Drawy board, fire again ott. EV calc

[swimrun]

Hey guys. First post in this forum, so hope question isn't moronic.

I was considering the hand below in a vaccum, and whether hero should fire again ott to charge the draws.

Hero (MP): $209.39 (209.4 bb)
BTN: $102.13 (102.1 bb)
CO: $38.68 (38.7 bb)
BB: $188.70 (188.7 bb)
SB: $94.21 (94.2 bb)

Preflop: Hero is MP with Q K
Hero raises to $3, CO calls $3, 2 folds, BB calls $2

Flop: ($9.50) Q J 8 (3 players)
BB checks, Hero bets $8, CO folds, BB calls $8

Turn: ($25.50) 7 (2 players)
BB checks, Hero bets or checks??

Giving villain range of {Ah2h-AhTh, KT+, QJ, JT, T9, J8s, Q8s, 88} by the time we get to the turn, we are ~62% favorite versus villain's whole range, and 11% dog versus those hands we're behind (2P, sets, str8s).

Making the following assumptions:
1. Villain will fold to any decently sized Tcbet if he cannot beat top pair, good kicker (ie our hand)
2. We put no more money in the pot if we bet and are called ott
3. If we don't Tcbet, villain will only bet R if he can beat top pair, good kicker, and we will fold to any such bet
3. We ignore complicating factors like rake, villain x/r ott, bluff otr etc

The EV if we check is: EV_(ch)=0.62*$25.5=$15.81

The EV if we bet needs 2 parts to calculate:

EV_(bet)=EV_(bet, villain folds) +EV_(bet, villain calls)

Villain's range has 81 combos, we beat 29 and expect 52 combos to fold (incl. KQo).

EV_(bet, villain folds)=(52/81)*$25.5
EV_(bet, villain calls)=(29/81)*(0.11*[$25.5 + 2*Tcbet] - Tcbet)

So EV_(bet)= EV_(bet, villain folds) + EV_(bet, villain calls)= $16.37 + $1.00 -0.28*Tcbet=$17.37 -0.28*Tcbet

Since any Tcbet is going to be of the order of $20, then it is much more +EV for us to check this turn.

I was a bit surprised by this when I did the calculation - hence this post to make sure there are no errors, but I guess it comes down to we are only slightly ahead ott of villain's draws, but are crushed if we are already behind. So the gain from charging draws is massively outweighed by when we're getting in our money almost dead.

Does that seem right?

[eldodo42]

I didn't check the calculations, but the qualatitative results are more or less what I'd expect. I do think you made two very questionable assumptions:

1. Your range for villain on the turn is a big tight. Does he fold AJ on the flop to a cbet? What about QT? I assume if he has J8s in his range then he also has QTs and probably also QTo.

2. You're assuming villain will not bluff river, but I think this is a giant assumption that saves you a lot of EV. A lot of villain's profit is from bluffing various scare cards on the river. He can bluff any heart and any card between A and 9. If he was bluffing game-theoretically, I'm pretty sure he would cost you a lot of EV. Therefore, a turn bet would not only fold out his actual equity, but also the EV he gets from bluffing the river.