This variant of NIM(n) is played by two players, who alternate of removing one or two stones/coins from a heap of originally n stones or coins. Between these moves, one stone or coin is remvoed randomly with probability 1/2. The player who cannot move anymore, since no stones/coins are left, loses.

White to move
Black to move
White wins !!!!!
Black wins !!!!!
Randomly remove nothing
Randomly remove one stone