When comparing two starting hands, the head-to-head probability describes the likelihood of one hand beating the other after all of the cards have come out. Head-to-head probabilities vary slightly for each particular distinct starting hand matchup, but the approximate average probabilities, as given by Dan Harrington in Harrington on Hold'em [p.125], are summarized in the following table.
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Favorite-to-underdog matchup Probability Odds for Pair vs. 2 undercards 0.83 4.9 : 1 Pair vs. lower pair 0.82 4.5 : 1 Pair vs. 1 overcard, 1 undercard 0.71 2.5 : 1 2 overcards vs. 2 undercards 0.63 1.7 : 1 Pair vs. 2 overcards 0.55 1.2 : 1
These odds are general approximations only derived from averaging all of the hand matchups in each category. The actual head-to-head probabilities for any two starting hands vary depending on a number of factors, including:
- Suited or unsuited starting hands;
- Shared suits between starting hands;
- Connectedness of non-pair starting hands;
- Proximity of card ranks between the starting hands (lowering straight potential);
- Proximity of card ranks toward A or 2 (lowering straight potential);
- Possibility of split pot.
For example, A♠ A♣ vs. K♠ Q♣ is 87.65% to win (0.49% to split), but A♠ A♣ vs. 7♦ 6♦ is 76.81% to win (0.32% to split).
The mathematics for computing all of the possible matchups is quite complex. However, a computer program can perform a brute force evaluation of the 1,712,304 possible boards for any given pair of starting hands in seconds.
This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia.
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