At first I disbelieved. I thought A > B. Then I wrote code myself and checked, and got that B > A. I believed this result. Then I thought about it and realized why my reason for A > B was wrong. But I still didn’t understand (and now I don’t understand either) why the described random process is not equivalent to randomly choosing 2, 4, or 6 every roll. I thought some more and now I have some doubts. My first doubt is whether there exists some kind of standard way of describing random processes and conditioning on them, and whether the problem as stated by notfnofn. Perhaps the problem is just underspecified? Anyway, this is very interesting.
At first I disbelieved. I thought A > B. Then I wrote code myself and checked, and got that B > A. I believed this result. Then I thought about it and realized why my reason for A > B was wrong. But I still didn’t understand (and now I don’t understand either) why the described random process is not equivalent to randomly choosing 2, 4, or 6 every roll. I thought some more and now I have some doubts. My first doubt is whether there exists some kind of standard way of describing random processes and conditioning on them, and whether the problem as stated by notfnofn. Perhaps the problem is just underspecified? Anyway, this is very interesting.