Gambling

IN A recent hold'em tournament, I got beaten on a pair of kings against 10-9 offsuit when my opponent flopped trip10s, beaten on a pair of queens against 5-5, when my opponent caught A-2-3-4 to make a five- high straight and then lost on 10-10 against A-6, all in the first hour of play. Well, these things happen to all of us. But it set me thinking about the odds. By a fortunate coincidence, the poker author David Sklansky has analysed the whole question in the latest issue of Poker Digest.

One of the key elements in tournament play, particularly in hold'em, is playing heads-up. Almost every decisive encounter, after the early stages, comes down to two players slugging it out, all in. So it is useful to know the true odds.

Most people know, intuitively, that a pair in the hole is about even money against a player holding two overcards before the flop, eg Q-Q v A-K offsuit or J-10 suited v 2-2. Or that in pair versus pair, like 10- 10 v 9-9 the higher pair is about a 4.5 to 1 favourite. There are 11 categories of matchups that can occur heads-up. Pair versus one overcard and one undercard, as in my third "bad beat" listed above, is about a 2.5 to 1 favourite. In this case the unpaired hand basically has three wins to hit a higher pair, while the hand with a pair has two redraws (chances to improve again.)

It can go the other way, of course. One of my sweetest memories in another event was outdrawing a rather bumptious opponent, who had aces wired, with Q-7 of hearts. I was all in, and had already stood up to leave the table, when down came a queen and a seven and then three hearts in a row.

Some hands one is just fated to win, though in this case I was bucking odds of greater than 5-1. As Sklansky comments, a player does not need to be all that accurate when deciding about whether to call all-in raises before the flop.

What one can say is that it is far better to be the aggressor and take the lead, and let the other man decide.