If you are one of 100 people playing American Eagle, a game where one person starts alone and has to tackle someone as people run past in order to "recruit" more tacklers for the next run across, and each tackler has an R*(1/200) chance of tackling someone as they cross, where R is the number of remaining runners (those who has not been tackled or recruited yet), how many times on average will they have to cross before everyone has been tackled and has been recruited as a tackler? How long before you have recruited a two-thirds majority?