OK, I did the math on the following scenario:
50NL, 100bb stacks ($50)
Hero is in MP with AKs,AKo opens to 1.75, villain is in BB with 22-TT and calls.
The flop comes A
9
3
Villain's strategy is to check/raise his sets and fold to any flop bet with less than a set (a common variant of a pure set mine).
I looked at 2 hero strategies:
- hero bets some amount, and villain folds with less than a set
- hero checks behind and folds to any bet on a later street (these always mean villain hit a set)
for #1, if hero bets the pot, then villain's check/raise sets strategy is worth $0.88. If hero bets $1.75 (slightly less than 1/2 the pot), villains EV for check/raising is $0.65. If hero bets 3/4 pot ($2.81) then villain's EV is $0.77.
for #2, villains EV is $0.77.
So, hero betting
- 1p loses money vs checking it down / folding to a bet (villain has a set).
- 3/4p give the same result as checking down
- making a small bet to fold the setminer is better EV than checking the hand down.
Naturally, if villain will call hero's flop bet when villain has TT, then hero's EV goes up and villain's down (assuming hero folds to future aggression and otherwise checks the hand down) because villain is putting in money way behind.