In the last couple of live games I’ve participated in, the “computer” or “internet” hand of Q7o has been mentioned. The pokerterms.com definition discounts the idea that the conventional explanation that a simulation showed it was the hand with the smallest positive win rate in heads-up play of the 169 hand combinations. In their section “Real Statistics,” they claim that Poker Stove shows Q2s and Q5o between Q7o and the 50% mark and that J5s is just under the mark.

I hate to differ with the venerable Poker Stove but I have my own sets of statistics, run for between two to twelve players. Each set is based on 500,000 hands of No-Limit Hold’Em. And the conventional explanation is right. Q7o will be the best hand 50.56% of the time in a two-player game. I don’t know what pokerterms.com was feeding their copy of Poker Stove but Q2s only wins 47.74% heads-up and Q5o is 48.51%. J5s is 47.35%, also on the down side.

Of course, that’s not the entire story. Poker isn’t just a binary win/lose proposition. There’s always the possibility of a tie, and some hands have relatively high possibilities of doing so. While a hand like AA will only tie 0.42% of its appearances, J5s will tie 5.13% of the times it shows up.

One way to evaluate a hand’s strength isn’t how often it wins but how often it doesn’t lose. If I don’t lose any chips, if I can split whatever other money might be in the pot, that’s acceptable. On that basis, Q7o looks marginally better. I wouldn’t normally play it, but in a brute-force statistical race, it only loses 46.02% of the time. It’s in the top 40% of possible hands, ranked on how often they lose. If you look at the range between a hand that loses 50% of the time heads-up (J6o loses 50.05%) and the best possible hand pre-flop (AA loses 14.02%), Q7o rates 11% better than statistical average. Q2s is at 5%, Q5o is 6%, and J5s is 7%.

Lots of ways to slice and dice statistics. Just a matter of making them useful.