many articles have been written lately about the game`s psychology, but in the meantime the other side of the game was paid less attention. Let’s try to make good the deficit. From a mathematical point of view, poker isn’t so difficult, as for example preference or blackjack: there is not possible to count the cards that are off game, and you don’t have enough cards in your hands to define the opponent’s possible combinations. But, at the same time there’s a list of simple rules from combinatory, probability calculus and games theories, and by using them you can avoid making some mistakes and considerably, increase your chances to succeed. Those rules are the base of the “poker mathematics”.
The playing deck for poker consists of 53 cards. So, the general number of possible five combinations is 2 598 960, the number of possible “pocket cards” (the cards received from the dealer at delivery) – 1326. All the correlations can be gathered in 11 combinations with a different number of correlations, so, for example, the number of correlations of the “four of a kind” combination is 624, “three of a kind” – 54912. The highest number of correlations, of course, has the “empty” combination (a set of cards that isn’t even close to any poker combination) – 1302540. Changing the combinations number into percents is easy to determine that the chances to receive an “empty” combination are 44%, “pair” – 46% , two “pairs” – 22%, “three of a kind” – 4, 5% and etc.
However, the main and final goal of the poker game is not so much to collect the strongest poker combination as to win the pot. To calculate the probability to win the pot is better to use the mathematical expectation. If describing the poker game strategy thru a mathematical expectation prism, the player should win as much as possible, having on his hands a “strong” combination or he can lose as less as possible having the “weakest” combination. With the help of this quantity you can define the average bet quantity.
Another quantity from the probability theory in poker is the dispersion. This is the dispersion form of an eventual quantity (detour from mathematical expectation). In poker, the higher the dispersion indicator, the often and bigger will be the loss on some starting hand (especially when lacking experience). It’s recommended to rookies to play the starting hands with high mathematical expectation and low dispersion. In the poker slang such strategy is called tight.
In this article we just show you a few mathematical tactics, used when playing poker. Separately, in each one of them we can find detailed researches with dozens of examples which will be good for everyone who wants to learn how to play poker on a serious level.
Finally, we recommend you to remember that in poker, as in other gambling there isn’t and can’t be a scheme of guaranteed win!