10 Mar '10 18:51

Two players are playing a game of one-card poker, which uses a three-card deck (Jack, Queen, King). Each player antes $1 for a total starting pot of $2, and then each player is dealt one card. The betting works as follows:

1. Player 1 goes first, and may either bet $1 or check.

2. If Player 1 bets, then Player 2 may either call the bet or fold. If Player 1 checks, then Player 2 may either bet $1 or check.

3. If Player 1 checks and Player 2 bets, then Player 1 may either call the bet or fold.

After all bets have been made, the winner collects the pot.

1. What is the optimal betting strategy for Player 1?

2. What is the optimal betting strategy for Player 2?

3. What is the expected outcome for each player using their respective optimal betting strategies?

1. Player 1 goes first, and may either bet $1 or check.

2. If Player 1 bets, then Player 2 may either call the bet or fold. If Player 1 checks, then Player 2 may either bet $1 or check.

3. If Player 1 checks and Player 2 bets, then Player 1 may either call the bet or fold.

After all bets have been made, the winner collects the pot.

**Questions**1. What is the optimal betting strategy for Player 1?

2. What is the optimal betting strategy for Player 2?

3. What is the expected outcome for each player using their respective optimal betting strategies?