I came across the following thought experiment, and I would like to understand whether the controversy around it is justified.
Imagine an experiment in which a mathematician is put to sleep with some kind of drug. He is located in a room that is designed in such a way as to keep him completely isolated from any kind of external information. The researchers have a sleep inducing drug that is able to put you to sleep and make you forget it was even administered. After the researchers have put the mathematician to sleep with this drug, they toss a fair coin. If it comes up heads they will wake the mathematician up once and administer the drug again. If it comes up tail they will wake him up twice, each time administering the drug again.
Whenever the mathematician is awoken during the experiment, they will ask him for his best guess regarding the result of the coin toss. Eventually the experiment ends, and the researchers will awaken the mathematician a final time and tell him the experiment has ended. During the experiment, what answer should the mathematician give as his best guess for the result of the coin toss ?
I think he should say that odds are the coin came up tail, but I am very curious what other people make of it, and whether there are any grounds for dissent at all.