I’m occasionally asked to draw brackets for upcoming backgammon tourneys, and one of the popular requests is for a 48 bracket – that seems to be the size of the field fairly often these days.
On my printable brackets page, I’ve supplied only brackets for the powers of two, with the idea that an in-between bracket like a 48 is really just a 64 with 16 fewer lines, so that you can run the tourney just fine by using the seeding lines on the 64 to allocate byes to the opponents of the lines seeded 49 to 64.
Some have complained, however, about the way that the 48 brackets I’ve supplied play. Specifically, they dislike the fact that some players get a second bye in the lower bracket before others have gotten a first bye anywhere. This is a valid objection, and one that I’ve taken too long to address. But I’ve done so now, and posted a 48 to the printable brackets page that’s better than the ones I’ve been supplying in spreading the byes more evenly.
The difference between the new bracket and the pruned 64 is a subtle rearrangement of the drops that is optimized for the case in which there are 40 entrants. The original bracket was drawn without considering where the possible byes dropped when the bracket was less than full. As it happened, this sent drops that might be byes into parts of the losers bracket where they might fall to players who had already had a bye.
I’d been aware of the problem, but had thought that it was unavoidable. But upon closer inspection, I saw that it was largely avoidable, at least for the 40-entrant case.
Presently I’ll see if there are needful changes to other brackets. Perhaps I need brackets for 12, 24, and 96 players. Or perhaps I just need to revise the drops on the 16, 32, and 128 brackets so that the drops fall better when used for tourneys of 10, 20, or 80 players.