Re: Quoridor Tourney

["markthom" <markthom@flash.net>]

> Okay, the tournament is underway.  However, I am concerned.
>
> There are four pools of four players each.  How do you determine who goes
> on to the second round?  It's relatively easy to have one pool come out
> with three players at 2-1.  Then what?  A three player round-robin to
> determine a winner?  It could easily be tied again.
>
> I'm not saying there's a system which avoids ties. but pools this small can
> be a problem.  Also, I was expecting to be playing more than 3 games at once.

The original description of the tournament specified preliminary rounds of "4 or 5 players," and that the players who win the most
games in the first rounds will advance to the next round. So in case of ties, both (or all 3) of the players with the most ties will
advance to round 2. This was implied where I said "The players who win the most games in each preliminary round will advance to a
final round, which I hope will also have 4 or 5 players. (If there are so many ties in the preliminary section that the final
section has too many players, I may decide to form two rounds and have the winners from each secondary round match off afterward.)"

It's an interesting question how many ties we should expect. I ran a simulation of 4 players with ratings 1750, 1680, 1600, and
1530, in which I made the probability of the higher-rated player winning = (d+270)/(d+540) where d is the difference in ratings.
(The formula was devised to give P=.5 when ratings are equal and P=.55 for a 60-point difference, which I supposed was a
conservative guess.) In 10000 rounds, about 12% of the simulations resulted in 3-way ties. Of course, my assumptions in that could
be goofy. Time will tell.

Thanks for the input! I'll remember for the next time I do one of these, to aim for larger groups.

Mark Thompson