An interesting design problem from a reader.

The tourney is for “Cold War”, a two-handed version of the famous board game Diplomacy. As many as 64 players are expected. The chief limitation is time – apparently even in its two-handed form, the game takes a long time to play. So minimizing the number of rounds is crucial.

A single elimination 64 bracket takes six rounds to play. A full double elimination can take as many as 13 rounds, but since time is at a premium, that can be pared down to 10 rounds. One round is saved by not having a recharge, and two more by shifting the lower bracket.

But an unusual feature of this particular game offers a third possible bracket structure. Each player can easily play two games at the same time! So perhaps we can give players a second chance by simply playing two separate 64 brackets at the same time, with a playoff between the two bracket winners as a seventh round if the two brackets are not won by the same person.

This is marvelously efficient. Each player gets to play until they lose twice, but you save at least three rounds, and maybe four if you would otherwise insist on a recharge, because a recharge is never needed.

How should such a bracket be drawn, and how does it compare with conventional single and double elimination brackets in the item of fairness (C)?