How to convince subjects that the computer is playing fairly
I'm imagining a system that chooses the computer's response not in a stochastic manner, but chaotically. Suppose you have some chaotic mapping function from the [0,1] interval to the {heads, tails} set. Choosing any real number in the set will get you some deterministic mapping to heads or tails. This mapping equation should be quite complex, but made visible to the user. Have them choose a number in [0, 1], and you'll get an output that appears random, but could be computed if the user chose to take the time. You just need to make the mapping function complex enough that it's not easily computable to rig the game, and also such that it maps 50% to heads and 50% to tails.