We can also consider the variant in which the Winning Flip is determined after people decide whether or not to switch.
In a follow-up to my own post, I should point out that your winning chances in this game depend on how your opponents are playing. If all of your opponents are playing randomly, then you have a negative expectation no matter what you do. If your opponents are not playing randomly, then you may be able to exploit patterns in their play to generate a positive expectation.
-- Kory
