Toy game: shoving turn for equity + bluffing denial
The board: A
2
2
Q
Stacks: 1x pot
Villain (OOP) has 1 combo of A
A
+ 9 combos of flushdraws (let's call it 20% equity with his flushdraws).
Hero has K
K
and villain checks to us on the turn.
Hero has the option between shoving and checking back.
If we shove, villain does not have the pot odds to call his flushdraws, so will only call with AA.
Should we shove despite only folding out worse and getting called by better?
****************
If we shove:
90% of the time villain will fold and we take down the pot.
10% of the time villain will call and we lose 1x pot.
Our EV of shoving turn: 90% * 1 - 10% * 1 =
0.8x pot
If we check (let's assume river is checked down first):
20% of the time, villain hits the flush with his 9 combos of flushdraws: 20% * 9 = 1.8 combos
He will also always beat us with his 1 combo of AA.
So on average he will have 1.8 + 1 = 2.8 winning combos on the river (28% equity).
Our EV of checking turn: 72% * 1 - 28% * 0 =
0.72x pot
Conclusion: Shoving turn purely for equity denial is correct in this example.
***************
If villain is allowed to bet the river:
However, there is one more reason we want to bet the turn: "Bluffing denial".
We want to deny villain the ability to bluff us of the best hand on the river!
20% of the time, the flush river will come and we have to fold 100%.
But that's okay, in this example, because on the flush river we never fold the best hand anyway.
(Of course we should have shoved turn, but that mistake is in the past).
80% of the time, the river is a brick and villain will value bet his 1 combo of AA and balance it with 0.5 combos of bluffs. We are indifferent between calling and folding so we call 50% of the time (MDF).
He will check 8.5 combos of air.
When he bets (15%) our EV is 0 and when he checks (85%) we win the pot.
So our total EV when villain is allowed to bet the river is:
20% * 0 + 80% * 0.85 =
0.68x pot
In conclusion: It is correct to shove the turn, not only for equity denial, but also for "bluffing denial".
Last edited by Zamadhi; 05-11-2023 at 04:32 PM.