On average, there'll be 50 units on the list that match Alice's claimed outcome, so bob does know with a 1/50 chance what Alice's unit was... Alice also knows the strength of bob's unit, in that she knows the results for 100 hypothetical battles against it... Actually, maybe this isn't a good idea at all ;-/
Some online card games work this way, and it should be extendable to any game with deterministic rules, as long as you're ok with deferring cheat detection until the very end of the game, when it's ok to reveal all the secrets. In a many-player game, if one player drops out half way through, there's no way to validate their actions (unless everyone gives their keys to a trusted 3rd party at the start).
both players exchange encrypted piece positions with each other at game start. at game end, the decryption keys are exchanged to determine if they had been telling the truth.