 While the player is still in the first stage, they are presumably able to influence the predictor's prediction, for example by committing to taking only one box.Burgess argues that after the first stage is done, the player can decide to take both boxes A and B without influencing the predictor, thus reaching the maximum payout.This assumes that the predictor cannot predict the player's thought process in the second stage, and that the player can change their mind at the second stage without influencing the predictor's prediction.