Football cup bracket generator

Because pairing them one against two, three against four and so on puts the two best teams in the same half, where they knock each other out early and the final is between the survivors of the easy side.

The usual bracket is built by folding instead: start with one and two, and each time the bracket doubles, every seed gets paired with the number that completes the new size plus one. For eight that gives 1-8, 4-5, 2-7, 3-6, and the top two can only meet in the final.

The fourth, not the third. The third sits in the second seed's half, so the two semifinals are one against four and two against three.

This surprises people, and it surprised the check written for this tool: the test was written expecting one against three in the semifinal and had to be corrected, not the code.

The bracket grows to the next power of two and the empty places become byes. With forty teams the bracket is sixty four and there are twenty four byes.

They are not handed out at random or to the bottom: they go to the best seeds, which is what makes a bye a reward rather than luck. With forty teams, seeds one to twenty four skip the first round.

Always one less than the number of teams, no matter how many byes there are. Each match eliminates exactly one team, and everybody except the champion is eliminated.

It is a good way to check any bracket, including this one: count the matches drawn and compare.