Prop bet

[DrPublo]

X-posted from the other gambling forum.

I'm playing 1/2 NL last night and the following prop bet comes up. Player A asks me to pick a hand to play heads up, AK or 22. I tell him 22. He suggests prop betting it as follows:

Each hand, he has an "imaginary" Ac Kc, and each hand I have an imaginary red 33 (after I lost the first two bets I switched to 33 from 22). I mean imaginary in the sense that it is as if we are dealing with a 56 card deck, with 2 Ac, 2 Kc, 2 3d and 2 3h. Every time a hand gets to a river, we compare our imaginary hands with the board, and the loser pays the winner $5. Duplicate cards are allowed, so he can make a pair of aces with 2 Acs, or a AAKKx flush, and I can make 6 treys, etc.

The question is who is a favorite in this bet. I think I am. If we were dealing with just a regular deck, 33 is basically a coinflip vs AK. But in our imaginary setup I have twice as many cards to hit a set, which gives me a huge advantage. Of course, he has 8 pair outs instead of 6, and when he flops a flush draw he has 11 outs to make it, instead of 9. So take some away from me there.

I also think there might be a bias based on the stipulation that the hand must see a river. I suspect that boards with As and Ks on them are more likely to see a river than boards with all low cards. I wonder how this affects the bet as well.

Anyway, if someone could help me run the numbers on this prop bet I'd be very interested.

The Doc