Each round consists of flipping all of the coins showing heads.
If fewer than half of the flipped coins come up heads the player loses.
Rounds continue until the player either loses or has one heads remaining.
The player wins by getting to one heads without losing.
What is the probability of winning this game?
Examples: 6→4→1 would be a loss. (1 is less than half of 4.) 6→5→3→2→2→2→1 would be a win.