The quest for the fairest-of-them-all bracket in the past few posts has led us to build a number of very peculiar-looking brackets, particularly the cascade bracket. A form of this bracket is used to good effect in the last stages of bowling tournaments. But it would, quite reasonably, be considered highly inappropriate in most other contexts.
So, let’s look for the magic mirror with a different set of constraints. The most significant one is this: in order to be eligible for the victory, the winning bracket must be fair as to both fairness (B) and fairness (C). This should yield a design that people might actually want to use.
Here are the rules:
- It’s got to run with exactly 32 entrants;
- It will be evaluated at luck = 3;
- It will pay two places, 65/35;
- With speed parameters 1 and 2, the final match has to start no more than 500 minutes after the tournament begins; and
- It’s got to have a measured fairness (B) of less than 1.00.
The parameters in rule 4 mean, in essence, that individual games average 22.5 minutes, but that they are moderately variable, with a general random variance on the length of each game, and another random speed factor that attaches to individual players (and stays with them throughout each trial. What I’m getting at, here, is the tendency for brackets to develop bottlenecks where their slow players are.
Rule 5 means, in essence, that it’s got to be a well-balanced bracket, with no significant advantages or disadvantages accruing to individual entry lines. The limit is 1.00 rather than zero because there’s always some level of fairness (B) from random variation, but in my experience this is less than 1.00 for a bracket which has no gross structural imbalances.
The rules also imply a hidden rule 6: It’s got to be something I can run in my simulator.
Let the games begin!