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?

For #2 to be 2nd, he must get to the finals -- so if #1 plays in the same "half" of the tournament, #2 will be defeated before getting to the final.

In this case, after #1 has been seeded, #2 has 3/7 odds of ending in "the same half".

Posted by e.g. on 2004-06-15 07:59:06