Nate Soares's distilled exposition of the Ultimate Newcomb's Problem, plus a quick analysis of how different decision theories perform, copied over from a recent email exchange (with Nate-revisions):
You might be interested in Eliezer's "Ultimate Newcomb's Problem", which is a rare decision problem where EDT and CDT agree, but disagree with FDT. In this variant, the small box contains $1k, and the big box is transparent and contains a number X whose primality you are unsure of. Omega will pay you $1M if the number in the big box is prime, and put a prime number in that box iff they predicted you will take only the big box. Meanwhile, a third actor Omicron chooses a number at random each day, and will pay you $2M if their randomly-selected number is composite, and today they happen to have selected the number X.
The causal decision theorist takes both boxes, reasoning that all they can control is whether they get an extra $1k, so they might as well. The evidential decision theorist takes both boxes, reasoning that this makes X composite, which pays more than making X prime by taking one box (the extra $1k being inconsequential). The functional decision theorist takes one box, reasoning that on days that they're going to get paid by Omicron the number in the big box and the number chosen by Omicron will not coincide, but recognizing that their decision about whether or not to one-box has no effect on the probability that Omicron pays them.
As for who performs better, for clarity assume that Omega makes the number in the big box coincide with the number chosen by Omicron whenever possible, and write for the probability that Omicron chooses a composite number. Then CDT will always see a composite number (and it will match Omicron's in the fraction of the time when Omicron's is also composite); EDT will see a number with the same primality as Omicron's number (that matches in the fraction of cases where Omicron's number is composite, and differs in the () fraction of cases where Omicron's number is prime); FDT will always see a prime number (that matches Omicron's in the () fraction where Omicron's is prime). The payouts, then, will be for CDT; for EDT; and for FDT; a clear victory in terms of expected utility for FDT. (Exercise: a similar ranking holds when Omega only sometimes matches Omicron's number conditional on that being possible.)