I can be more interesting reframed as such:

The player is the AI, and the predictor is the AI programmer.

The AI programmer can look into the innards of the AI ie. the source code and can thus predict with high accuracy what the AI will do.

What is a winning strategy for the AI?

Or taken another way, you can have AI's that have access to each other's source code and are competing for some scarce resource, how do you design an AI that 'wins' when it's behaviour is known it's opponent?