Heads Up Proposition

[The Spy]

I recently began a study of heads up poker, although I'm focusing primarily on limit. I'm a mathematician and have been examining the game from a theoretical standpoint. Initially I assumed poker hand rankings were transitive, but it always fun to investigate.

So I'd like to offer the following heads up proposition to anyone willing to accept it:

1. Choose from the following three poker hands: A[img]/images/graemlins/spade.gif[/img]3[img]/images/graemlins/club.gif[/img], Q[img]/images/graemlins/diamond.gif[/img]J[img]/images/graemlins/diamond.gif[/img], 2[img]/images/graemlins/spade.gif[/img]2[img]/images/graemlins/club.gif[/img].

2. Based on the hand you chose, I will choose one of the remaining two hands to play against you. The third hand (which neither of us wanted) will be shuffled back into the deck.

3. We both go all-in pre-flop, for say $1000.

Anyone up for it?