A friend asked me for a specialized bracket for a backgammon tourney he’s running soon. He wants a 128 bracket that’s a full double elimination with a progressive consolation as a third bracket. There’s an unexpectedly nice one available.
Most backgammon tourneys do not attempt double elimination – it simply takes too long to play. But a few, especially among those played on longer, holiday weekends do.
I recalled from earlier work that there’s a remarkable “super shift” that squeezes an extra round out of the second bracket in a 128DE, and also scores well on fairness. But what happens when you need a third bracket? In every other case, adding a third bracket to a shifted bracket necessitated some pretty ugly compromises.
In this particular case, however, there’s something astonishingly nice: 128SSthirdA. Unlike any other third bracket I’ve ever drawn, it is a strictly progressive consolation, with no split or overlapping round drops. What’s more, it avoids rematches entirely for the first three rounds of the consolation, and they’re infrequent after that.