Let N be a very large integer. (Ideally, N would be infinity, but this is a parable.) There are two games which are offered to Fred, the P and Q games, and he must play the one or the other. In each, a fair coin is tossed N times, whether or not Fred plays, and each time it comes up heads, Fred gets something of positive value +V, and each time it comes up tails, Fred gets something of negative value -V. In the P game, the coin tossed is a penny, and in the Q game, it's a quarter. To an ordinary person, the rational choice which game to play would be entirely arbitrary. Moreover, as it happens (based on priors and other evidence), the following three hypotheses are live, and have, let us suppose, equal probability 1/3:
(H1) Fred is perfectly self-interested, and knows exactly how each toss of each coin would go. When two outcomes are equally good, he chooses randomly. (Two sub-hypotheses that I won't distinguish: (a) The coins are indeterministic, and Fred has middle knowledge; (b) The coins are deterministic, and Fred can predict perfectly.)
(H2) Fred is perfectly self-hating (i.e., tries to minimize his own utility), and knows exactly how each toss of each coin would go. When two outcomes are equally good, he chooses randomly.
(H3) Fred has no knowledge of how future coin tosses will go and chooses which game to play at random.
You now observe that Fred chooses the P game. You also observe the first toss of the P game, and see that it's tails, while the first toss of the Q game is heads, and so Fred gets -V, but would have got +V had he played the Q game (suppose that the outcomes in the Q game aren't affected by whether Fred plays or not). You don't get to observe any further steps in the game.
Question: How should your observation affect your probabilities of the three hypotheses?
The qualitative intuitive answer is easy. Your observation does not affect the probability of H3 at all. It increases the probability of H2 by exactly the amount by which it decreases the probability of H1. If, however, H1 were initially more probable than H2, as typically it would be, then the probabilities of both H2 and H3 would be increased.
But the interesting question is as to the details: Just how much do the probabilities change?