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 kn...
Just developing my second idea at the end of my last post. It seems to me that in the Newcomb problem and in the counterfactual mugging, the completely trustworthy Omega lies to a greater or lesser extent.
This is immediately obvious in scenarios where Omega simulates you in order to predict your reaction. In the Newcomb problem, the simulated you is told "I have already made my decision...", which is not true at that point, and in the counterfactual mugging, whenever the coin comes up heads, the simulated you is told "the coin came up tails". And the arguments only go through because these lies are accepted by the simulated you as being true.
If Omega doesn't simulate you, but uses other methods to gauge your reactions, he isn't lying to you per se. But he is estimating your reaction in the hypothetical situation where you were fed untrue information that you believed to be true. And that you believed to be true, specifically because the source is Omega, and Omega is trustworthy.
Doesn't really change much to the arguments here, but it's a thought worth bearing in mind.