Play RANDOM NIM(n,p) against the computer

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.

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

with initial stones, and probability

Results: