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New combinatorial games are introduced, of which the most pertinent isMaharaja Nim. The rules extend those of the well-known impartial game ofWythoff Nim in which two players take turn in moving a single Queen of Chess ona large board, attempting to be the first to put her in the lower left corner.Here, in addition to the classical rules a player may also move the Queen asthe Knight of Chess moves. We prove that the second player's winning positionsof Maharaja Nim are close to the ones of Wythoff Nim, namely they are within abounded distance to the lines with slope $\frac{\sqrt{5}+1}{2}$ and$\frac{\sqrt{5}-1}{2}$ respectively. For a close relative to Maharaja Nim,where the Knight's jumps are of the form $(2,3)$ and $(3,2)$ (rather than$(1,2)$ and $(2,1)$), we also demonstrate polynomial time complexity to thedecision problem of the outcome of a given position.

Maharaja Nim, Wythoff's Queen meets the Knight