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.
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" Gc in Randomly paired and Swiss tournaments having the properties:
The "mid-score" Smid = R/2.
The above properties carry over to McMahon tournaments on making the following changes:
- The average grade of opponents of players in group Gc is approximately equal to Gc.
- The average score of players in group Gc is approximately equal to Smid.
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.
- Gc is the bar.
- Score is replaced by the McMahon score.
- Smid corresponds to the McMahon score of players at the bottom of the bar winning half their games.
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
Examine ranking and pairing quality for different pairing strategies and weight models via Monte-Carlo tournament simulation to improve the performance of the pairing algorithm.
Complete rewrite of GoDraw in Linux. Very similar interface. Gabow N cubed matching. Any weight model.