Dividing the Pie

In the last post, I suggested that the new version of fairness (C) would make it possible to compare the fairness of different payout schedules for a given format. After a few experiments (and a bit of reflection) later, it’s clear that this will require significantly more work. The assessment of payout schedules must also be informed by the equity considerations that sound in fairness (B).

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Fairness ($), Part II

The new tournament simulator is nearing usability, and there will be some significant results very soon, I hope.

In the meantime, I have progress to report on improving on one of the chief fairness metrics. Fairness (C) is defined, qualitatively, as the degree to which a tourney design rewards superior performance. But the method heretofore used to measure this quality can be criticized as too narrowly focused on the overall winner of the tournament. In this post, I’ll propose an extension of the metric that considers not just the overall winner, but every place for which there is prize money.

The redefined fairness (C) metric will be useful not only for comparing the fairness of particular tournament designs, but also for determining the payouts themselves.

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Big Brackets

I”ve added a few brackets to the printable brackets page, including some for 64- and 128-team tourneys. I’ve also added guides in the notation from the last post identifying the structure for the brackets that were already there, and adopted a naming convention for new printable brackets whereby the name of the file itself is a variant of the notation.

The lowers for these big tournaments are provided mostly as a curiosity, as it’s uncommon for a double-elimination or consolation format to be used on a field so large. But there are, from time to time, practical uses for big brackets.

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A Notation for Bracket Structure

Tourneygeek has been quiet for a while, but that is not (or at least not mostly) because I’ve been idle. The new simulator is nearly ready to run, and there should soon be plenty of results to report. I hope these will include substantial progress on such matters as a coefficient of competitiveness, fairness (D), and new measures of efficiency based on modeling playing time.

In the meantime, I’ve been coding several basic tournament designs for the new simulator format. In the course of this, I’ve developed a shorthand way of describing lower brackets that is handy for showing how they are (or are not) shifted.

The idea is to show how the drops from the rounds in the bracket above are distributed among the rounds in the bracket receiving the drops.

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We’ll Send a Car for You

I remember watching some television show, so many years ago that I cannot hope to remember the details or even the name of the show, that had one line of dialog that has stuck with me.

A man has gone to Las Vegas ready to become wealthy by using a secret betting system he’s devised. Things go badly. He’s broke and broken, and the casino has cut off his credit – it’s time for him to quit. He’s granted an interview with the casino manager, and complains that they’re kicking him out they’re afraid of him, because he’s got a system! Then comes the line I remember:

If we’d known you had a system, we’d have sent a car for you.

This post builds on yesterday’s post, Card Sense, by discussing gambling systems: the ones that will, indeed, get you kicked out of a casino, and the ones that may inspire them to send a car for you.

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Card Sense

People who are good at playing one game are often good at others. In particular, there seems to be a general ability, sometimes called “card sense”, that seems to enable a player who is good at one card game to excel at other card games.

Card games may have this distinctive skill because of the way that almost all card games, and very few other games, incorporate the element of chance.

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