I'm not sure how to word this problem mathematically, but this is the general gist. Imagine your sitting in the middle seat of a car with 3 seats. A bag full of chocolate (for the purpose of this question, it's never ending) and it passes from left to right, then back. An example of the order is let the left person be 1, middle person be 2, and right person 3. It would go like this; 1,2,3,2,1,2,3,2,1,... .
My question is as this sequence tends to infinity who would have the bag for the longest period of time, and in what ratio?
Thanks
The sequence just repeats the pattern $1,2,3,2$ until infinity, so after $4\cdot n$ steps, the sequence is on $1$ $n$ times, on $3$ $n$ times, and on $2$ the remaining $2n$ times.
So, the middle person has the bag for half the time.