The Internet Hand

In the last couple of live games I’ve participated in, the “computer” or “internet” hand of Q7o has been mentioned. The 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 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.