Suppose we have $n+1$ people in a circle ${0,1,2,3....n}$, we pass around a broccoli stick. The person $k$ has probability $p$ to pass the stick to $k+1$ and probability $q = 1-p$ to pass it to the $k-1$ person. And $p>0.5>q$.
NOTE: THIS IS NOT A SYMMETRIC WALK!
One wins if he is the last person remaining that has not touched the stick.
Where should a person situate to get the best possibility of winning?
I Want to calculate P(person i-1) gets the stick, passes it to i+1 without going through i. And P(person i+1) gets stick, passes it to i-1 without going through i, then condition.
