Two players ante $1. Player I is dealt an Ace or a Two with equal probability.

Two players ante $1. Player I is dealt an Ace or a Two with equal probability.

Player I sees the card but player II does not. Player I can now decide to Raise, or Fold. If he Folds, then player II wins the pot if the card is a Two, while player I wins the pot if the card is an Ace. If player I Raises, he must add either $1 or $2 to the pot. Player II now decides to Call or Fold. If she Calls and the card was a Two, then II wins the pot. If the card was an Ace, I wins the pot. If she Folds, player I takes the pot. Model this as an extensive game and solve it using Gambit.
Two players ante $1. Player I is dealt an Ace or a Two with equal probability.