I recently answered an email someone sent me about a prop bet he had with some friends of his. Two players are given a hand: player one gets two cards, and player two gets only one card. He wanted to know who had the better odds for a particular scenario. Since it only took about 10 minutes to code up, I went ahead and computed the answers for all two-card vs. one-card matchups.
The puzzler challenge, should you choose to accept it:
What matchup of two cards vs. one card provides the closest to break-even equity before the flop?
1) Assume normal hold'em rules - the board will have five cards in it, and each player can either play the board, use one hole card, or (in one player's case) both hole cards.
2) No compute programs! Only I get to cheat.
3) No ranges of hands - we are looking for a specific hand vs. hand scenario (eg AsKh vs. Td)
4) I will reply periodically, noting whomever has the best answer as this goes on and if/when someone gets the best possible solution.