Re: Quoridor Tourney

[Randall Bart <barticus@att.net>]

'Twas 00:00 -0500 on Friday 1/10/2003 when owner-pbmserv-users@gamerz.net 
wrote:
>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.

That's way more work than I put into that question.  In a four player round 
robin, there are six games.  2^6=64.  Of those 64 possibilities, there are 
8 three-way ties.  8/64=12.5%.  If the chances of winning aren't 50-50, it 
will end up a little less.
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