[Retros] Number of positions and games. Yefim 02/09/2005

TregerYefim at aol.com TregerYefim at aol.com
Wed Feb 9 11:26:04 EST 2005

Hello from Yefim!
I am preparing my opinion at your S(PG) question. But before that
I want to give two easy ways to calculate upper bound of number of positions
and a way of calculating PG (or all games).
1. There are 13 distinctive pieces and 64 squares. Number 13^64 gives us
amount of
diagrams. Multiplying it by 288 (turn to move, castling and e.p. properties)
we get A<=288*13^64; approx=6*10^73;
2. Let all 32 pieces be in a box and we begin setting them on (at first)
empty board (64), them
on 63 board, and so on. This gives us:
64*63*...*34*33=64!/32! (amount of diagrams)
Also, multiplying by 288 we get:
288*64!/32! aprox=1,4*10^56;
3. Upper bound of games. Let 32*27=1024 number of moves in every position (27
is maximum for Queen).
Then 1024^1,4*10^56 gives us amount of games (assuming all positions are in
every game in any order, no repetitions...).

All of this are not very big numbers and I am sure somebody's computer will
find those positions and S(PG) for them:). Good luck!
Yefim 02/09/2005
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