[W. Deranged]

[ QUOTE ]
You have to draw here.

[/ QUOTE ]

That's what everyone else said, that's what I did, and now I'm almost positive it was the wrong play.

Here's the thought:

When SB check-calls and stands pat, I feel I can pretty confidently put him on a hand (he was pretty ABC). I think that his range is pretty much every 9-high hand and some of the worst 8s, say all 87 hands.

There are 7 choose 4 = 7*6*5*4/4*3*2 = 35 hands that are 9 high, one of which is a straight. Of those 9 high hands, 6 choose 3 = 20 combinations are 98 hands, one of which is a straight. So we have 19 98-hands out of 34 9-high hands. Since I have 98-perfect, I am beating more than half of the possible 9 high hands.

We then have to consider what is the likelihood that he has an 8 high hand. I figure he would bet any 86 hand or better. So his range includes probably no more than the 87 hands, of which there are 5 choose 3 = 10 possibilities, one of which is a straight. So maybe 9 possibilities.

If we add those in, I am beating 18 of his 43 possible hands, which is over 40% of his possible hands. My thought is that we don't really need to discount his range because I hold an 8 in my hand, because it is pretty likely that the two other players are both drawing very strong, probably both to 7s or maybe to something like my 8432 draw. If both hands remaining include 7s and not 8s, I think it actually may be slightly more likely that SB has a 98.

One of the easy things about the decision is that I do know that if I draw and hit any card 5-7 I will beat SB. My thought is that, particularly with the deck likely crippled at this point with 4 players remaining in the hand, it is unlikely that I have a better-than 40% chance of improving (in fact, I very clearly do not).

Therefore, my thought is that the most likely way for me to beat the SB villain is simply to stand pat.

Now, as for the other two players. Based on the action I think it is quite likely that at least one and probably both are drawing very strong, probably to 7s. In that case, in the majority of cases where either of them hit, they will beat my 98 and will beat any hand that I could draw to and hit . The only situation in which they hit and I would have wished I would have drawn is if the best hand either of them make is an 87; namely, only if one or both hit an 8 do I want to have drawn.

So, if either of the two drawing players hit, I'm probably screwed anyway.

So I think it is really quite clear that the best way for me to win this hand is to stand pat.