N+1 kids in a circle. Distribution of k'th child to stop a game.

[guyov1]

N+1 children in a circle, passes a box between them.
Proabilty 0.5 to pass a box to the left or to the right.
When all the chidlren "touches" the box, the game ends.
Need to find distribution of random variable k, which define the k'th child to stop the game.

 

[CompuChip]

An equivalent problem is: "what is the chance that a 1D random walk will first cross the starting axis after k steps?"
Is there anything about random walks in your textbook?

 

[guyov1]

But isn't it different? Because here we deal with a cirlce.
So if you compare it to 1D walk, you can also cross,lets say, the far right or end of the path and finish there.

It's like a 1D walk in a loop.

 

[flatmaster]

You could take the random walk. everyone has touched the box when the WIDTH of the distribution is N+1. Or N? I think a width of N. THere's always weird stuff on the boundry