In a basketball tournament, there are teams named 1 through 8, such that a lower number team is better than a higher numbered team. (1 is best, 2 is second best... 8 is worst) Also, a better team will always win over a worse team. (There are no upsets)

?-\__
?-/  |
     |--\
?-\__|  |
?-/     |
        |-WINNER
?-\__   |
?-/  |  |
     |--/
?-\__|
?-/

Here is the grid for the tournament

If the better team always wins (there are no upsets) and if the pairing is completely random, what is the easiest way to figure the probability that team 2 doesn't win second place?

If we see Winner as the root node, which is Guaranteed to be '1' because the best team can not be beat. The onle Team that can beat Team 2 is team one, on the second ply (the Final round) either team 1 has already eliminated team 2, or team 2 remains. If Team 2 has already been eliminated then team 1 and team 2 were already put into competition, so they stem from the same node in ply 2. However if team 2 is still around then it stems from the other node. As there are 2 nodes each with an equal amount of team, then the odds are 50:50.

So the answer is that there is a 50/50 P(0.5) chance that team 2 come second.

Posted by seant on 2004-06-18 20:40:56