What does your intuition tell you about the solution to this problem?

The Monty Hall problem is a well known example of a problem that confounds most people’s intuition. I have a simpler problem whose solution goes against my intuition. See what you think.

Two running clubs A and B hold a competition in which randomly selected members from each club are paired against each other. Club A wins every race.

In an attempt to save face, the captain of team B says that since all the races are timed, the right thing would be to compare the fastest runners on each team, then the two second fastest and so on. The captain of team A agrees. What are the possible outcomes of this re-arrangement?

I will let you think about this a while before giving the answer this evening. It is relatively easy to figure out the result of the races between the two fastest and the two slowest runners. The general case is a little more involved but requires the same type of reasoning.