When it's time to settle a decision, my two kids always argue about who gets heads in a coin toss. So, my new decision making method is to throw a red marble in a bag full of blue marbles. The kids take turns picking marbles - the winner is the first one to get the red marble.
My intuition tells me that the first one to pick should have a slight advantage. However, I have worked it out a number of ways, and it seems to me that as long as you start with an even number of marbles in the bag (including the winning marble), each person has a 50% chance of winning.
Can someone confirm this for me?
While we're here - anyone want to take a shot at figuring out if this technique can be generalized to select a winner from a group of children? I'm thinking maybe the number of marbles has to be a multiple of the number of kids to ensure that it's a fair game.