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This game is a subset of "pawn can only promote to dead pieces not placed back on the board". In this game, you do not have a choice of promotion (you have to promote into the first one available); normally if you play "pawn can only promote to dead pieces not placed back on the board", you can choose which one if there is more than one option.
One version of this "pawn can only promote to dead pieces not placed back on the board" variant already exist here called a modest proposal ( http://chessvariants.org/other.dir/modest-various.html ) On modest proposal pawn can promote on 7th and 8th rank, but only promote if they want and stay there immobile if they dont do it. then if they have some dead piece not placed back on the board" they can promote to one of those pices. I said "One version of this..." because there are MANY ways of doing it 1-Pawn cant go to last square if there inst pieces to promote. 2-Pawn can go to last square in this case and just sit there immobile, forever. 3-Pawn can go to last square, you pass all your next turns, until enemy capture one of your pieces making you able to promote, you lose or there is a draw. 4-Pawn can go to last square, and sit there immobile, until you lose a piece and that allow you to promote, if more than one pawn on last square, first ones to reach that square promote to this piece and others dont. 5-Pawn can go to last square, and sit there immobile, until you lose a piece and that allow you to promote, if more than one pawn on last square, you can select wich pawn will promote to the piece. 6-Pawn can go to last square, and sit there immobile, until you lose a piece and that allow you to promote, if more than one pawn on last square and you lose some piece all pawns on the last square promote at the same time to this piece. Rule 6 is a special rule, this kind of variant here, is usually made with the idea "i need more pieces to play chess than the ones that will come with the game (if you want to be exact 8 extras, bishops, queens, rooks and knights to each side)" and rule 6 dont fix this problem, if you have 3 pawns at last rank and no dead piece and then you lose a queen, you will need 2 extra queens to put in the place of the 2 extra pawns at last rank.
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