Erdős numbers for chessplayers

The "Erdős number" is part of the folklore of mathematics and associated scientific fields.  It is named after Paul Erdős, a famously collaborative mathematician, and traces networks of co-authorship of scientific papers.  For example, if you co-authored a paper with  Erdős (a lot of people did!) then you have an Erdős number of 1.  If you co-authored a paper with one of his co-authors, your number is 2, and so on.  Almost everyone in mathematics has an Erdős number less than 9.  Even people in different branches of science often have Erdős numbers, and surprisingly low ones.  For example, mine is 5, via a paper I wrote with statistician Elizabeth Thompson who herself has a number of 4.  This means that a whole group of cancer researchers who probably have never heard of Paul Erdős, but who are co-authors on papers with me, have numbers of 6.  The network even reaches into economics, linguistics, and social sciences, as well as astronomy, physics, and computer science.

I started thinking about the chess equivalent when I noted that I am only a few links away from someone who beat Bobby Fischer.  I decided that the chess equivalent has to involve wins (not draws or losses):  how many steps are you away from beating Bobby Fischer?  My "Fischer number" is 3!  I beat Joseph Frantz, who beat Viktors Pupols, who famously beat Bobby Fischer in 1955.  (Viktors is still a force to be reckoned with; last weekend in the Washington Open an IM tried a fancy gambit on him and was blown off the board.  I could get to a Fischer number of 2 if only I could beat Viktors, but I have never managed better than a draw.)

That was almost too easy--Viktors' game is quite famous, and I didn't have to go outside my local community.  What about a "Carlsen number"? I was stumped by this one until I thought of Jim Tarjan's win vs. Vladimir Kramnik at the Isle of Man last year.  Tarjan is in Oregon, a chess community closely linked with mine in Seattle.  A little database search yielded two Seattle players who have beaten Tarjan, and from there it was easy to make the links.  My Carlsen number is 5:  I beat Ignacio Perez, who beat Anthony He, who beat Jim Tarjan, who beat Vladimir Kramnik, who beat Magnus Carlsen.  (If only I could have beaten Anthony He the time he dropped the exchange to me!  Then I'd be a 4.)  It's possible there's a shorter path but I couldn't find one.

Figuring out these numbers can take a bit of detective work, but it's fun!  I suspect that, just as with Erdős numbers, most tournament chessplayers actually have a Fischer or Carlsen number, and that most are smaller than you'd think.

I will try to have tournament reports shortly; I've gotten a bit behind.