I think that about 25% of the time there is no "fake" coin. Either that or the weight differential is so small as to be negligible with lots of coins on the scale.
Upon further review - I'm just not that good at the game.
We've posted an update.
1) solve the problem you mentioned
2) ensure that the game will be lost if a wrong move is made
3) make the result more random if a correct move is made
de Novel Games