You’re playing an unknown game, all you know about it is that the grandmaster is an expert player and you don’t even know the rules nor the name of the game.
If I also know that the game has (a) no luck component and (b) no mixed strategy Nash equilibrium (i.e. rock beats scissors beats paper beats rock), then I have enough information to make a within epsilon accurate prediction. If I don’t know those facts about the game, then you are right.
But your references to occurrences like spontaneous combustion is beside the point. The task is: assign likelihood of grandmaster winning or not winning. There are many possibilities that don’t correspond to either category, but predict-the-outcome doesn’t care about those possibilities. In the same way that I don’t advise my clients about the possibility that a mistrial will occur because the judge had a heart attack when I discuss possible litigation outcome.
Correct me if I’m wrong, but I don’t think that “The task is: assign likelihood of grandmaster winning or not winning.” captures what Omega is doing.
For each game you play, either the grandmaster will win or he will not (tertium non datur). Since it is not possible for Omega to be wrong, the only probabilities that are assigned are 0 or 1. No updating necessary.
Say you play 5 games against someone, and they will go W(in)L(oss)WLL, then Omega would predict just that; i.e. it would assign “Pr(game series goes “WLWLL) = 1”.
If Omega knows whether you will accept, it also knows whether you’ll have a heart attack—or some event—barring you from accepting, since that affects the outcome. It doesn’t need to label that event “heart attack”, but still its genesis needs to be accounted for in the model, since it affects the outcome.
I don’t want to dispute definitions, but I wouldn’t says Omega erred in predicting your choice if you had a heart attack before revealing whether you would one-box or two-box. As far as I’m concerned, Omega is not known for predicting who will and won’t be able to play, just what they will do if they play.
If I also know that the game has (a) no luck component and (b) no mixed strategy Nash equilibrium (i.e. rock beats scissors beats paper beats rock), then I have enough information to make a within epsilon accurate prediction. If I don’t know those facts about the game, then you are right.
But your references to occurrences like spontaneous combustion is beside the point. The task is: assign likelihood of grandmaster winning or not winning. There are many possibilities that don’t correspond to either category, but predict-the-outcome doesn’t care about those possibilities. In the same way that I don’t advise my clients about the possibility that a mistrial will occur because the judge had a heart attack when I discuss possible litigation outcome.
Correct me if I’m wrong, but I don’t think that “The task is: assign likelihood of grandmaster winning or not winning.” captures what Omega is doing.
For each game you play, either the grandmaster will win or he will not (tertium non datur). Since it is not possible for Omega to be wrong, the only probabilities that are assigned are 0 or 1. No updating necessary.
Say you play 5 games against someone, and they will go W(in)L(oss)WLL, then Omega would predict just that; i.e. it would assign “Pr(game series goes “WLWLL) = 1”.
If Omega knows whether you will accept, it also knows whether you’ll have a heart attack—or some event—barring you from accepting, since that affects the outcome. It doesn’t need to label that event “heart attack”, but still its genesis needs to be accounted for in the model, since it affects the outcome.
I don’t want to dispute definitions, but I wouldn’t says Omega erred in predicting your choice if you had a heart attack before revealing whether you would one-box or two-box. As far as I’m concerned, Omega is not known for predicting who will and won’t be able to play, just what they will do if they play.