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Buypoint Chess. Buy your fighting force - each piece costs a number of points.[All Comments] [Add Comment or Rating]
Rodrigo Zanotelli wrote on 2013-03-12 UTC
With all paws being on their original positions, all players having 31 points to spend (and having to spend exactly 31 points), players being able to choose at max 3 rooks (to not mess with castling rules) and being able to choose at max 7 pieces (the back rank): Each player would be able to choose 7 different ways of starting the game.

The math and the positions on wolfram alpha:

Of course this assumes that choosing the same pieces, will produce the same starting position. With players that brought the pieces being able to choose where each piece will start this number will be higher.