Exercise $5\mathrm{.}1.$#PHGM

Discuss how well the standard approach to game playing would apply to games such as

tennis, pool, and croquet, which take place in a continuous physical state space.

Exercise $5\mathrm{.}3.$#TPNZ

Describe how the minimax and alpha$-$beta algorithms change for two$-$player, non$-$zero$-$

sum games in which each player has a distinct utility function and both utility functions are

known to both players. If there are no constraints on the two terminal utilities, is it possible

for any node to be pruned by alpha$-$beta? What if the player's utility functions on any state

sum to a number between constants $-k$ and $k,$ making the game almost zero$-$sum?

$3,$

Exercise $5\mathrm{.}3.$#CHET

Suppose you have a chess program that can evaluate $5$ million nodes per second. Decide

on a compact representation of a game state for storage in a transposition table. About how

many entries can you fit in a $32-$gigabyte in$-$memory table? Will that be enough for the three

minutes of search allocated for one move? Can you estimate how many table lookups can

you do in the time it would take to do one evaluation?