Example 2. (Card game) Each of two players begins by putting a dollar in the pot. Player 1 is then dealt a card that is equally likely to be High or Low, she observes her card, but player 2 does not. Player 1 may see or raise. If she sees, she shows her card to player 2. (Player 2 does not have any card for player 1 to see, but you can imagine her holding a fixed card with value between High and Low.) If player 1's card is High she takes the money in the pot, and if it is Low player 2 takes the money in the pot; in both cases the game ends. If player 1 raises, she adds a dollar to the pot and player 2 chooses whether to pass or meet. If player 2 passes, player 1 takes the money in the pot. If player 2 meets, she adds a dollar to the pot, and player 1 shows her card. If the card is High, player 1 takes the money in the pot, while if it is Low player 2 does so. High (1/2) 1,-1- See b Raise Chance Low (1/2) See -1, 1 Raise 2. Pass Meet Pass Meet 1,-1 2,-2 1, -1 -2,2 Figure 2. An extensive game that models the card game. The number in parentheses beside each label of the moves of chance is the probability with which that move occurs. An extensive game that illustrates this situation is shown in Figure 2. Player 1 has two information sets, one containing the single history High or node b, and one containing the single history Low or node c. Player 2 has one information set, consisting of the two nodes d (or history (High, Raise)) and e (or history (Low, Raise)). This information set reflects the fact that player 2 cannot observe player 1's card. Note that the requirement that the set of action at every history (or node) within an information set be the same is satisfied at player 2's information set.