[cartman]

If we rule out an 8 for our opponent, this narrows his possible holdings on the flop to a pair, Ace high, a diamond draw, a gutshot, a pure bluff.

Against Ace high on the flop (now top pair), we have 0 outs.
Against flopped pairs lower than 8's we have 9 outs. Against pocket pairs higher than 8's we have 6 outs. Against most diamond draws we have 31 outs (because he has 15 against us). Against gutshots we have 36 outs (because he has 10 against us). Against most pure bluffs we have 30 outs (because he has 6 against us).

If we assume that we will either win or lose one big bet on the river (except for the few times that he checks and we check because the river wasn't a K, J, or an A), then we are getting 6 to 2 odds on a call down. To justify this we must win the pot 2 out of 8 times, or 25%. That means we need to have, on average, 11.5 outs.

So given that he bet the flop what percent of the time do we think he had?:

A high (0 outs)
Pair <8's (9 outs)
Pair >8's (6 outs)
Diamond draw (31 outs)
gutshot (36 outs)

I think I remember calculating that, on a non-paired board with a possible flush AND straight draw, a player who will bet any pair or any draw will have a pair about 70% and a draw about 30%. With just a straight draw OR a flush draw possible, the same player will have a pair about 80% and a draw about 20%.

The board being paired would skew these somewhat toward draws but make betting with A high a real possibility also.

I don't know how to properly weight these, but calling down looks more compelling than it did on first glance.



But is it compelling enough?

If you call the turn, can you really call the river if a diamond hits?



Cartman