Quiz May 10 ‘07 Games

MAX coin: p(left)=1/4 MIN coin: p(left)=1/2 Assume that MAX and MIN are rational players. a) [4pts] What is the expected minimax value at the root (the score) for MAX when s/he plays this game? b) [2pts] What should MAX’s first move be? c) [4pts] For a single game and again assuming rationality, is it possible that MAX will ever score: I) 10, II) 15, III) 3, IV) 13 ? Explain your answer. L R

Solution a)35/4 = 8.75 b)MAX should make the move to the right c)I) No, MIN will never make a move that leads toward 10 for MAX II) No, MIN will never make a move that leads toward 15 for MAX III) Yes, since MIN will make a move that might lead to a terminal state with value 3 for MAX IV) Yes, since MIN will make a move that might lead to a terminal state with value 13 for MAX