BrainKing - Forum di discussione (Chess variants (10x8))

Chess variants (10x8)

Sam has closed his piano and gone to bed ... now we can talk about the real stuff of life ... love, liberty and games such as
Janus, Capablanca Random, Embassy Chess & the odd mention of other 10x8 variants is welcome too

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... speculation on who has an advantage or the benefits of potential moves is not permitted while that particular game is in progress)
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6. Novembre 2003, 04:35:40

Grim Reaper

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Argomento: Re: Total Number of Gothic Chess Positions

More on the pawn count...

Originally I had the non-captured pawn permutaion count at 774,468,423,574,600,034,220 which, as Thad pointed out, seems a little high. When using the concept of the "rammed pawns" constrained to a rank, there are actually 30 different configurations possible per file.

You can have an unmoved pawn in the a-file on a2, and the black pawn can be one of 5 different squares in the same file, a7,a6,a5,a4 or a3. If the white pawn were on a3, then there are 4 squares for the black pawn, etc.

There are always 5-r permutations for the black pawn for each rank of displacement, r, the white pawn has moved.

So, there are 5+4+3+2+1 = 30 possible configurations per file. The total number of permutations is therefore 30^10, which is 590,490,000,000,000. This is only 590 trillion, a lot less than 774 quintillion!