The Infinite Swiss Bracket

Probability Level 3

The Swiss bracket is a popular reseeding method in Chess events, after each round all participants have $x$ wins and $y$ losses, and everyone with $x$ wins and $y$ losses are placed in the same pool. For example, after 2 rounds, participants can either have 2 wins and no losses, 1 win and 1 loss, or no wins and 2 losses.

Given a Swiss bracket for an infinite number of participants, $\frac{n}{64}$ is the proportion of participants with 4 wins after 6 rounds, what is $n$ ?

The answer is 15.

1 solution

Thomas Hurrell
Dec 14, 2018

This is actually a binomial distribution question, there are exactly 2 outcomes and a fixed probability of success. Mathematically this can be represented as $X$ ~ $B(6,0.5)$ , the probability that n is 4 ( $P(X=4)$ ) is $\frac{15}{64}$ , so $n=15$

The Infinite Swiss Bracket

The answer is 15.

1 solution

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