Re: Maximum possible chess moves
- From: hrubin@xxxxxxxxxxxxxxxxxxxx (Herman Rubin)
- Date: 10 Jan 2006 14:12:34 -0500
In article <1136876689.653126.208400@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Proginoskes <CCHeckman@xxxxxxxxx> wrote:
>Jose Capco wrote:
>> Dear NG,
>> I dont know if this has already been discussed before, but I'll just
>> write the problem here. It could be placed in a more suitable
>> newsgroup, but I only frequently post here and this is still a
>> combinatoric problem.
>> We were discussing with a few fellow chessmates in the the chess-server
>> (FICS) about the longest possible chess moves that can be done
>> deliberately by two chess player while still following the rules of
>> chess. Most important to note is the 50 move rule, which says that a
>> game is a draw if upon the 50th move there is no pawn move or exchange
>> of pieces and the draw is claimed after the 50th move (and we assume
>> this will be done if it happens). Someone came with a wild number 5980
>> or a few figures higher, but I couldnt follow his line of thought. I
>> thought I pose this problem here for the combinatorics and chess
>> enthusiast :)
>This should be in the FAQ.
>Several replies have been given, with different numbers, and I will add
>one more; this one has a reference, though, so you can read it at your
>leisure, if your local university gets the Journal of Recreational
>Mathematics. This answer depends on the K+N+N vs. K+P being given 100
>moves, as opposed to 50.
>In "The Longest Game" (Journal of Recreational Mathematics, Vol 14(4),
>1981-82, pp. 241-245), Sidney J Rubin gives 6148 as an answer.
>He also gives the longest game at the grandmaster level as 193 moves,
>by Mashian-Stepak. However, in 1989, this was surpassed by Ivan Nikolic
>and Guran Arsovic, who played a game lasting 269 moves. This record may
>also have been broken.
> --- Christopher Heckman
I have seen chess problems which require many hundreds of moves.
Consider the following situation; each player is down to a
king and a rook. Suppose the kings are in their home rows,
and the rooks are in fixed columns, not occupied by the
kings. Then there are 7 positions for each rook not
resulting in check, or 49 pairs of positions. Let us say
that each of these 49 pairs of positions is occupied 49
times, to avoid the 50 move rule. Now also each rook has
at least 6 columns not blocked by the king (those columns
can be used as well, but it gets more complicated) or
checking the opposing king, and this would leave at least
30 pairs of columns, assuming the rooks are on different
columns. I have also not considered which columns the
kings occupy; this would give another factor of 64, and
changing the rows would give another factor of 64; I have
overestimated slightly on adjacent rows or the same row,
but other considerations should more than cover this.
So we now have 49x49x30x64*64=295034880 as a lower bound.
It is harder to compute if we have other pieces as well,
but I would be surprise if we could not at least square
this number.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@xxxxxxxxxxxxxxx Phone: (765)494-6054 FAX: (765)494-0558
.
- References:
- Maximum possible chess moves
- From: Jose Capco
- Re: Maximum possible chess moves
- From: Proginoskes
- Maximum possible chess moves
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