Dear Kory, your argument pushed me off balance. I checked your table and found it absolutely true. Then it occurred to me that you made the same assumption as in my post shortly prior to yours: a priviledge of "ME" to switch, barring the others. I continued your table to situations when the #2 player is switching and then when #3 is doing it - all the way to all 3 of us did switch and found that such extension of the case returns the so called 'probability' to the uncalculable (especially if there are more than 3 players) like a many - many body problem. Cheers John
Why would it matter if the other players switch? Based on the description of the game at http://tinyurl.com/4oses I thought the "winning flip" was determined solely by what each player's original flip was, not what their final bet was. In other words, if two players get heads and the other gets a tails, then the winning flip is automatically tails, even if the two players who got heads switch their bet to tails.
Assuming this is true, it's pretty easy to see why it's better to switch--although it makes sense to say the winning flip is equally likely to be heads or tails *before* anyone flips, seeing the result of your own coinflip gives you additional information about what the winning flip is likely to be. If I get heads, I know the only possible way for the winning flip to be heads would be if both the other players got tails, whereas the winning flip will be tails if the other two got heads *or* if one got heads and the other got tails.