Tourneygeek grows in a haphazard fashion. For me, that’s what makes it fun to write – I can speculate when I’m feeling speculative, analyze when I’m feeling analytical, draw new brackets when I’m feeling (slightly) artistic, or add new features to my tournament simulator when I’m feeling geeky.
But readers can be forgiven for not sharing my mood of the moment. So in this post, I try explain how the various threads – theory, practice, individual games, resources, and geekery – have developed, and show how to follow the main themes from post to post.
Continue reading “A Guide to Tourneygeek”
So far, revisiting the question of the relationship between fairness and bracket shifts has largely confirmed what was found earlier.
The bracket shift’s influence on fairness (C) is benign for both 16s and 32s. This is chiefly because it tends to mitigate the unfairness of dropping the loser of the upper-bracket final directly into the lower-bracket final, dropping it instead to the semifinal of the lower bracket. In 32s, then, the late shift is better than the early shift. And in both 16s and 32s, the drops balance better for high-luck events than they do for low-luck events.
Perhaps it will be worthwhile to look at 64 brackets also, though it’s hard to imagine the results being much different. For this post, however, I’ll look at the one design parameter that has been found to favor unshifted brackets in the past: seeding.
Continue reading “BBBR: Seeding”
In the last post, I brought the fairness (C) analysis up to date with respect to shifted and unshifted 16 brackets. In this post, I’ll do the same for 32s, with attention to the two different shifts available.
Continue reading “BBBR: 32s”
The last post discussed, in general terms, the main source of unfairness in the second bracket, and suggested how to tell whether the use of a shift exacerbated or ameliorated that unfairness. It’s time to put the method to the test.
To avoid another source of unfairness that can obscure the fairness problems inherent in the bracket, we’ll discuss only full brackets – that it, brackets with no byes and a number of players that’s an even power of two
We’ll start by looking at the smallest bracket that can be shifted, the 16 bracket. The traditional way to draw this bracket is A.B.|.C.|.DX (16lowerus). It can be shifted, however, by pushing the C and D drops into earlier rounds, eliminating the two consolidation rounds before them, but adding one later: A.B.C.D.|.X (16lowershift).
Does that make the bracket play better, or worse?
Continue reading “BBBR:16s”
One of the earliest important results in tourneygeek was that the shifted bracket was, for many purposes, not just a clever way to save a round in a two-bracket tourney, but a way to enhance fairness (C) at the same time. See Building a Better Bracket and subsequent posts.
Recently, however, Slow, Shifty Brackets showed that shifted brackets were, for one particular type of tourney, slower to run than unshifted brackets. This may be added to the finding in Seedy and Shiftless that in some cases unshifted brackets outperform shifted ones with respect to fairness (C).
The initial posts on the virtues of shifted brackets are so old that they preceded the availability of the current simulator, and used a version of the fairness (C) measure that no longer seems adequate. So it’s high time to take another look at the bracket shift to make sure we have a clear understanding of its virtues and faults.
Here I’ll begin by talking about what would make a shifted bracket more fair or less fair as compared to an unshifted bracket of the same size. In subsequent posts, I’ll use simulation results to show when shifted bracket are better on fairness (C), and when they’re worse.
Continue reading “Building a Better Bracket Redux”
The design problem that’s been the focus of the last several posts is for the monthly backgammon tourney of the Columbus Backgammon Club, directed by Chris Yep. Chris started by sending a rather innocent-sounding question: should be adopt a shifted bracket for his main-and-consolation event?
Several days and more than sixty simulation runs later, we have an answer: No.
But in the course of finding that answer, we explored a number of issues, and put a finer edge on the bracket he will run. He’s reallocated the prize pool, a bit, and found that he can add to the length of one of the rounds, improving fairness, at a minimal cost in the time needed to run the event. Here are the analyzed brackets for the design with those adjustments: columbus1, and columbus2.
What Chris didn’t realize going into the project is how many moving parts there are to the design of a simple tourney. But he was ready to engage with all of them. Like many directors, I think Chris is used to hearing a lot of objections from his players, and he wants to have an answer for every one of them. I wish him luck.
I learned some things, too, and have a number of things I think I need to look into.
I very much enjoy working through real design problems, and encourage readers to send me queries if you think I can be of help. Or even if you think I can’t – I’d love to get a question or two in the form of, “Here’s my design – don’t you agree that it’s the acme of perfection?” I’m willing to bet that even if I can’t convince you that there’s something you need to change, I can at least raise an issue or two that you haven’t thought through completely.
So, keep those design questions coming!
This post will summarize the learning from the last couple, which can then be safely ignored.
In my original “pie” post, Dividing the Pie, I briefly discussed the possibility of using the fairness (C) measure to find optimal ways of dividing a prize fund for a particular tourney. But I then said it wouldn’t serve that purpose because the payout scheme would always devolve into a winner-takes-all.
That was incorrect, but incorrect in a really trivial and unuseful way. What I found, after many, many rounds of simulation, was that that happens in some very low-luck scenarios, but not in the more typical case. Well, it turns out that what does happen in a more typical case is that the payout scheme devolves into an equally unhelpful share-the-wealth division.
Nothing to see here. Move along. I had a bad idea, and then spent a couple of days discovering that it was, indeed, a bad idea – just bad in a novel way.
Sorry to have wasted your time. Please come back. I promise to write something better soon.
So why don’t I just delete the posts?
Continue reading “Revenge of the Pies”
In the last post, Dividing the Pie, Redux, I used an iterative method in an attempt to derive a fairness-(C)-optimal payout schedule for the unshifted, 13-player tourney first introduced in Getting the Most from an Afternoon.
My earlier idea, from Dividing the Pie, was that this wouldn’t work because the was fairness (C) is defined would always prefer a winner-takes-all payout scheme. But this was not the case. I determined that the best payout scheme was 35/30/35.
In this post, I’ll use more or less the same method in an effort to understand, better, just what’s going on.
Continue reading “More Pies to Divide”