3 MAX X O X O X . . . MAX (X) O A 1 A 2 A 3 3 2 2 X O X - - PDF document
deterministic chance perfect information chess, checkers, backgammon go, othello monopoly imperfect information battleships, bridge, poker, scrabble blind tictactoe nuclear war MAX (X) X X X MIN (O) X X X X X X 3 MAX X O X
deterministic chance perfect information imperfect information chess, checkers, go, othello backgammon monopoly bridge, poker, scrabble nuclear war battleships, blind tictactoe
X X X X X X X X X MAX (X) MIN (O) X X O O O X O O O O O O O MAX (X) X O X O X O X X X X X X X MIN (O) X O X X O X X O X . . . . . . . . . . . . . . . . . . . . . TERMINAL X X −1 +1 UtilityMAX
3 12 8 6 4 2 14 5 2
MIN
3 A 1 A 3 A 2
A 13 A 12 A 11 A 21 A 23 A 22 A 33 A 32 A 31
3 2 2
MAX
3 12 8
MIN
3 3
MAX
3 12 8
MIN
3 2 2 X X 3
MAX
3 12 8
MIN
3 2 2 X X 14 14 3
MAX
3 12 8
MIN
3 2 2 X X 14 14 5 5 3
MAX
3 12 8
MIN
3 3 2 2 X X 14 14 5 5 2 2 3
.. .. .. MAX MIN MAX MIN V
Black to move White slightly better White to move Black winning MIN MAX
2 1 1 4 2 2 20 1 1 400 20 20
1 2 3 4 5 6 7 8 9 10 11 12 24 23 22 21 20 19 18 17 16 15 14 13 25 MIN MAX
2
CHANCE
4 7 4 6 5 −2 2 4 −2 0.5 0.5 0.5 0.5 3 −1
DICE MIN MAX
2 2 3 3 1 1 4 4 2 3 1 4 .9 .1 .9 .1 2.1 1.3 20 20 30 30 1 1 400 400 20 30 1 400 .9 .1 .9 .1 21 40.9
8 9 2 6 6 6 8 7 6 6 7 6 6 7 6 6 7 6 7 4 2 9 3 4 2 9 3 4 2 3 4 3 4 3 6 4 8 9 2 6 6 6 8 7 6 6 7 6 6 7 6 6 7 6 7 4 2 9 3 4 2 9 3 4 2 3 4 3 4 3 8 9 2 6 6 8 7 6 6 7 6 6 7 6 6 7 7 2 9 3 2 9 3 2 3 3 3 4 4 4 4 6 MAX MIN MAX MIN 8 9 2 6 6 6 8 7 6 6 7 6 6 7 6 6 7 6 7 4 2 9 3 4 2 9 3 4 2 3 4 3 4 3 6 4 8 9 2 6 6 8 7 6 6 7 6 6 7 6 6 7 7 2 9 3 2 9 3 2 3 3 3 4 4 4 4 6 6 4 8 9 2 6 6 8 7 6 6 7 6 6 7 2 9 3 2 9 3 2 3 7 3 6 4 6 6 7 3 4 4 4 6 6 7 3 4
−0.5 −0.5
MAX MIN MAX MIN MAX MIN