Probability in Multi-way Pots?

[IlliniFan97]

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’m going to use very rough numbers) I 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 player 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.

[elitegimp]

What you want to do is combine all your opponents into one uber-opponent and count the outs. Back to your example:

flop is Ad 8h 5h

you have As Kd
your opponents have
* Ac 3s
* 6s 7s
* 2c 2s
* Jh Th

Then there are 9 hearts that beat you, 2 threes (since you already counted the 3h), 1 two, 3 fours, and 3 nines. So 18 cards that you do not want to see (although you have redraws against some of them), and 39 unknown cards means you win roughly (21/39)*(20/38) = 28% of the time (2.5:1). Again, this is not accounting for your redraws.

Note that if every one calls you down you will be getting 4:1 from every bet you make, so you should definitely bet!

[AaronBrown]

As a practical matter, with more than one opponent, it rarely pays to consider specific hands that might be out there. Instead concentrate on your hand, which you know.

Consider two extreme situations. First, you have a hand that is worthless now, but might improve to a royal flush. Clearly, you have the same odds against one player as against many. You like the big pot, because it pays you more when you hit. Second, you have a solid hand, say two high pair (obviously this depends on the board). You're in good shape against one player, but among several you're likely to be second best. Since second best doesn't pay any more than last, it's a bad hand.

Fish are never bad, but you have to know how to play them. In this game, you sit back until you get high suited connectors and pairs. A pair of twos is almost as good as a pair of Aces, because you'll probably need threes or better to win. You can fold nine hands out of ten preflop, as long as you keep getting three or four callers to showdown against your nuts. Throw away your hands that are likely to be pretty good, you need hands that have a pretty good shot to be great.