Author: Shep
Date: 00:45:18 01/26/00
Go up one level in this thread
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. --- Shep --- Shep
This page took 0 seconds to execute
Last modified: Thu, 15 Apr 21 08:11:13 -0700
Current Computer Chess Club Forums at Talkchess. This site by Sean Mintz.