# Game Playing Consider the following game: When it is their turn to move, players must first choose w 1 answer below »

Game Playing

Consider the following game:

When it is their turn to move, players must first choose which of two weighted coins,

A and B, to flip.

Coin A comes up heads 75% of the time and tails the other 25%.

If heads, the player must make move AH and if tails he or she (or it) must make move AT.

(To do this problem, you neednt know exactly what each move means.)

Coin B comes up heads 10% of the time and tails the other 90%.

If heads, players must make move BH and if tails they must make move BT.

Assume it is the computers turn to play, and the game tree looks like the one below, where the values at the leaf nodes are the results of calls to the utility function, SBE (higher scores are better for the computer).

(1)  Explain what move the computer should make.

(Hint: think about expected-value calculations. Also, you might want to do parts it b and c first.)

(2)  Now assume that there is no randomness and the players simply can choose any of the four moves (AH, AT, BH, or BT). Apply the minimax algorithm to the tree below and explain which move the computer should make. As in part (a), assume it is the computers turn to play. Show transcribed image text Game Playing Consider the following game: When it is their turn to move, players must first choose which of two weighted coins, A and B, to flip. Coin A comes up heads 75% of the time and tails the other 25%. If heads, the player must make move AH and if tails he or she (or it) must make move AT. (To do this problem, you neednt know exactly what each move means.) Coin B comes up heads 10% of the time and tails the other 90%. If heads, players must make move BH and if tails they must make move BT. Assume it is the computers turn to play, and the game tree looks like the one below, where the values at the leaf nodes are the results of calls to the utility function, SBE (higher scores are better for the computer). (1)  Explain what move the computer should make. (Hint: think about expected-value calculations. Also, you might want to do parts it b and c first.) (2)  Now assume that there is no randomness and the players simply can choose any of the four moves (AH, AT, BH, or BT). Apply the minimax algorithm to the tree below and explain which move the computer should make. As in part (a), assume it is the computers turn to play.