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I find it interesting that the Queen can move with the same capabilities as the Rook and the Bishop, but cannot 'jump' or move like the Knight, I understand that this would overpower the queen but theoretically could make the game more interesting, quicker, or more strategic.

I want to know, what are the practical implications of giving the Queen this extra move-set?

Are there any obscure chess variations where this is allowed?

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    One practical implication would be that it could checkmate an enemy king at the edge of the board without help from any other piece. – RemcoGerlich Feb 1 '15 at 21:33
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Are there any obscure chess variations where this is allowed?

There are. One name for the queen+knight hybrid piece is the Amazon. As noted in the Wikipedia entry on the Amazon piece I just linked to, the Amazon appears in the variant sometimes called Turkish Great Chess, a game played on a 10x10 board and featuring besides the Amazon (which is typically called a Giraffe in Turkish Great Chess) two other fairy chess pieces: a bishop+knight piece (Vizir) and a rook+knight piece (War Machine). (Those sorts of pieces appear under yet different names in the Capablanca Chess and Seirawan Chess variants as well.)

Turkish Great Chess

A second variant that is mentioned in the Amazon Wikipedia entry is The Maharaja and the Sepoys, which provides a severe test for the might of the Amazon: namely, it pits a lone Amazon (Maharaja) against a standard chess army on an 8x8 board. An Amazon is capable of checkmating a king by itself, and that is its objective, while the standard army is tasked with checkmating the very mobile Amazon.

Maharaja and the Sepoys

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