I see it in a similar way and think about it in the following two steps. First convince the predictor that you will either choose AB or B - and he will always p

I see it in a similar way and think about it in the following two steps. First convince the predictor that you will either choose AB or B - and he will always predict exactly this - then actually choose either AB or B, but both choices are not necessarily the same. Of the four possibilities you can safely ignore AB-B because it is worse then unproblematic AB-AB. If you want the million you have to convince the predictor that you will choose B and that means you have to either do B-B or B-AB. But you can only perform B-AB if you manage to fool the predictor and especially you can not do B-AB in a deterministic universe without free will (let's ignore that you don't even have control over the first step in that scenario). B is definitely the right choice in the first step and then changing to AB is the best choice in the second step, but whether you can actually do this depends on your stance on free will and the like.