This is a spot that seemed counterintuitive to me. Its pretty simple back of the envelope stuff so it isnt going to be totally accurate but the result isnt close enough to make that matter.

Someone raises QQ preflop, we 3bet AK and they 4bet QQ to 33bb. At this point there is too much dead money to fold (given that we know they have QQ). We also have no fold equity preflop with only a potsized bet remaining. So we have 2 choices:

1) Shove and flip.
2) Call. Shove if the flop is A or K high and check/fold otherwise.

If we shove and flip then the total hand is breakeven (more or less).

If we call then we will have lost 33bb 2/3 of the time when an A or K doesnt flop. We will win 100bb 1/3 of the time when we shove and he calls. The total EV (from the start of the hand) for this line is

-2/3 * 33 + 1/3 * 100 = -22 + 33 = +11bb.

Obviously better than breakeven even though we are check/folding most flops. In fact in order for shoving preflop to be better they have to fold QQ at least 2/3 of the time on an A or K high flop for a pot sized bet postflop (or fold QQ preflop to a 5bet shove). I suspect most players would feel too committed at this point both preflop and on the flop for us to have anywhere near enough fold equity for shoving preflop to be better than calling.

This might be obvious to some/most of you already but I was under the impression AK "likes to see all of the cards" so it suprised me a little.

Practically this also allows us to lose less to AA and KK the times we miss the flop (alot more often since they hold 2 of our cards). We miss folding weaker pairs preflop but I dont think many people 4bet/fold preflop anyway for 100bbs.


Disclaimer: The maths in this hand has obviously been simplified alot. I have used the total wins and losses of the hand where I should have used the EV from the point of the decision. The reasoning behind this is that, if we can turn a breakeven (or marginal loser) of a hand overall into a winner overall by playing 1 decision differently, then that decision is obviously the more +EV of the options. I have done a more "correct" analysis of the hand too (which actually works out even more in our favour) but would be alot more complicated to post.