The Chances Volume 2: The chances of winning a knockout tournament

So, a knockout tournament. This time, it’s not three strikes, yer out, it’s one strike, bye bye. Here are the basic rules for a knockout tournament.

2^x (2 to the power of x) teams will compete(We’ll use 2^4, or 16).

There will be 2^x/2 (2 to the power of x over 2(8 for us)) matches in the first round. The winners will go to the next round, who will then face each other, and the winners move on, and the process repeats until there is one team remaining. That team will win.

(For the chances, lets just say everyone has the same chance of winning.)

So, the bracket can be like this:

First Sixteen (Use () for match assorting)

(1     2)     (3     4)     (5     6)     (7     8 )    (9     10)     (11     12)     (13     14)     (15     16)

Winners: 1, 4, 5, 8, 9, 12, 13, 16

Quarter-Finals (These brackets{} will be used for sorting matches up.)

{1     16}     {4     9}     {5     8}     {12     13}

Winners: 1, 4, 8, 13

Semifinals (Use [] for match assorting)

[1     8]          [4     13]

Winners: 1, 4

Finals

1     4

Winner: 1

So, saying that every number has 50% of winning a match, and winning the tournament takes 4 wins, that means we do:

(1/2)^4     (a half to the power of four.)

or

1/(2^4)      (1 over 2 to the power of 4)

This equals 1/16, which, in percent, is 6.125%!

The odds get worse if you increase how many people in the tournament to 32, or 64.

32 people: 3.6125%.

64 people? 1.5625%!

128 people? 0.78125%!

So, if there were any bets that fantasy league would turn every team with equal strength and bet that this team’s going to win, you could be very lucky if you actually won. This is also why you shouldn’t buy lottery tickets because of….

THE CHANCES!

Thanks for reading.

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The Chances Volume 2: The chances of winning a knockout tournament

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