Maths of poker

It is said that poker was not gambling. This is true, because if it was, then it would be playable in the casinos as long as possible. The casinos, where poker is available to play, give only the conditions for the game (table, dealer, cards, etc) and therefore take commission (rake).The casinos do not have benefits against the players neither on short or long term. Thus, the players play against each other, and each collects their winnings from other players, the case gets some commission after the games. So it is not gambling, but logical game, where luck is also needed. If this is true, then the logical relationships can be deduced from the mathematical foundations.

Chances

The game is played with 52-french card, which includes four colors, with 13 cards per color. The chance to pull out a card is 1:52, it is almost 2% (1.923).

The calculation of probabilities

Probability is equal with our favorable outcome devided all possible events. The poker players do not use percent unit in their calculation, the probabilty of positive outcomes, but use so-called "out of". Thus, 3 cards can also means the formation of a winning combination for a player, out of 3 and approximately 6%. All of the combination can be calculated as 5 cards are choose from 52 cards. In poker all of the possible card combinations is n! / k! * (n-k)! where "n!" is n factorial, "k!" is k factorial, ie, the "n" under the "k" words, where n is the total number of cards, here 52 and k is the 5 good cards.

Chances (probabilities) of winning combinations can be determined as a figure (eg, place, or in pairs, or poker) how many ways can occur. For example, occurrence of poker is 13 * 48. So poker is likely to emerge: 13 * 48 / 52 under 5. The following table summarizes the way as to develop all the poker combination of probabilities.

Probability of the figures

The above table shows the probabilities of developing the figures. These are the theoretical probabilities. The odds change largely during the game. In preflop part of the game, as a departure strategy may have role of these theoretical probabilities. If the player gets a pair in hand, (s)he will think about chance of a drill, or poker. In the base of associated color and/or number of cards can be calculated chances of row or flush. The player is highly influenced by the actions of the opponent's behavior, the position, the pot and the amount of capital. The game progresses we get more information, which influent chances so the probabilities are changing. Thus, we can think, it is enough worthy to river, or threw in the cards earlier. Simple program which is in the "preflop card prediction" menu can be applied to the start-up strategy. This little program will propose to our actions on the basis of the position, behavior of opponent, your cards in your hand. After the flop, before the turn, and before the river, you bet if it's worth. That is, if you assume less risk than the expected gain. How well will it work? It is necessary to consider how much is the pot and how much should be given. This will be the amount of money that you're going to win. The pot and the call to be granted must be compared, the amount of the increase in proportion to the probability of winning the pot. For example, if $ 1 is in the pot and you have to give 20 cents, your chance is 1:5, ie 20%. If you look your cards in your hand and also look the number of cards (outs) what in the next round of possible benefits to you, and compares the 5 (from 1:5) to the number of outs. In that case when you got greater number than 5, you can specify the call. Thus you got more than 20% chances to win the pot. This is a very rough calculation, but it is not so deep mathematics to be win!