The reason the game is known as Bogus Nim is that some moves may increase the size of one of the heaps. If this happens, such an increase may be immediately countered by reduction to the previous size. The winning player has no need in those moves. As the foregoing argument shows, the losing player gains nothing by increasing one of the heaps. The heap increasing moves are known as reversible. They are harmless because they may be only made a finite number of times, so that, like Nim, Bogus Nim is liable to terminate.
- J. H. Conway, On Numbers And Games, A K Peters, 2001
- R. K. Guy, fair game, Comap's Explorations in Mathematics, 1989
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