For pairs it is 6×(number of higher ranks)/1225. The probability of domination in a two player game is easy to calculate. Each cell in the table above for pairs was based on 7.8 million hands, and 21.7 million for the non-pairs. Methodology: These tables were created by a random simulation. That said, the following tables present the probability of every two-card hand being dominated, according to the total number of players. In the former case (K-5 over Q-5) only three cards can help Q-5, the other three queens. For example Q-5 is dominated by K-5 or Q-7.

A non-pair is dominated by another non-pair if there if there is a shared card, and the rank of the opponent's non-shared card is greater the dominated non-shared card.

Only three cards will help the Q-5, the other three queens.

A non-pair is dominated by a pair greater than the lower card.

In the case of 5-5, three cards only will help the Q-5, the other three queens. For example, Q-5 is dominated by Q-Q or 5-5.

A non-pair is dominated by a pair of either card.

Only two cards help the J-J, the other two jacks.

There are four types of domination, as follows. To be more specific, a dominated hand is said to rely on three or fewer outs (cards) to beat the hand dominating it, not counting difficult multiple-card draws. In Texas Hold 'Em a hand is said to be dominated if another player has a similar, and better, hand. On this page Texas Hold'Em Dominated Hand Probabilities Introduction

Odds starting hands texas holdem