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

[joshman1204]

22 is actually a slight underdog to AKs. If this were 22 vs AKo then it would be very slightly +EV.

[tylerdurden]

[ QUOTE ]
22 is actually a slight underdog to AKs. If this were 22 vs AKo then it would be very slightly +EV.

[/ QUOTE ]

22 has a tiny edge over AKs if one of the 2's is the same suit as the AK.

See if he'll give you 66 instead.

[Pinlifter]

[ QUOTE ]
22 has a tiny edge over AKs if one of the 2's is the same suit as the AK.

See if he'll give you 66 instead.

[/ QUOTE ]

66 does nothing to block wheels. Ask for TT it has double the blocking power of 22.

Pinlifter

[DrPublo]

[ QUOTE ]
[ QUOTE ]
22 is actually a slight underdog to AKs. If this were 22 vs AKo then it would be very slightly +EV.

[/ QUOTE ]

22 has a tiny edge over AKs if one of the 2's is the same suit as the AK.

See if he'll give you 66 instead.

[/ QUOTE ]

In the bet I actually moved to 33 at some point. 33 is better than 22 because whenever the board makes two pair, 22 loses to AK. However, whenever the board makes 2 pair with XX22, 33 beats AK. So 33 is probably a favorite.

But thats not the point. Here we're talking about IMAGINARY CARDS in a 56 card deck. Has anyone ever prop bet like this?

The Doc

[randomstumbl]

Without even needing to do the math, I'm 90% sure you're a dog. He makes a pair more often and he makes a flush more often and it started out close to a coinflip to begin with.

What really tells me you're a dog is that he offered you a prop bet. Almost no one will ever offer you a prop bet like this without handing you the short end of the stick.

[jedi]

[ QUOTE ]
[ QUOTE ]
22 has a tiny edge over AKs if one of the 2's is the same suit as the AK.

See if he'll give you 66 instead.

[/ QUOTE ]

66 does nothing to block wheels. Ask for TT it has double the blocking power of 22.

Pinlifter

[/ QUOTE ]

Huh? 66 will give you a 6-high straight. Am I misunderstanding something?

[tylerdurden]

[ QUOTE ]
[ QUOTE ]
22 has a tiny edge over AKs if one of the 2's is the same suit as the AK.

See if he'll give you 66 instead.

[/ QUOTE ]

66 does nothing to block wheels. Ask for TT it has double the blocking power of 22.

[/ QUOTE ]

As someone pointed out already, 66 doesn't need to block wheels, it already dominates them.

TT is a better hand against AKs, though. I just figured that it was so high that the other guy wouldn't give it to you. 66 is low enough that it still seems harmless, but has the edge.

[PokerDork]

The fact that you aren't actually taking two 2's and the Ac and Kc out of the deck is what makes you a dog here. Do you see why?

[DrPublo]

No, I don't see why. THis is my question.

He still needs to hit, and althoug he hits more often, I hit more often as well. And when we both hit I win the vast majority of the time.

Please explain more.

The Doc