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Parparov Roman communicated this variant, which is his favourite variant.
The board is the usual board. The pieces move as usual. The goal is usual too - to checkmate your opponent's king.
But, the variance is that when you take an opponent's piece you must return it to the board immediately wherever you want, with the following conditions:
You can put a bishop on the square which color is different from the one bishop went on before.
So, usually the point of the game is to create a stalemated set of pieces of your opponent like Qb1, Ra1, a3, Bc1, c3, pawns d2, d3, d4, c2, b2, b3, b4, a2. There are some nice absolute stalemate positions for 15 pieces, when your pieces set out for hunt for the lonely black king.
The games usually last 50+ moves. Blitzes with 7 minute controls are fine.
The classical variations could be:
1.e4 d5 2.exd(d7)(- return the pawn to d7) d6 3.Qh5 Nf6 4.Qxf7+!(d7) and the black's queenside is feeling slightly awkward.
1.e4 e6 2.d4 c5 3.dxc(e7) blocking the bishop and the kingside.