Yep, that will definitely give 50%, which satisfies the OP.
The next step is how to remove that alternating correlation if someone figures out the pattern.
How about before each "for keeps" flip, you flip twice, and do the following:
1) both heads (after inversion adjustment): don't invert the "for keeps" flip
2) both tails (after inversion adjustment): invert the "for keeps" flip
3) one of each: do another pair of flips until you don't get one of each
Of course, at the time of the "for keeps" flip, you'd still have information about how it was likely to come out, so all betting or whatever would have to be done before the pre-flips. But this should break the alternating correlation at least.
The next step is how to remove that alternating correlation if someone figures out the pattern.
How about before each "for keeps" flip, you flip twice, and do the following:
1) both heads (after inversion adjustment): don't invert the "for keeps" flip
2) both tails (after inversion adjustment): invert the "for keeps" flip
3) one of each: do another pair of flips until you don't get one of each
Of course, at the time of the "for keeps" flip, you'd still have information about how it was likely to come out, so all betting or whatever would have to be done before the pre-flips. But this should break the alternating correlation at least.
