materials (including lectures and notes and homework). You must show all your work, step by step. Late submissions will not get full credit! Make a game tree for the game of Nim with starting position one pile of height 3 and two piles of height 1. Which player (Max or Min) has the optimal strategy to win and what should their first move be? Extra credit problem [1.5pts] Suppose they are playing "opposite Nim (with the same piles as before), where you win if there is nothing left, at which point your payoff is $m, where m is the level at which this happens (remember that the game starts with Max playing at level 0). What is the optimal strategy for Max (will he win or loose?). materials (including lectures and notes and homework). You must show all your work, step by step. Late submissions will not get full credit! Make a game tree for the game of Nim with starting position one pile of height 3 and two piles of height 1. Which player (Max or Min) has the optimal strategy to win and what should their first move be? Extra credit problem [1.5pts] Suppose they are playing "opposite Nim (with the same piles as before), where you win if there is nothing left, at which point your payoff is $m, where m is the level at which this happens (remember that the game starts with Max playing at level 0). What is the optimal strategy for Max (will he win or loose?)