Author: J. Wesley Cleveland
Date: 12:07:41 01/26/00
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On January 26, 2000 at 03:45:18, Shep wrote: >On January 26, 2000 at 00:42:33, Les Fernandez wrote: > >>Does anyone know what the maximum number of pieces for Knight, Bishop, Rook and >>Queens that can legally be arrived at in a game. For instance I think I >>remember a post which talked about it but that was some time ago. It mentioned >>something about if white had (ie 9 queens then black could only have ????) If >>someone has this information and can clearly list the variations for one side >>having the max # of a particular piece and what the opposite side can have as a >>max # I would really appreciate it! > >If my maths are not completely wrong, it's not so hard: >Let's first consider the "obvious" case: >the maximum number of pawns that can promote is 8 (rather trivial to see: >for each pawn to promote, one opponent pawn must be removed from the respective >file). >So both sides combined can have a maximum of 8 extra Q/R/N/B. >Thus the maximum number of pieces on the board is: > queens 2+8=10 > rooks/bishops/knights= 4+8=12 > >Now there's a catch: e.g. White can promote its b-pawn without black having to >remove its b-pawn! All you have to do is this: > 1. move the black b-pawn to b5 > 2. move the white b-pawn to the c-file by capturing a black piece on the >c-file. > 3. advance the pawn to c5, then capture another black piece on b6 => voila! >However, although this method allows you to promote *all* 16 pawns, it also >involves capturing pieces, and each side only has 8 non-pawn pieces to capture, >so it's not hard to see you're not actually "winning" anything (i.e. getting any >extra pieces) this way. >Because, suppose you're promoting all 8 black pawns plus an extra white pawn >using the method above, then you'd have to capture two black pieces, so although >the number of QRNB increases by one by promotion, it decreases by 2 due to the >two captures needed. > >q.e.d. You are doing an extra capture here. e.g. d4 c5 d5 nc6 dc6 and now both the white pawn at c6 and the black d pawn can queen. I believe (but have not tried) that with 8 captures you can have all 16 pawns promote.
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