PART 1 • A tree of possibilities
new chess positions. After Black's first reply, that number increases to
exactly 900 possible positions. Assuming exactly thirty possible moves
in each new board position, watch what happens to the numbers each
time the players go one half-move (one ply) ahead:
White's first move
Black's first move
White's second move
Black's second move
White's third move
Black's third move
White's fourth move
Black's fourth move
(1 ply):
(2 ply):
(3 ply):
(4 ply):
(5 ply):
(6 ply):
(7 ply):
(8 ply):
30 positions
900 positions
27,000 positions
810,000 positions
24,300,000 positions
729,000,000 positions
21,870,000,000 positions
656,100,000,000 positions
I wanted to keep going, but black smoke started rolling out of my
calculator. If you don't believe the numbers, try it yourself (but quit when
you see smoke). In our imaginary position, after just four moves for both
players (eight plies, in computer chess terms), there are more than six
hundred and fifty billion possible board positions, billions of combinations
of pieces on the board. So the next time you meet a strong chess player
and he claims that he sees “everything” four moves ahead, you have my
permission to say, “Liar, liar, pants on fire!” (And if you want his pants to
really be on fire, do all of that multiplication on your calculator again and
then stick it in his back pocket when he's not looking.)
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