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<p>Geoff:</p>
<p>1) Your probabilities are incorrect : 86.6 +(2*1.8) + (2*0.4)
does not add up to 100%.</p>
<p>2) You state: "We have agreed so far that setting the bar at 1k
or 1d produces an unfair tournament". <b>False.</b> The
tournament is perfectly fair - one player has a greater chance of
winning than others (based on previous results) but this does not
mean it is a foregone conclusion. Heather Watson and Serena
Williams both enter Wimbledon and they have equal opportuities to
win - you don't say "Serena is so much stronger than Heather
therefore she should be handicapped to give Heather a chance" (or
to ban Heather from entering because she is considered to have no
chance at all). <br>
</p>
<p>3) Please remember that the purpose of a Go Tournament is for
people to enjoy themselves - not to produce a "perfect" result.
And the strongest players - those affected by your analysis -
would rather play even games than handicap games. Until you can
provide a consensus view to the contrary, please stop this
ridiculous idea of handicap games at the top of the draw.</p>
<p>Toby. <br>
</p>
<br>
<div class="moz-cite-prefix">On 02/10/2018 12:10, Geoff Kaniuk via
tournament-org wrote:<br>
</div>
<blockquote type="cite"
cite="mid:c80314a8-72ae-fa57-78a5-2cd3fbf81bb4@kaniuk.co.uk">
<br>
There is overwhelming support for a bar at 1k with a spread from
2k to 1d, and a few suggestions allowing handicap above the bar.
<br>
<br>
It seems that we expect the 5d to win no matter where we set the
bar, but in order to run a McMahon tournament we are going to set
the bar to 1k anyway.
<br>
<br>
One guide to setting the bar is that all players above the bar
should have a reasonable chance of winning the tournament. As
stated we assume that all players are correctly rated. This means
we know the win probability for each pairing.
<br>
<br>
Let us suppose the bar is at 1k in our entry of:
<br>
5d 1d 1d 1k 1k 2k 2k 3k 3k 4k 4k 5k .....
<br>
<br>
Then given a plausible tournament, the top players have these
chances of winning all three games:
<br>
<br>
PLAYER OPPONENTS PER ROUND PWIN PROB WINNER
<br>
1k 1k 1d 5d 0.50*0.40*0.02 = 0.40%
<br>
1d 1k 1d 5d 0.60*0.50*0.06 = 1.8%
<br>
5d 1k 1d 1d 0.98*0.94*0.94 = 86.6%
<br>
<br>
I think this makes it clear that the 1k and 1d have effectively no
chance to win this tournament. Not much changes if you set the bar
to 1d.
<br>
<br>
Going back to basics, the McMahon system is designed to provide a
fair pairing at every round. It does this by assigning an initial
MMS determined by your grade. The fairness comes about because we
assume grades are realistic and always pair players on the same
MMS where possible.
<br>
<br>
The winner is the player who ends on the maximum MMS. If there is
only one strongest then he or she will have a massive advantage.
Hence we have a bar - and in the old days there were plenty of 4d
and 5d around in the top group so no problems.
<br>
<br>
If an an even pairing is not possible, then it is common for
players below the bar to play with handicap - often MMS
difference-1 but this can of course be varied.
<br>
<br>
<br>
We have agreed so far that setting the bar at 1k or 1d produces an
unfair tournament. Therefore in order to continue play in the
spirit of McMahon, we should consider raising the bar to 5d. For
the sake of clarity this is equivalent to setting the bar at 6d.
<br>
<br>
In the example given, setting the bar at 1k produces an odd number
in the bar, so one player chosen at random will have to play
down. The 5d therefore might play a 2k in round 1.
<br>
<br>
Setting the bar at 6d avoids this kind of problem. We pair for the
smallest MM difference so the 5d will play the 1d in round 1 with
a handicap of 3 stones by usual rules.
<br>
<br>
This levels the playing field somewhat but calculations show that
this still favours the 5d and better would be: handicap is the
straight MMS difference.
<br>
<br>
My conclusion is that in these anomalous cases setting the bar
anywhere without handicap goes against the basic principles of
McMahon pairing.
<br>
<br>
In looking at variants of setting the bar with handicap say in a
super-group just leads to complications (e.g. when top players who
miss rounds are supposed to be below the bar).
<br>
<br>
The simplest and most elegant solution to this problem is just to
set the bar to 1 higher than the highest grade. Assign handicaps
by straight MMS difference where needed. Then let McMahon do its
job without any further interference.
<br>
<br>
Geoff
<br>
<br>
<br>
33 Ashbury Close, Cambridge CB1 3RW 01223 710582
<br>
<br>
On 02/10/2018 00:21, Richard Wheeldon via tournament-org wrote:
<br>
<br>
<br>
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</blockquote>
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