This is now turning into another basic maths post, but this time about calling with draws (implied odds). I would appreciate people looking it over in case I've made some fundamental error(s).
6max 100nl - effective stacks $100
UTG opens to $4, MP calls, fold, Hero (BTN) calls with 9hTh, fold, fold.
POT ~ $12
UTG bets $8, MP folds, Hero ?
Our read on UTG is that he has an overpair and flop fold equity = 0. Should we call?
On the Flop
We will hit one of our 8 outs on the turn 8 out of 47 (I know we could argue 45 since he has AA/KK/QQ but for simplicity...), or 17% of he time. If we make the call on the flop we are calling $8 to win $20, or 40%. If there was no more money behind we have to fold. However, there are 2 more streets and there is money behind. So the question is, given that we hit one of our outs on the turn how much more money do we have to extract by the river in order to make our flop call profitable in the long run?
We are calling $8 with a 17% chance to hit the nuts, so we need to win at least $47 (8/0.17) at the end of the hand (another $27), to be BE on our call. Is this likely? Yes. So we make the call.
On the Turn
Pot = $28
Board = 7c8s3d 2h
UTG bets $21, Hero ?
We will still hit one of our 8 outs approximately 17% of the time on the river. If we make the call on the turn we are calling $21 to win $49, or 43%. If there was no more money behind, we have to fold. However, there is one more street of money behind. So now the question is, given that we hit one of our outs on the river how much more money do we have to extract on the river in order to make our turn call profitable in the long run?
We are calling $21 with a 17% chance to hit the nuts, so we need to win at least $124 (21/0.17) at the end of the hand (another $75), to be BE on our call. Is this likely? Well...
If we call, the pot on the river will be $70, so we would have to be certain that we could extract an overpot size bet on the river. If villain is likely to bet and we reraise in position, we may get it. If we know villain is likely to pot control check and fold to an overbet, then we can't make the turn call and must fold.
So in general calling the flop is always good, but folding to a brick on the turn is often the correct play, especially if we're OOP, and also depending on villain's tendencies with regard to river betting. A FD is probably even more of a clear fold on the Turn considering how obvious they are when they come in.