Re: How many chess games are there?...and who wins?

On 27 Nov 2006 21:33:10 -0800, "Reef Fish"
<large_nassua_grouper@xxxxxxxxx> wrote:


Ray Johnstone wrote:
How many chess games are there?...and who wins?

I resign. My opponent wins. There could be infinitely many such
games except I probably won't live that long.

http://members.iinet.net.au/~ray/Chessgames.htm

ray@xxxxxxxxxxxx
www.iinet.com.au/~ray

It appeared you already had done the research on the solution to
this problem you posed to this lowly group of mostly non-mathe-
maticians.

If not for the chess law of "at most 50 moves", the count would be
infinite because if we are down to King and Rook each, there
must be infinitely many different moves that are not perpetual
checks but cycles of moves that will never end.

Given that idea, I find your QUESTION of counting number of
different games require some kind of additional conditions, such
as "must each player attempt to win"?
No, it includes for example Fool's Mate where Black's second move is
mate.But maybe even here White was trying to win.
If not, then each move
will have a tremendous number of POSSIBLE pieces of possible
locations nearly all of which are silly but valid moves that will lead
to a loss.

Perhaps Ramanujan had that kind of "possible valid moves" in
mind when he did the counting to 10^10^50, while Hardy thought
Ramanujan was off by a factor of 10^10^45. :-) On any
mathematical count, I put my money on Ramanujan, whom
Erdos rated 100 as a mathematician while he rated himself only
25, and Littlewood of Hardy and Littlewood 50.
I don't think Ramanujan said anything about the number of games.

In any event, I think the counting of chess moves and hence number
of possible games, a question that requires a tighter definition of
what constitutes a move, in counting the total number of possible
50-move games.
The laws of chess define the chess move(s).
"50-move" refers to the drawn game resulting from 50 moves without a
capture or pawn move.

-- Reef Fish Bob.

ray@xxxxxxxxxxxx
www.iinet.com.au/~ray
.

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