Re: Why few fight for crown

[David KUIJT <kuijt@umiacs.UMD.EDU>]

Poster: David KUIJT <kuijt@umiacs.umd.edu>



Alfredo suggested a variant on Crown, where a contestant could win and
decide to pass it instead to the next person below because he could not
serve. 

> This being the case, one solution to the problem
> of small Crown Tourneys is this: Let people enter
> the lists without any intention of ruling.  The
> new Sovereign would be the the best fighter that
> day of those who *do* so intend.

Crown tournaments are a heap (in mathematical sorting terms), not a
perfect ordering.  When you remove the top element from a heap, the next
highest element is not obvious.  You must run a comparison between two or
more candidate elements to determine the next-highest.  The fact that the
bulk of the tournament is double-elim makes it even more complicated. 

In non-mathematical terms, let me illustrate the problem this way: after
the finals of Crown are over, you have the Winner (W), the Finalist (F)
who did not win, the Semifinalist who lost to the eventual Winner (Sw),
and the Semifinalist who lost to the eventual Finalist who lost (Sf).  If
W passes on the duty of being King, it is possible (even likely) that F
has not fought Sw.  So you must fight F versus Sw before knowing which one
to ask next.  And if that person passes also, the situation gets very
complicated.  It is possible that a combatant may fight exactly two fights
and lose them both, and be the third-best fighter in a double-elim
tournament, if he only fights the best and second-best fighter.


> The important thing is that there would be enough
> entrants in Crown Tourney to make it interesting.
> That is the important thing, isn't it?
> 
> -- Alfredo

Alfredo makes a funny!

The number of entrants is about as important to me as the colour of the
bunting.  There are a lot of interesting and problematic elements of Crown
Tourneys, and the number of entrants is WAY down on the list.

Dafydd

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