Node 10 Black Node 6 UP is Black (gain $1) DOWN is Red (lose $1) Red Black Node Node 11 Red Black Black Node 1 Node 7 Red Red Black Black Start- Node 0 Node 4 End - Nede 12 Red Red Black Black Node 2 Node 8 Red Red Black Node 5 Node 13 Red Black Node 9 Red Node 14 Problem Use backwards induction to solve for the profit to player from this game of 4 cards. Solution Determine probability of each path. Work backwards: node 12, 7, 8, 3, 4, 5, 1, 2, 0. Compare cash in hand to expected value to decide to play or to stop. Hint The value for 2-cards is $0.50. And the value for 52-cards is $2.52. The value for 4-cards is in between these values. Questions 1. What is the expected profit at node 0 (value of the game)? 2. What is the most money the player can receive and what cards would produce this? 3. What is the most money the player can lose? 4. Where did we use iterated expectations? 5. Where did we use rational expectations? 6. What is the most you would pay to play this game? Node 10 Black Node 6 UP is Black (gain $1) DOWN is Red (lose $1) Red Black Node Node 11 Red Black Black Node 1 Node 7 Red Red Black Black Start- Node 0 Node 4 End - Nede 12 Red Red Black Black Node 2 Node 8 Red Red Black Node 5 Node 13 Red Black Node 9 Red Node 14 Problem Use backwards induction to solve for the profit to player from this game of 4 cards. Solution Determine probability of each path. Work backwards: node 12, 7, 8, 3, 4, 5, 1, 2, 0. Compare cash in hand to expected value to decide to play or to stop. Hint The value for 2-cards is $0.50. And the value for 52-cards is $2.52. The value for 4-cards is in between these values. Questions 1. What is the expected profit at node 0 (value of the game)? 2. What is the most money the player can receive and what cards would produce this? 3. What is the most money the player can lose? 4. Where did we use iterated expectations? 5. Where did we use rational expectations? 6. What is the most you would pay to play this game