Play RANDOM NIM(n,p) against the Computer

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

Your move
Computer to move
You win !!!!!
Computer wins !!!!!
Randomly remove nothing
Randomly remove one stone

with initial stones, and probability

Erich Prisner, 2012