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

[TregerYefim at aol.com]

       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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