MacMahon and Swiss Tournaments

[Robert Jasiek]

In the td mailing list information about MacMahon has been asked for, so:
From my experience of having visited many European tournaments
and seen different programs I can give some useful information
about McMahon (MM).

McMahon features:
- tournament with an announced number of R rounds (generally fixed)
- the average player is expected to participate in more than R/2
- according to announcement or check of present players before first
round a minimal valid rank (e. g. 25kyu) is set equal to a MM-value of
zero, Z
- according to announcement or check of present players before first
round a maximal valid rank, called MM-bar, B, is set for distinguishing
all players who should have a realistic chance to win the tournament;
e. g. 3dan; the MM-bar should not exclude too many players from the
top and not include too many players what could lead to awful
opponents' scores
- all players of rank that equals Z or is lower get Z as their value
- each rank greater than Z gets a MM-value that increases by 1 each
rank until B
- all ranks over B become B
- each player gets his proper starting MM-value before the first round
- the Swiss system is a special case of MM with B=Z=0 and useful for
tournaments with full handicaps or for some championships that
cannot be played as round-robin (e. g. WAGC or a local blitz
tournament)
- after each round for each player his MM-value is increased by 1 or
0.5 or 0 if he wins, ties / misses, loses
- before the first round pairing parameters are fixed: in decreasing
order of importance MM-value, second value, third value
- useful second and third values for not too small tournaments are
SOS, SODOS
- SOS = sum of opponents' scores, where score = current MM-value
- SODOS = sum of defeated opponents' scores
- further criteria may be: B/W choice, not same opponent again, not
same city
- each critirion may have a corresponding probability value
- not all criteria for all players can be fit
- an algorithm (in a program) chooses a proper pairing for all players
- in tournaments up to 30 persons hand draw might be enough

MM result:
- before the tournament criteria for determining a winner are set
- useful are in decreasing order: points, second value, third value
- points = win and tie points
- second value, third value: as used in pairing algorithm, e.g.
SOS, SODOS
- for a single player the element of luck of draw is rather high as
to values of decreasing importance; it may be wise to ignore a
third value and have more than one winner or second place getter
- it may be a good idea to spend prices on players under B with a
sufficiently high points value

Handicaps:
- normally none
- maybe only below some rank used
- often reduced handicap as to MM-value difference, e. g. difference
minus 2

Algorithms:
- a pairing needs to be fair, i.e. especially to avoid one player to be
paired too often to players with greatly differing MM-values
- not all players can be paired optimally in all rounds
- Christoph Gerlach (Germany) has proved in his diploma (which
can be obtained from him as a manuscript) that a global optimum
for all players and all rounds exists and can be detected by a
proper algorithm

Program:
- I strongly recommand to use "MacMahon" by Christoph Gerlach.
It implements an algorithm for a global optimum of a pairing, has
many criteria options and a documentation. It runs with windows.
A 386+ is recommanded, at least 8MB are very useful for quick
pairings (a few minutes for a few hundred people). I do not know
whether it is free or currently has a tax of about 0.5DM per player.
I do not know whether it is available in the net . His address:
Christoph Gerlach, Lange Laube 24, D - 30159 Hannover
(Germany). The program has been used for many German and
several European tournaments including EGC.

SuperMM:
- in a championship that needs to determine the true champion
a MM tournament might have a super MM group if too many
strong players participate and cannot be distinguished in too few
rounds
- super MM is B+1 and donated too a seeded part of all B players
- seeding is always questionable, but sometimes more than 10
rounds or so is not enough with many strong players

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Robert Jasiek
jas...@berlin.snafu.de
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