Game Nim

The game of Nim(N,m,k) involves m players who begin with a pile of N stones and alternate turns, removing stones from the pile. Each player must remove between 1 and k stones on their turn. The objective is to avoid taking the last stone. We will look at the case when N = 51, m = 2, and k = 3. We have a small finite number of states(N+1 states), and action space only includes k actions {1,2,3}, that is, the number of stones that can be removed from the game.

Configuration:

I trained the QLearner versus a Random player, 1e4 iterations. With the following parameters:

• N=51; k=3; m=2; Discount= 0.99; Alpha= 1/sqrt(n+2); n: #iterations epsilon=1-(1/log(n+2))

• Q-Learner always starts the game.

• Tested the Q-Learner against a random player 1e3 times.

It wins around 99% of the time.