Does your variant evoke different intuitions about observational knowledge?
No. Our intuitions agree here. When I wrote the comment, I didn't understand what point you were making by having the problem be about a mathematical fact. I wanted to be sure that you weren't saying that the math version was different from the coin version.
I'm still not certain that I understand the point you're making. I think you're pointing out that, e.g., a UDT1.1 agent doesn't worry about the probability that it has computed the correct value for the expected utility EU(f) of an input-output map f. In contrast, such an agent does involve probabilities when considering a statement like "Q evaluates to an even number". I'm not sure whether you would agree, but I would say moreover that the agent would involve probabilities when considering the statement "the digit 2, which I am considering as an object of thought in my own mind, denotes an even number."
Is that a correct interpretation of your point?
The distinction between the way that the agent treats "EU(f)" and "Q" seems to me to be this: The agent doesn't think about the expression "EU(f)" as an object of thought. The agent doesn't look at "EU(f)" and wonder whether it evaluates to greater than or less than some other value EU(f'). The agent just runs through a sequence of states that can be seen, from the outside, as instantiating a procedure that maximizes the function EU. But for the agent to think this way would be like having the agent worry about whether it's doing what it was programmed to do. From the outside, we can worry about whether the agent is in fact programmed to do what we intended to program it to do. But that won't be the agent's concern. The agent will just do what it does. Along the way, it might wonder about whether Q denotes an even number. But the agent won't wonder whether EU(f) > EU(f'), although its ultimate action might certify that fact.
FWIW, here is my UDT1.1 analysis of the problem in the OP. In UDT terms, the way I think of it is to suppose that there are 99 world programs in which the calculator is correct, and 1 world program in which the calculator is incorrect. The utility of a given sequence of execution histories equals the number of world programs in which the answer on the test sheet is correct.
Ignoring obviously-wrong alternatives, there are two possible input-output maps. These are, respectively,
f_1: Try to write your calculator's answer on your test sheet. If Omega appears to you, make the answer(s) on the test sheet(s) in the opposite-calculator world(s) be identical to the answer on your test sheet.
f_2: Try to write your calculator's answer on your test sheet. If Omega appears to you, make the answer(s) on the test sheet(s) in the opposite-calculator world(s) be the opposite of the answer on your test sheet.
I assume that, according to the agent's mathematical intuition, Omega is just as likely to offer the decision in a correct-calculator world as in the incorrect-calculator world. From this, it follows that the expected utilities of the two input-output maps are, respectively,
f_1: p(Omega offers the decision in a correct-calculator world)*100 + p(Omega offers the decision in an incorrect-calculator world)*0 = 50;
f_2: p(Omega offers the decision in a correct-calculator world)*99 + p(Omega offers the decision in an incorrect-calculator world)*99 = 99.
So, the agent will make the test sheet in each world agree with the calculator in that world.
(In particular, anthropic consideration don't come into play, because UDT1.1 already dictates the non-centered quantity that the agent is maximizing.)
I think considerably more than two things have to go well for your interpretation to succeed in describing this post... I don't necessarily disagree with what you wrote, in that I don't see clear enough statements that I disagree with, and some things seem correct, but I don't understand it well.
Also, calculator is correct 99% of the time, so you've probably labeled things in a confusing way that could lead to incorrect solution, although the actual resulting numbers seem fine for whatever reason.
The reason I used a logical statement instead of a coin, was...
Consider the following thought experiment ("Counterfactual Calculation"):
Should you write "even" on the counterfactual test sheet, given that you're 99% sure that the answer is "even"?
This thought experiment contrasts "logical knowledge" (the usual kind) and "observational knowledge" (what you get when you look at a calculator display). The kind of knowledge you obtain by observing things is not like the kind of knowledge you obtain by thinking yourself. What is the difference (if there actually is a difference)? Why does observational knowledge work in your own possible worlds, but not in counterfactuals? How much of logical knowledge is like observational knowledge, and what are the conditions of its applicability? Can things that we consider "logical knowledge" fail to apply to some counterfactuals?
(Updateless analysis would say "observational knowledge is not knowledge" or that it's knowledge only in the sense that you should bet a certain way. This doesn't analyze the intuition of knowing the result after looking at a calculator display. There is a very salient sense in which the result becomes known, and the purpose of this thought experiment is to explore some of counterintuitive properties of such knowledge.)