In the first round of the FIFA World Cup, there are groups of 4 teams, which play each other in order to qualify to the second round. It is generally said that if a team wins its two first matches, it is assured its qualification. Is this true?
Some notes for non-soccer fans... The two top teams (points-wise, or after tie-breaking rules are applied) in each group qualify for the next round. Each team plays the three others. A win gives three points; a draw, one, and a loss, zero.
This is not true.
Consider the following situation: the four teams are A,B,C and D.
A wins against B and C, but loses against D.
B loses against A, but wins against C and D.
C loses all games (poor guys !)
D wins against A and C, but loses against B.
Points:
A has 6
B has 6
C has 0
D has 6
A has six points but could, due to tie-breaking rules, not be allowed
to go to the next round, with probability 1/3. This is however the only
situation where this is the case, so in most cases, the rule holds.
(corrected after Joe's comment).
Edited on July 25, 2006, 6:29 am
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