For March’s poker series we will be looking at the important of math at the poker table; maybe not anyone’s favourite poker topic, but an important one nonetheless. To start off, we will take a look at starting hand match-ups, specifically when considering heads-up poker probabilities.
At its very basic, this is the heads-up probability of one hand beating the other after all the cards have come out. Heads-up probabilities vary slightly for each particular starting hand match-up. However, the approximate average poker probabilities, as summarized by poker pro Dan Harrington in Harrington on Hold’em are:
Pair vs. two undercards – 4.9:1
Pair vs. lower pair – 4.5:1
Pair vs. one overcard, one undercard – 2.5:1
Two overcards vs. two undercards – 1.7:1
Pair vs. two overcards – 1.2:1
An important thing to notice in this table is that a pocket pair is only a pre-flop underdog to a higher pocket pair. These odds are general approximations only derived from averaging all of the starting hand match-ups in each category.
The actual heads-up 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, procimity of card ranks between the starting hands, and the possibility of a split pot. For example, pocket aces versus K,Q (both in spades and clubs) is 87.65% to win, but the same-suited pocket aces against a 7,6 in diamonds is only 76.81% to win.
The mathematics for computing all the possible poker starting hand match-ups are really quite complex, so we will be taking these in small courses throughout the next month. Come back later this week to learn about the starting hand poker probabilities when playing against multiple opponents.
