The solution has nothing to do with hacking the counterfactual; the reflectively consistent (and winning) move is to pay the $100, as precommitting to do so nets you a guaranteed $1000 (unless omega can be wrong). It is true that “The player will pay iff asked” implies “The player will not be asked” and therefore “The player will not pay”, but this does not cause omega to predict the player to not pay when asked.
The solution has nothing to do with hacking the counterfactual; the reflectively consistent (and winning) move is to pay the $100, as precommitting to do so nets you a guaranteed $1000 (unless omega can be wrong). It is true that “The player will pay iff asked” implies “The player will not be asked” and therefore “The player will not pay”, but this does not cause omega to predict the player to not pay when asked.