Is this prop bet +EV?

[DrPublo]

I'm thinking I should post this in the probability forum but maybe people have seen it before. I'm playing 1/2 NL at a local card club, talking to a guy whos play I respect. Out of nowhere, he asks me "Heads up, would you take AK or 22?" Of course, I've heard this one before and I know 22 is marginally ahead, etc etc. That's not the point of the question.

I tell him 22, and he tells me ok, now prop bet it. The game works like this. Every hand, we both have two imaginary cards (i.e., we're dealing with a 56 card deck). I have red 22, he has Ac Kc. If the hand makes it to a river, the losing hand pays the winning hand $5. Duplicate cards are ok (i.e., I can make 6 deuces, and he can make an AAKK high flush). Repeat every hand.

Is this +EV long term? My thinking is yes, because if it were just AK v 22 out of the remaining 48 cards, it's roughly 50/50. In our game I now have 4 cards with which to hit a set, which is a huge improvement. Of course, when he makes a flush draw he also has 11 outs to make it instead of 9. So that gives him a little edge.

Also, I think the fact that the bet is only valid if the hand goes to a river is of some consequence. Hands with As and Ks on the flop tend to go to a river more often then hands with a deuce on the flop, I would think. So he gains some there as well.

What do people think of this prop bet?

The Doc