I figured that if Omega is required to try its best to predict you and you are permitted to do something that is physically random in your decision making process, then it will probably be able to work out that I am going to choose just one box with slightly more probability than choosing 2. Therefore, it will gain the most status on average (it MUST be after status since it obviously has no interest in money) by guessing that I will go with one box.
I figured that if Omega is required to try its best to predict you and you are permitted to do something that is physically random in your decision making process, then it will probably be able to work out that I am going to choose just one box with slightly more probability than choosing 2. Therefore, it will gain the most status on average (it MUST be after status since it obviously has no interest in money) by guessing that I will go with one box.
.51 1000000 + .49 1001000 = 1000490