You are the chair of a committee that has 11 members (including yourself). You want to hand over the chairship to one of the other members, using the following scheme:
The whole committee sits around a round table. You flip a fair coin. If it comes up heads, you pass it to the person on your right, and if it comes up tails, you hand it to your left. The person who receives the coin repeats the procedure, flipping it and passing it right or left, depending on the outcome of the flip. This process keeps going until all but one members of the committee have had the coin come into their hands. The lone member who has not yet touched the coin is then declared the new chair.
Which of 10 other people in the committee is most likely to become the new chair, using this scheme?