PAIRING DEVELOPMENT

### WEIGHT MODEL

Weights in McMahon Pairing (January 2012) is an article summarising the weight models used in MacMahon and Open Gotha and proposes generalisations and extensions.

Weights in McMahon Pairing-REVISED (May 2015) provides a summary of Weights in McMahon Pairing with corrections and completions.

### McMAHON BAR

Determination of the McMahon Bar
(August 2015) Develops a Monte Carlo algorithm to establish the bar in a tournament with R rounds from the player entry per grade.
It shows that there is a unique "Equilibrium Grade" G_{c} in Randomly paired and Swiss tournaments having the properties:
- The average grade of opponents of players in group G
_{c} is approximately equal to G_{c}.
- The average score of players in group G
_{c} is approximately equal to S_{mid}.

The "mid-score" S_{mid} = R/2.
The above properties carry over to McMahon tournaments on making the following changes:
- G
_{c} is the bar.
- Score is replaced by the McMahon score.
- S
_{mid} corresponds to the McMahon score of players at the bottom of the bar winning half their games.

The toursim program is written as a general tournament simulation program, and used to generate all the data presented in the document. The program and data is released under the GNU General Public Licence.

### EXACT SCORE DISTRIBUTION

Exact McMahon Score Distribution (September 2016) develops an algorithm for the individual scoring probability distribution in small Swiss and specialised McMahon tournaments.

### OPTIMISATION OF PAIRING ALGORITHMS

Pairing Quality - Background and plan (August 2018)
An introductory document formulating basic ideas to explore the effect of weight parameters and pairing strategy on the pairing quality.

### GODRAW-LINUX

Complete rewrite of GoDraw in Linux. Very similar interface. Gabow N cubed matching. Any weight model.
To do.