Why should we talk and write about variants of chess ? The normal chess is difficult enough and not yet fully understood, so let's be glad to improve on that game.
But anyhow, 1) Fairy Chess has non-orthodox pieces, combining e.g. Q+N, R+N and B+N. 2) Barasi Chess 3) Progressive or Scottish Chess 4) Protean or Frankfurter Chess 5) Marseillaise or double-move Chess 6) Cylindrical Chess 7) Snooker Chess 8) Reverso 9) Varied baseline Chess 10) Burmese Chess 11) Rifle Chess 12) Pocker Knight Chess and EIGHTEEN more variants, to be found in " The even more Complete Chess Addict "
You understand that I am against any variant, so I am not making clear any details.... Perhaps Chessopedia can help you !
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