Omega can be replaced by amnesia

I agree that this takes us into the world of Sleeping Beauty problems. But those are much harder. This makes things worse.

Problems where CDT loses can be (probably mechanically) transformed to "strategy-equivalent" problems where CDT wins. That's at least interesting.

It even suggests a decision theory. Just transform the problem and use the strategy that CDT recommends for this new problem.

Flip a coin. If tails, induce amnesia, ask the player for $100, if they pay, keep it, game over. If heads, induce amnesia, ask the player for $100, if they pay, return their money and award them an additional $10000, game over.

EDIT: Emile noted you can omit the amnesia.

0.5*U(die)+0.5*(0.5*U($0)+0.5*U(-$100) = 0.5*U(die)+0.25*U($0)+0.25*U(-$100)

0.5*U(die) + 0.5-U(-$100)

I don't see this. For example, the mixed strategy of one-boxing half the time and two-boxing half the time generates very different results in the transformed problem than in the original Newcomb's Problem.

Conventionally, you are not allowed access to a random number generator in Newcomb's Problem - and so can't use a mixed strategy. Any such usage would tarnish Omega's reputation. Omega - being a mind-reading superintelligence - can fairly easily discourage such a tactic by punishing randomising agents economically - and letting the punishment strategy be known.

I don't see this. For example, the mixed strategy of one-boxing half the time and two-boxing half the time generates very different results in the transformed problem than in the original Newcomb's Problem.

Nope? Let's say you flip a coin. Then your expected winnings are

• 0.5x(0.5x1000000+0.5x(1000000+1000))+0.5x(0.5x0+0.5x(0+1000)) = 500500 dollars

in both versions if Omega follows the rule:

• if you one-box with probability p, Omega fills box B with probability p

What is the transformation of the Hitchhiker, for example?

Put the player in front of an ATM and give them the amnesia drug. If they don't pay you $100, take them to the desert and dump them there. If they paid, put the money from the first round back into their bank account and give them the amnesia drug again. If they pay you again, keep their money. And the player knows these rules.

I don't have the general transformation down yet.

I could change the rules and decide not to stand for such tricks (mixed strategies) either. EDIT: No, I couldn't.

And on the other hand, Omega could deal with mixed strategies perfectly well, and I don't really understand why people make it so that he explicitly doesn't tolerate mixed strategies in their problems. For example, in Newcomb's Problem, if you one-box with probability p, Omega can just fill box B with probability p - for example if p=0.5 your expected winnings in Newcomb's Problem are $500,500.

The first time you enter the room, the boxes are both empty, so you can't ever get more than $1,000,000. But you're otherwise correct.

Well I like it. Make a poll. If it gets over 30 votes I'll honor it.

You won't one-box every time. There is always some chance, however small, that you will two-box, and vice versa.

You point out perhaps the only potentially meaningful difference, and it is the main salient point in dispute between one-boxers and two-boxers in the Omega problem.

First subpoint: With Omega, you are told (by Omega) that there is certainty--that he is never wrong--and you have a large but finite number of previous experiments that do not refute him. Any uncertainty is merely hoped for/dreaded. (There are versions in which there is definite uncertainty, but those are clearly not similar to the OP.)

Second subpoint: If there is truly, really, actually no uncertainty, then correlation is perfect. It is hard to determine cause and effect in such conditions with no chance to design experiments to separate them. I'd argue that cause is a low-value concept in such a situation.