[JoshCole]

For some calculations you can make them simpler and do them faster, but for other calculations you can't. When two things that try to predict things by making things simpler apply themselves to predicting each other... well.

In order to think about this sensibly you have to think through the consequences of the infinite self-reference. Logic fails here. So does evidence. For example if you observe that your opponent is playing badly, modeling them as a bad player doesn't work, because if you choose to do this, they could exploit the bad model by playing better than that model would predict. So even though the evidence suggests that they are a bad player, the self-reference considerations forces you away from acting as if they actually are.

So lets say you play rock? They play paper. Lets say you play scissors? They play rock. Lets say you play paper. They play scissors.

Lets say you fully determine everything they are going to do using your complete knowledge of physics and you play rock because your model told you that they would play scissors... They will play paper; obviously.

Lets say you anticipate that and you play scissors. Then they play rock. As long as you claim that you can figure everything out, it means they could figure everything out. The harder you push against this, the harder it pushes back. You have to move with the force, diverting it, not fight against it. You've got to take advantage of the inevitability of being unable to overpower, not try to overpower. You have to act as if you can do everything at once, because the undecidability allows you to do so. Not try to determine everything, because if you try to, then you can't, because others try to do the same thing.