Followup to: Counterfactual Mugging.

Let's see what happens with Counterfactual Mugging, if we replace the uncertainty about an external fact of how a coin lands, with logical uncertainty, for example about what is the n-th place in the decimal expansion of pi.

The original thought experiment is as follows:

Omega appears and says that it has just tossed a fair coin, and given that the coin came up tails, it decided to ask you to give it $100. Whatever you do in this situation, nothing else will happen differently in reality as a result. Naturally you don't want to give up your $100. But Omega also tells you that if the coin came up heads instead of tails, it'd give you $10000, but only if you'd agree to give it $100 if the coin came up tails.

Let's change "coin came up tails" to "10000-th digit of pi is even", and correspondingly for heads. This gives Logical Counterfactual Mugging:

Omega appears and says that it has just found out what that 10000th decimal digit of pi is 8, and given that it is even, it decided to ask you to give it $100. Whatever you do in this situation, nothing else will happen differently in reality as a result. Naturally you don't want to give up your $100. But Omega also tells you that if the 10000th digit of pi turned out to be odd instead, it'd give you $10000, but only if you'd agree to give it $100 given that the 10000th digit is even.

This form of Counterfactual Mugging may be instructive, as it slaughters the following false intuition, or equivalently conceptualization of "could": "the coin could land either way, but a logical truth couldn't be either way".