The coin toss may be known to Omega and predicted in advance, it only needs to initially have 50⁄50 odds to you for the expected gain calculation to hold. When Omega tells you about the coin, it communicates to you its knowledge about the toss, about an independent variable of initial 50⁄50 odds. For example, Omega may tell you that it hasn’t tossed the coin yet, it’ll do so only a thousand years from now, but it predicted that the coin will come up tails, so it asks you for your $100.
This is a big issue which I unsucessfully tried to address in my non-existing 6+ paragraph explanation. Why the heck is Omega making bets if he can already predict everything anyway?
That said, it’s not clear that when Omega offers you a bet, you should automatically refuse it under the assumption that Omega is trying to “beat” you. It seems like Omega doesn’t really mind giving away money (pretty reasonable for an omniscient entity), since he seems to be willing to leave boxes with millions of dollars in them just lying around.
What is Omega’s purpose is entirely unknown. Maybe he wants you to win these bets. If you’re a rational person who “wants to win”, I think you can just “not worry” about what Omega’s intents are, and figure out what sequence of actions maximizes your utility (which in these examples always seems to directly translate into maximizing the amount of money you get).
Quantum Coins. seriously. they’re easy enough to predict if you accept many worlds. as for the rest…
entertainment? Could be a case of “even though I can predict these humans so well, it’s fascinating as to just how many of them two-box no matter how obvious i make it.” It’s not impossible-we know that we exist, it is not impossible that some race resembling our own figured out a sufficient solution to the lob problem and became a race of omegas...
That’s just like playing “Eeny, meeny, miny, moe” to determine who’s ‘it’. Once you figure out if there’s an even or odd number of words, you know the answer, and it isn’t random to you anymore. This may be great as a kid choosing who gets a cookie (wow! I win again!), but you’re no longer talking about something that can go either way.
For a random output of a known function, you still need a random input.
The trick with eeny-meeny-miney-moe is that it’s long enough for us to not consciously and quickly identify whether the saying is odd or even, gives a 0, 1, or 2 on modulo 3, etc, unless we TRY to remember what it produces, or TRY to remember if it’s odd or even before pointing it out. Knowing that doing so consciously ruins its capacity, we can turn to memory decay to restore some of the pseudo-random quality. basically, by sufficiently decoupling “point at A” from “choose A” to our internal cognitive algorithms...we change the way we route visual input and spit out a “point at X”.
THAT”S where the randomness of eeny-meeny-miney-moe comes in...though I’ve probably got only one use left of it when it comes to situations with 2 items thanks to writing this up...
The coin toss may be known to Omega and predicted in advance, it only needs to initially have 50⁄50 odds to you for the expected gain calculation to hold. When Omega tells you about the coin, it communicates to you its knowledge about the toss, about an independent variable of initial 50⁄50 odds. For example, Omega may tell you that it hasn’t tossed the coin yet, it’ll do so only a thousand years from now, but it predicted that the coin will come up tails, so it asks you for your $100.
This requires though that Omega have decided to make the bet in a fashion which exhibited no dependency on its advance knowledge of the coin.
This is a big issue which I unsucessfully tried to address in my non-existing 6+ paragraph explanation. Why the heck is Omega making bets if he can already predict everything anyway?
That said, it’s not clear that when Omega offers you a bet, you should automatically refuse it under the assumption that Omega is trying to “beat” you. It seems like Omega doesn’t really mind giving away money (pretty reasonable for an omniscient entity), since he seems to be willing to leave boxes with millions of dollars in them just lying around.
What is Omega’s purpose is entirely unknown. Maybe he wants you to win these bets. If you’re a rational person who “wants to win”, I think you can just “not worry” about what Omega’s intents are, and figure out what sequence of actions maximizes your utility (which in these examples always seems to directly translate into maximizing the amount of money you get).
Quantum Coins. seriously. they’re easy enough to predict if you accept many worlds.
as for the rest… entertainment? Could be a case of “even though I can predict these humans so well, it’s fascinating as to just how many of them two-box no matter how obvious i make it.”
It’s not impossible-we know that we exist, it is not impossible that some race resembling our own figured out a sufficient solution to the lob problem and became a race of omegas...
That’s just like playing “Eeny, meeny, miny, moe” to determine who’s ‘it’. Once you figure out if there’s an even or odd number of words, you know the answer, and it isn’t random to you anymore. This may be great as a kid choosing who gets a cookie (wow! I win again!), but you’re no longer talking about something that can go either way.
For a random output of a known function, you still need a random input.
The trick with eeny-meeny-miney-moe is that it’s long enough for us to not consciously and quickly identify whether the saying is odd or even, gives a 0, 1, or 2 on modulo 3, etc, unless we TRY to remember what it produces, or TRY to remember if it’s odd or even before pointing it out. Knowing that doing so consciously ruins its capacity, we can turn to memory decay to restore some of the pseudo-random quality. basically, by sufficiently decoupling “point at A” from “choose A” to our internal cognitive algorithms...we change the way we route visual input and spit out a “point at X”.
THAT”S where the randomness of eeny-meeny-miney-moe comes in...though I’ve probably got only one use left of it when it comes to situations with 2 items thanks to writing this up...