Wednesday, July 13, 2005

Multi-Way Pot Odds?

Posted a question to 2 + 2 here. Anyone out there have any additional thoughts about Multi-Way pots? Here's the full text if you don't want to follow the link:

I did a search, but couldn't find previous posts on determination of probability if you are in a multi-way pot (I either got a huge list or nothing depending on how I tried to search). Anyone have a link to an old discussion or a book recommendation?

I’m curious as there are so many players that are new to the game and understanding odds that there seem to be very few heads-up pots at the micro limits where I play. I understand odds in heads-up situations, but what happens in multi-way action? Do I subtract the odds for the players with fewer outs from the player with the more outs? I have been trying to reduce this by choosing tables with a low number of players seeing the flop, but at micro-limits the turnover is pretty high so it is difficult to find tables with a low percentage seeing the flop.

Here’s an example, I hold AsKd and raise 3XBB pre-flop into a 10-player table. I have 3 callers (pretty typical in a lot of micro-limit games where players “just want to see a flop”). The flop is Ad 5h 8h. I have top pair, top kicker. However, there are other hands out there, with the heart flush draw being the hand with the most outs. So I (I’m going to use very rough numbers) have a 60% win rate vs. the flush. Say there is one player with Ax offsuit, they have a (roughly) 10% to hit two pair with one of the three remaining undercards. Say there is a player with a 67(suited or unsuited, I’ve seen both call), they have a (roughly) 20% chance to hit their open-ended straight. Say the last pair has a small pocket pair that they didn’t hit their set, they have (roughly) 8% to hit their set. Do I just take my 60% probability vs. the flush and subtract 10% from the Ax draw, 20% from the straight draw and 8% for the set draw, leaving me with odds to win of 22%?

If this is the case, too many fish can actually be a huge hit to your probability of winning at these low limits. Is too many fish a bad thing?

Obviously, I should have paid more attention in my Probability Class…thanks for the help.


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