I’ve updated my comment. You are correct as long as you pre-commit to a single answer beforehand, not if you are making the decision after waking up. The only reason pre-committing to heads works, though, is because it completely removes the Tuesday interview from the experiment. She will no longer be awoken on Tuesday, even if the result is tails. So, this doesn’t really seem to be in the spirit of the experiment in my opinion. I suppose the same pre-commit logic holds if you say the correct response gets (1/coin-side-wake-up-count) * value per response though.
If you say heads every time, half of all futures contain you; likewise with tails.
I’ve updated my comment. You are correct as long as you pre-commit to a single answer beforehand, not if you are making the decision after waking up. The only reason pre-committing to heads works, though, is because it completely removes the Tuesday interview from the experiment. She will no longer be awoken on Tuesday, even if the result is tails. So, this doesn’t really seem to be in the spirit of the experiment in my opinion. I suppose the same pre-commit logic holds if you say the correct response gets (1/coin-side-wake-up-count) * value per response though.