You might as well precommit to one-box at 1:1 odds anyway. If Omega has ever been observed to make an error, it’s to your advantage to be extremely easy to model in case the problem ever comes up again. On the other hand, if Omega is truly omniscient… well, you aren’t getting more than $1,000 anyway, and Omega knows where to put it.
If there is visibly $1,000 in box A and there’s a probability 0 EU(one-boxing), unless one is particularly incompetent at opening boxes labelled “A”. Even if Omega is omniscient, I’m not, so I can never have p=1.
If anyone would one-box at 1:1 odds, would they also one-box at 1:1.01 odds (taking $990 over $1000 by two-boxing) in the hope that Omega would offer better odds in the future and predict them better?
I wouldn’t one-box at 1:1.01 odds; the rule I was working off was: “Precommit to one-boxing when box B is stated to contain at least as much money as box A,” and I was about to launch into this big justification on how even if Omega was observed to have 99+% accuracy, rather than being a perfect predictor, it’ll fail at predicting a complicated theory before it fails at predicting a simple one...
...and that’s when I realized that “Precommit to one-boxing when box B is stated to contain more money than box A,” is just as simple a rule that lets me two-box at 1:1 and one-box when it will earn me more.
You might as well precommit to one-box at 1:1 odds anyway. If Omega has ever been observed to make an error, it’s to your advantage to be extremely easy to model in case the problem ever comes up again. On the other hand, if Omega is truly omniscient… well, you aren’t getting more than $1,000 anyway, and Omega knows where to put it.
If there is visibly $1,000 in box A and there’s a probability 0 EU(one-boxing), unless one is particularly incompetent at opening boxes labelled “A”. Even if Omega is omniscient, I’m not, so I can never have p=1.
If anyone would one-box at 1:1 odds, would they also one-box at 1:1.01 odds (taking $990 over $1000 by two-boxing) in the hope that Omega would offer better odds in the future and predict them better?
I wouldn’t one-box at 1:1.01 odds; the rule I was working off was: “Precommit to one-boxing when box B is stated to contain at least as much money as box A,” and I was about to launch into this big justification on how even if Omega was observed to have 99+% accuracy, rather than being a perfect predictor, it’ll fail at predicting a complicated theory before it fails at predicting a simple one...
...and that’s when I realized that “Precommit to one-boxing when box B is stated to contain more money than box A,” is just as simple a rule that lets me two-box at 1:1 and one-box when it will earn me more.
TL;DR—your point is well taken.