Quote:
Originally Posted by kekeeke
it's just a math question, getting an extra 135$ while he has little equity or making him fold it and letting him have his 135$
i am bad at math and too lazy, but i kinda want that last 135$ with ace high you know
There is value in getting villain to fold anything >= a gutshot. Even K5+BDFD only has ~30% equity where he would need ~32% to call. Some non-dominated hands such as 98 no BDFD have as little as ~21% equity.
I'm going to give 25% equity for the air range we're targetting when we flat call (seems reasonable by playing with ranges). I'm assuming that he treats his entire air range the same and that he folds it when we shove the flop.
If he doesn't bluff his air on the turn it's a mistake to call the flop and let him freeroll us. There is some turn bluff frequency, 'b', where we meet the EV of a flop shove.
We win the pot with a flop shove, so after we call our EV needs to be the size of the pot on the turn to be at least as good.
P = b*(.75*(P+270)-135)+(1-b)*.75P
P = b(.75P+.75*270-135-.75P)+.75P
b = P/(3*270-4*135)
= ~54%
If Villain continues to bluff >54% of the time on the turn (regardless of whether or not he hits the turn) it is better than shoving the flop with respect to the air portion of his range.
If villain ever hits SDV on the turn and checks to us that is very good for us. We might also be able to further improve the EV of a call by folding or bluffing certain turns when checked to, like Kx.