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Tournaments
I played in my first F2F tournament in a while a few weeks back. Nine
players entered the nonexpert division, meaning that two players did
not get a firstround bye and seven did.
I was wondering if tournaments have ever tried to equalize the effect
of byes by handicapping later matches. For example, suppose 12
players enter, playing 11point matches. I don't have my match equity
table handy (or memorized) but it seems that leading 30 to 11 would
be about 67% match equity, roughly. It would seem to be fair, then,
that 8 players would play the first round, and each winner would start
the secondround match with a 30 lead. This would give each of the 12
players a 1/3 chance of reaching the third round.
Has anyone ever done this in practice?


Carlo Melzi writes:
Just a few time ago I started to study something similar, because one of
my friend gave me the idea. Unfortunately, some problems were just too
big:
1) The system 67%33% works only if the total numbers of players is 12 or
24, because there is the same number of byes and preturns.
In all the other situations, a player who had to play a preturn would
clearly prefer to play a player who had a bye in the second round, in
order to start with an advantage (67% vs. 50%).
Thus, we should rearrange third, fourth (and so on) rounds to give the
same probability of winning the tournament to all the players AFTER the
draw.
I studied the "10players" tournament and the math should be this:
A,B,C,D play a preturn. The winners (let's say A and C) play then E and F
having a score advantage that gives them 67% in the match.
G,H,I,L play normally their round.
In the semifinals, the winners of AE and CF should start with a 60%
advantage versus (let's say) G and I.
This way every player would have a 10% chance to win the tournament AFTER
the draw.
A,B,C,D: 50*67*60*50=10
E,F: 33*60*50=10
G,H,I,L: 50*40*50=10
As you can see, this is rather complicate (and it's even more with more
players).
2) It's not always so easy to give precisely 66.67% in a match (in a 7pts
tournament, using Neil's Numbers, starting from 20 gives 63% and 30
gives 69.5%; 0  3 gives 66%.......but it's no more a 7pts tournament!!!
:) )


Steen Ladelund writes:
In Aarhus, Denmark where I live, we have a tournament every two weeks
where we auction the byes. I think this is a beutifull, simple and fair
way of dealing with byes in knockout designs involving entry fees.
I wonder if its used elsewhere?

Steen Ladelund * Dep. of Theor. Statistics,
office H2.14 * University of Århus.
tlf: (+45) 8942 3499 * Ny Munkegade, bygn. 530
Email: ladelund@imf.au.dk * 8000 Århus, Denmark.




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