You're having coffee with friends sitting around a table on a work break. You paid for everyone's coffee the last time, and so you propose a method for randomly assigning that task to another person this time. Your proposal involves flipping a fair coin until a particular event happens. Here are the details:
You flip first. If it's heads, you pass the coin to your left; tails, you pass the coin to your right.
The person receiving the coin flips it and passes it left or right according to the same algorithm.
And so on.
As the process continues, more and more of the persons will receive the coin.
At some point, there will be just one person who has not received the coin.
That person must pay the bill.
Is this a fair method?