Poker probability (Texas hold 'em)
This article will discuss mathematical odds in Texas Hold'em, a game variant of the card game poker, portrayed.
- 2.1 Starting hands heads up
Starting hand
For the strength of a starting hand is roughly the following table. The smaller a figure is, the better the hand. Offsuited hands are left and below the main diagonal, the same color hands ( suited ) to the right or above the main diagonal.
To determine the probabilities for a starting hand, there are basically two ways
Result set
Calculate the number of ways that you meet a certain hand. For example, to get AA, there is provided one ignores the order, six ways, namely A ♠ A ♥, A ♠ A ♦, A ♠ A ♣, A ♥ A ♦, A ♥ A ♣, A ♦ A ♣. The formula for this is
So
( n! pronounced n factorial )
Overall, there are
Different starting hands. It follows for the probability of two aces
Conditional Probability
At fifty-two cards, there are four aces in the deck. The probability to get an ace, so is
The probability of getting an ace with a missing card is an Ace, is
Thus follows a probability of ...
That ... you get 2 aces in distributing.
Analyzing the probability
Overall in Texas Hold'em 1326 different starting hands are possible. The colors were included in the bill.
By the previous calculations, we know that you get two aces on average every 221 hands.
Analysis of the starting hands
As in poker, all colors have the same value, many of the 1,326 possible starting hands are at least equivalent before the flop. Therefore hands are divided basically into three groups before the flop
Following the probabilities of certain hands
Starting hands heads up
In heads up the opposing player can
Have different starting hands. After the flop, that number drops to
Possible hands.
In total there are heads-up
Different ways confrontation which cards have the players on hand. We now assume that two players keep their hand up after the river and so we see a showdown. There are
.
Opportunities for the community cards. It follows that
So are around 3.68 billion possibilities for the distribution of community and hole cards.
Note: Mathematically it makes no difference whether initially have played more players, but who have their cards aside ( not stored and handed out cards are in the bill both equally disregarded ). But in the game, the opponent only a bad hand would naturally dropped. Here is thus implicitly assume that there have been only two players from the beginning ( first definition of heads up ) and that it is a completely new leaf.
Comparison of two starting hands
The following table contains probabilities for the outcome of a clash between the starting hands of two players
These figures are not to be stated exactly, may finally also the colors of the cards have influence on the result.
Example: A ♠ A ♣ K ♠ Q ♣ wins against to 87.65 % ( 0.49% for split pot ), against 6 ♦ 7 ♦ but only to 76.81 % (0.32 % for split pot ).