You might also find the following cases interesting (with self-locating uncertainty as an additional dimension), from this post.
Sleeping Newcomb-1. Some researchers, led by the infamous superintelligence Omega, are going to put you to sleep. During the two days that your sleep will last, they will briefly wake you up either once or twice, depending on the toss of a biased coin (Heads: once; Tails: twice). After each waking, they will put you back to sleep with a drug that makes you forget that waking. The weight of the coin is determined by what the superintelligence predicts that you would say when you are awakened and asked to what degree ought you believe that the outcome of the coin toss is Heads. Specifically, if the superintelligence predicted that you would have a degree of belief pin Heads, then they will have weighted the coin such that the ‘objective chance’ of Heads is p. So, when you are awakened, to what degree ought you believe that the outcome of the coin toss is Heads?
Sleeping Newcomb-2. Some researchers, led by the superintelligence Omega, are going to put you to sleep. During the two days that your sleep will last, they will briefly wake you up either once or twice, depending on the toss of a biased coin (Heads: once; Tails: twice). After each waking, they will put you back to sleep with a drug that makes you forget that waking. The weight of the coin is determined by what the superintelligence predicts your response would be when you are awakened and asked to what degree you ought to believe that the outcome of the coin toss is Heads. Specifically, if Omega predicted that you would have a degree of belief pin Heads, then they will have weighted the coin such that the ‘objective chance’ of Heads is 1−p. Then: when you are in fact awakened, to what degree ought you believe that the outcome of the coin toss is Heads?
You might also find the following cases interesting (with self-locating uncertainty as an additional dimension), from this post.