Let's try these hands:

Holdem Hi: 1370754 enumerated boards
cards win %win lose %lose tie %tie EV
Ad Kh 75421 5.50 1279357 93.33 15976 1.17 0.060
Qs Qc 248836 18.15 1116752 81.47 5166 0.38 0.183
As Ac 1030521 75.18 324257 23.66 15976 1.17 0.757

A pushes with AK. Player B must have a good hand in order to call. Pretty much any good hand he has, you have dominated.

I think that if B doubles up, A still has a greater chip size than you. I think that a call here is in order. Chances are you will come in third anyway if you fold, so why not try and triple up. You are going to get blinded away within the next two hands. Tripling up gives you a better chance to survive the blinds, because if you double up twice in a row, you will have a chance to avoid being all-in with the blinds.