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.
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.