I think the analysis for “bomb” is missing something.
This is a scenario where the predictor is doing their best not to kill you: if they think you’ll pick left they pick right, if they think you’ll pick right they’ll pick left.
The CDT strategy is to pick whatever box doesn’t have a bomb in it. So if the player is a perfect CDTer, the predictor is 100% guaranteed to be correct in their pick. The predictor actually gets to pick whether the player loses 100 bucks or not. If the predictor is nice, the CDTer gets to walk away without paying anything and a 0% chance of death.
I think the analysis for “bomb” is missing something.
This is a scenario where the predictor is doing their best not to kill you: if they think you’ll pick left they pick right, if they think you’ll pick right they’ll pick left.
The CDT strategy is to pick whatever box doesn’t have a bomb in it. So if the player is a perfect CDTer, the predictor is 100% guaranteed to be correct in their pick. The predictor actually gets to pick whether the player loses 100 bucks or not. If the predictor is nice, the CDTer gets to walk away without paying anything and a 0% chance of death.