The bathtub is winnable. And you can master the whole game by just overthinking a bit.
For example: If you won a round by cutting paper with scissors, you don't choose paper after that, you choose stone. The AI thinks you will choose paper, after you chosed scissors, because you will think it chooses stone. A bit abstract, but it worked most of the time quite well. Just put some points in charisma and you will win a lot faster.