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The rules of antichess specified in Wikipedia state that the rules of regular chess should be followed except

 Capturing is compulsory.
 When more than one capture is available, the player may choose.
 The king has no royal power and accordingly:
     it may be captured like any other piece;
     there is no check or checkmate;
     there is no castling;
     a pawn may promote also to king.
 Stalemate is a win for the stalemated player.

It doesn't specifically call out who would choose what piece a pawn gets promoted to. It makes sense to me that since the game is antichess, when you promote a pawn it is a bad thing and your opponent would get to choose what piece it should be. Is this the correct way of playing or do you get to promote your own pawns?

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Your summary of the rules left out an important one, namely, how else can you win a game besides being stalemated. The answer is that the player who runs out of men wins. (I suppose you could consider having no men to move a kind of stalemate.) And "antichess" is a new name for the chess variant traditionally known as Losing Chess or Giveaway Chess.

The answer to your question is that, when a pawn reaches the 8th rank, the owner of the pawn decides what to promote it to. I have looked at several books on chess variants, and haven't found a clear statement on that point. Apparently, it never occurred to the writers that anyone would think that the opponent gets to choose the promotion rank.

The rules for Losing Chess at The Chess Variant Pages (surely a more authoritative source than Wikipedia) do not say anything about the opponent choosing the promotion rank of a promoted pawn. Some of the endgame studies in John Beasley's article involve pawn promotion, and it's clear that the owner of the pawn is doing the choosing. Here's one from Hans Klüver (Chess Amateur 1923):

[FEN "8/P6/8/k7/P7/8/8/8 - - - 0 0 "]

Losing Chess. White to play and "win".

The solution:

1.a8N! Kxa4 2.Nb6 any 3.Na4 Kxa4

Of course if Black controlled the promotion he would choose a queen or rook.

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    Thanks for the thorough answer. I have an app that uses the same rule but I usually play that the other way. It definitely changes my strategy when playing. – tgarner Jan 28 '14 at 2:48
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    Can you choose to promote to a pawn or in other words not promote? – Joshua Sep 10 '18 at 23:34
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    @Joshua I always understood that a pawn can promote to K, Q, R, B, or N. – bof Sep 10 '18 at 23:41

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