3-handed holdem preflop rankings

I'd like to rank the holdem starting hands for 3-handed poker. Can anyone do this for me or explain how I might go about figuring it out?

[elitegimp]

There is a website with the rankings done already, if you want the URL send me a PM and I'll post the link (I'm not at home right now, and odds are I'll forgot to post by the time I get home).

To do it by hand, you want to write a program to cycle through all 169 possible starting hands, and for each hand deal out the remaining 50 cards into two hands every possible way (690900*), and then deal the remaining 46 cards into all of the possible 5-card boards (1370754*), and count how many times the hand wins. Note that this involves 169*690900*1370754 = $an extremely large number$ iterations. Anyway, after all that is done, rank the 169 starting hands in order of how many times they won (with the hand that wins the most being the best).

Example:

Hand 1 = AA.

Out of the 50 remaining cards, deal your opponents' hands (Say Opps have 22 and 22). Then deal Board #1 (say 33334). You win, so add 1 to whatever variable counts wins by AA. Then you keep your opponents hands the same, and deal out Board #2 (say 33335). Do this until you've dealt all 1370754 boards possible when you have AA and your opponents each have 22, then change your opponents hands (say to 22 and 23). Lather, rinse, and repeat for all possible hands your opponents can have when you have AA... then deal yourself a different hand (say AK), and do it all over again. As you can imagine, it requires a lot of calculations! (Don't forget to give yourself partial victories when you and one or both opponents split!)

You could also use a "Monte Carlo" method: it's not precise, but for each hand you randomly choose 2 opponents and randomly choose a 5 card board... do a large number of these simulations per hand (maybe a million?), and the percentage of wins should be close to what you get calculating every case.

* If I did my math right [img]/images/graemlins/smile.gif[/img]

[AaronBrown]

It pays to start with the Wizard of Odds.

This tells you your chance of winning if each hand is dealt to showdown. It's not the same as equity, however. Hands that play well against the hands most people play are more valuable than hands that play well against the hands nobody plays. Deceptive hands (like one-gappers) can be more valuable than higher rated hands (like connectors).

[elitegimp]

http://gocee.com/poker/HE_Val_Sort.htm (you want the column for "2 opponents")