Here, as promised, are the f(b:X) tables for the five different versions or our hypothetical 128-player double elimination tourney.
(As the formal notation gets a bit unwieldy for a bracket as large as a 128, I’ve named the shifts after the files in the last post.)
The take-aways: the best of the shifted brackets are always better than the unshifted bracket. In the high-luck scenario, all five versions do a remarkably good job of equalizing the final. The “early” shift (which is the only shift that, like the unshifted version, sends the G drop to the lower final) does consistently worse than the other shifts, and for high-skill events it’s even worse than the unshifted bracket.
Somewhat to my surprise, the “super” shift, which squeezes an extra round out of the tourney, does quite well – event to the point of being the best performer for a high-luck event. I’m not ready to anoint it a best practice and post it to the printable brackets page, but it certainly bears further investigation.
| luck = 1 | 26.45 | 26.57 | 24.93 | 25.01 | 25.45 |
| unshifted | early | middle | late | super | |
| H | 11.7 | 12.6 | 10.5 | 9.0 | 8.8 |
| I | 23.7 | 22.2 | 21.4 | 23.0 | 20.1 |
| J | 5.4 | 27.4 | 26.8 | 4.7 | 26.3 |
| K | 6.3 | 32.2 | 30.6 | 5.6 | 27.4 |
| L | 2.5 | 10.1 | 10.0 | 11.8 | 22.6 |
| M | 17.1 | 3.7 | 2.7 | 15.7 | 21.3 |
| N | 1.3 | 8.1 | 22.7 | 5.6 | 17.0 |
| O | 22.7 | 3.0 | 2.9 | 2.9 | 7.2 |
| P | 0.8 | 0.9 | 2.8 | 2.4 | 1.7 |
| Q | 23.6 | 7.8 | 1.0 | 1.1 | 3.5 |
| R | 0.3 | 3.7 | 3.2 | 3.3 | |
| S | 7.7 | ||||
| T | 3.9 | ||||
| luck = 3 | 97.12 | 96.16 | 93.46 | 92.85 | 92.41 |
| H | 13.3 | 7.6 | 7.5 | 6.9 | 6.4 |
| I | 8.4 | 6.9 | 6.2 | 6.1 | 5.0 |
| J | 5.8 | 4.7 | 5.0 | 3.8 | 4.0 |
| K | 14.9 | 5.0 | 4.5 | 11.7 | 3.7 |
| L | 2.6 | 2.5 | 2.5 | 4.4 | 3.5 |
| M | 19.0 | 7.1 | 1.6 | 3.0 | 2.8 |
| N | 1.3 | 4.2 | 16.6 | 2.2 | 2.2 |
| O | 17.7 | 1.0 | 5.5 | 7.2 | 3.0 |
| P | 0.6 | 0.2 | 3.4 | 3.1 | 1.0 |
| Q | 14.4 | 5.0 | 0.3 | 0.1 | 0.5 |
| R | 0.1 | 0.0 | 0.3 | 0.4 | |
| S | 4.4 | ||||
| T | 0.1 |
tourneygeek.com 
The supershift would definitely work better in a 256 bracket than a 128, but if you have 256 entrants, you probably don’t want to go double-elimination.
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Even 128 is an awful lot of entries for a double elimination. But perhaps that’s true, in part, because it takes to darned long to run them, and it you can do it in eleven rounds with the compressed lower bracket, maybe it’s more feasible than it gets credit for. There’s at least one large backgammon tourney that wants to run a double elimination with well over 64 entrants.
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{A.B.C.D.E.F.G.H.X} works with 256. For 16 or 256 player tournaments you can have a perfect losers bracket. This doesn’t work with any other numbers in between. The next perfect losers bracket comes with a 65536 player tournament.
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