Do Two Singles Make a Double?

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)?

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TGT: Fairness

Here is another draft from my slowly-growing manuscript, Tourneygeek’s Guide to Tournaments. TGT Fairness

Only the first five pages, discussing fairness in general and fairness (A), are new, but because this now completes a first full chapter I’m also including the previously posted parts of the chapter than discuss fairness (B) and fairness (C).

As before, comments and criticisms are welcome.

Setting the Luck Parameter

One interesting bit of NCAA tourney trivia is that this year, apparently for the first time ever, one of the tens of millions of brackets submitted to online bracket challenge games was entirely correct through the first two rounds, or 48 games, of the tourney.

The chance that this bracket will remain perfect through the remaining 15 games is very small, but there will be many eyes on it. One year, there was a $1,000,000,000 prize offered for a perfect bracket (though, apparently for legal reasons, that prize is no longer on offer).

In a related discussion, I ran across a tidbit of expert opinion that may be useful in helping calibrate tourneygeek’s simulator.

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Learning from Ottawa, part III

In the last post, I compared the double-elimination portion of the Ottawa Men’s Bonspiel curling bracket against a slightly revised version of itself. But the more important comparison to make is with the a more conventional version of a double-elimination for 91 teams. And, as I’ll show, comparing the Ottawa bracket to a more conventional approach unexpectedly seems to open new avenues of inquiry for bye management.

As discussed in BBBR: 128s, there are a number of suitably-sized brackets from which to choose a comparator. In deciding which to use, I came upon another surprising virtue of the Ottawa-adapted format: it runs in just ten rounds, and there are almost no long waits except those caused by byes. The quickest of the 128s is the “128supershift“, which takes 11 rounds. So, to capture as much of the virtue of the Ottawa adaptation as possible in a (not very) conventional format, I chose the supershift.

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Learning from Ottawa, part II

In the previous post, I suggested that the first parts of the Ottawa Men’s Bonspiel design could be adapted to a large double-elimination tourney in other contexts. It’s time to put it to the test.

In the last post, I linked to brackets for the Ottawa design, both (nearly) as it was played in Ottawa, and with a few technical adjustments intended to improve fairness. In this post, I’ll look at the effect of those technical adjustments.

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Learning from Ottawa

The bracket from the City of Ottawa Men’s Bonspiel tourney discussed in the last post had a number of features that make it look like it would be fun to play. In this post, I’ll consider whether a truncated version of the Ottawa bracket might make a good double-elimination bracket for a 91-team tourney in some other event.

This post will show the way the Ottawa-style brackets would look, both (nearly) as drawn by the Ottawa organizers, and with a few of my own alterations to eliminate some small sources of unfairness that seem to me gratuitous. In a later post, we’ll test these designs against a more conventional bracket.

The result, I’m guessing, is that the Ottawa bracket gives up a good deal of fairness (C) in exchange for its other virtues. Chief among these virtues is the way the tourney is experienced by the vast majority of players who lose in an early round.

In an ordinary double-elimination tourney, losing in an early round is very dispiriting. You know that you have a path back to glory, but you also know that that path is a long one, and your chance of success small. But you have a different prospect in Ottawa. Here the A, B, and C rounds losers all drop into a pristine new bracket, a bracket in which you have as good a chance as anyone else to win a named trophy.

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Extreme Participation: Ottawa Curling

Reader metzgerism alerts me to the fact that in curling, “three-game guarantees are practically sacrosanct”. He also mentioned a tourney being held right now. The City of Ottawa Men’s Bonspiel.

This event carries a concern for the value of participation to a level I have never before encountered in a bracketed tourney. The draw for this tourney can be found here. Participants are guaranteed not just three but five games (though it appears that for a particularly unlucky or inept team, one of the five games may be a bye).

This is a complicated structure indeed, but it’s worth taking a close look at it.

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