The less I know about chess, the more certainly I can predict the outcome if I play against a grandmaster.
Alright, let's take this to the extreme. 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.
Task: Perfectly predict the outcome of you playing the grandmaster. That is, out of 3^^^3 runs of such a (first) game, you'd get each single game outcome right.
All the components of your reasoning process that have a chance to affect the outcome would need to be modelled, if only in some compressed yet equivalent form. For certain other predictions, such as "chance to spontaneously combust", many attributes of e.g. your brain state would not need to be encompassed in a model for perfect predictability, but for the initial Newcomb's question, involving a great many cognitive subsystems, a functionally equivalent model may be very hard to tell apart from the original human.
Congruency / isomorphism to the degree that there is a perfect correspondence with a question as involved as Newcomb's would map to a correspondence for a vast range of topics involving the same cognitive functions.
As to your observation, it may be that there cases where for certain ranges of predictive precision, knowing less will increase your certainty. Yet, to predict perfectly you must model perfectly all components relevant to the outcome (if only in their maximally compressed form), and using the model to get the outcome from certain starting conditions equals computation.
Where did 3^^^3 pop out of? Outside of mathematics, "always" never means "always", and in the present context, Omega does not have to be perfect.
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.