Flop and turn action were pretty quick. River bet had a definite (but not very long) pause before it.

Ugh. This aint a fun spot to be in. I think his weak turn bet is indicative of a weak hand rather than a big one and you're probably good here enough to make the call very slightly +EV. It could be diamonds, or a small PP trying to play back at you, or even 88-TT thinking it's taking you to valuetown.

Just looked at it again and I guess QQ-AA is also possible. I hate you for not having reads, this is a very difficult hand.

Bah. CALL.

tough spot. what do you think about a turn raise?

I think we should've bought schlep some punctuation marks for Xmas.

Fold. I don't think he's on a FD as often as 64/33/55/77/QQ/KK/AA. Then again, he seems to have sized his turn bet in order to leave himself a PSB on the river, so maybe he does want you to fold.

Here I will use some of the concepts, that were analysed in the 'Mathematics of Poker' without going into much detail.

I think that it's likely that opponent has us on a range 88-QQ here, may be even 99-JJ. So now we are in a regime of when opponents effectively knows our cards, while we can only assign a certain range to him. His range with respect to our holdings can be divided into, 'nuts' these are the hands that beat us, and 'dead' hands, i.e. the hands that he could have on the river to bluff with.

1. 'nut hands' : 33, 55, 77, 46s, AA, . - 17
2. 'dead hands' : 57s (2), 68s (4), and a whole bunch of diamond suited hands
67d, 78d, 89d, A7d, AKd, AQd, KQd - 13.
So we have about equal amount of 'dead' and 'nut' hands, we could add some weird JTd or TT into a mix of dead hands, one can also argue about AA or AKd being included, but I would take this estimation for simplicity. (If we take another estimation of his range we will need to adjust our calling frequency accordingly.)

1. River call.
When number of 'dead' hands = amount of 'nut' hands, and he bets pot on the river his optimal bluffing strategy would be to bluff half of his 'dead' hands, and value bet all his 'nut' hands. In this case he is indifferent to our caling or folding. While from our side we can insure that we are not exploited by calling in 50% cases, this way we will gain in equity each time he deviates from optimal bluffing frequency. (One just can flip a coin in order to decide to call or not.)

So the answer to call or fold question given the assumptions, would be to call in half the cases, this will be optimal unexploitable strategy.

2. Turn call.
Another question, would be if we can play this hand differently. If we take the same distribution of hands for the opponent on the turn, i.e. half 'nut' hands and half drawing hands, then the best line is indeed to call. (We have enough of equity in the pot to make a call better than a fold. If we raise AI opponent can respond by folding all draw hands and call with 'nut' hands, giving us 0EV) Though we should fold if a diamond falls on the river.
My estimations of EV for a turn call gives about +20$. Compared to 0 EV for folding and raising.


Cliff notes:
Calling on turn is better than folding or raising.
We should call river in 50% cases if we don't have a read and think that half of his hands beat us.
EV of this play starting from turn will about 20$.

Edit: Found a mistake in calculations, EV of a turn call is about 10-20$.
With a new estimation, folding turn is better.