Artificial Intelligence and Soft Computing: Behavioral ... - Arteimi.info

MIN move
MAX move
MIN
move
MAX move
MIN move
MAX move
Symbol: Minimizer’s move , Maximizer’s move
Fig. 4.12 (a): State Space for the NIM game.
7
6+1 5+2 4+3
5+1+1 4+2+1 3+2+2 3+3+1
4+1+1+1
3+2+1+1 2+2+2+1
3+1+1+1+1 2+2+1+1+1
2+1+1+1+1+1
In the MINIMAX algorithm, to be presented shortly, the following
conventions will be used. The MAXIMIZER’s success is denoted by +1,
while the MINIMIZER’s success by -1 and a draw by a 0. These values are
attached with the moves of the players. A question then naturally arises: how
do the players automatically learn about their success or failure until the game
is over? This is realized in the MINIMAX algorithm by the following
principle: Assign a number from {+1, 0, -1} at the leaves depending on
whether it is a success for the MAXIMIZER, MINIMIZER or a draw
respectively. Now, propagate the values up by checking whether it is a
MAXIMIZER’s or MINIMIZER’s move. If it is the MAXIMIZER’s move then
its value wiil be the maximum value possessed by its offsprings. In case it is
a MINIMIZER’s move then its value will presume the minimum of the values
possessed by its offsprings.