Some things that make chess engines non-deterministic: 1) Most chess engines use an opening book instead of calculating moves early in the game. These books are often programmed probabilistically, so it may have 4 reasonable responses to a given move and pick one randomly. 2) Many engines are programmed to "ponder", that is do optimistic calculations during the opponents turn. This means that the time taken by you to make the move could potentially affect the calculations performed by the engine.