Monday, May 10, 2010

How long is a piece of string?

Or rather, how long should World Championship matches be? More than twelve games? Ok. Sixteen ok, but not fourteen? Um, why? Back to twenty four, because that's what it used to be? Really? That's a good enough reason? Back to adjournments as well? Ok, what about more than 16, since it was not enough in 2000 for Kasparov to beat Kramnik, and we all know Kasparov was the better player really? But maybe 12 was enough in 2008, since Anand won, and we all like Anand?

For a long time we've had no good answers to these kinds of questions. And how could there ever be a definitive answer to such a question? Well, I think I've just worked it out. For the sake of argument, let's suppose that Grandmaster Alexandra Kosteniuk is correct in saying that:
To tell you the truth, although the match of such players are always awaiting with big interest and enthusiasm, the strategy for this kind of matches nowadays are rather uninteresting. Players, like Anand or Topalov, or even Kramnik are trying to minimize their risk and play positions with a small plus for White and try to hold a draw in boring and slightly worse endgames [with black].

A match is not a tournament, even if you win with the score +1 it's enough to get the title. This makes players play differently, not in an open and exciting style they usually play in tournament, but rather in very academical and unrisky ways.
In other words - that the recent lengths of these matches have been open to gaming.

So the answer to how long should a World Championship match should be? Now it's easy, almost obvious. The match should be sufficiently long that such a strategy doesn't make sense - that is, it doesn't make sense to aim for one victory and no losses, by changing style and openings. And the way to do that?

To make the matches sufficiently long that each player will almost certainly lose one game. Right? Except, there's a problem with gaming there too. Topalov as everyone knows is not as hot a rapid players as Anand or Kramnik; thus against Topalov, both Anand and Kramnik could aim for a drawn match confident that the rapidplay tiebreaks are likely to favour them. So instead, matches should be sufficiently long that each player will almost certainly lose two games.

And how can we calculate such a length? We take the player who generally produces more unbeaten runs. We double the length of their longest unbeaten run, and add the number two to it. That's how long each World Championship should be.

And what would that mean in practice? Um, I dunno. Anyone skilled at database use want to work this out? Perhaps retrospectively too?


Jonathan B said...

16 games I say.

I don't agree with the idea that tournament chess is more interesting than matchplay. In fact I feel very strongly that the opposite is the case.

dfan said...

I've been objecting to 12-game matches on historical principle but I have to admit that now that we've reached 12 games, this one feels like it's been about the right length.

ejh said...

This one has been outstandingly the best of the twelve-game matches though.

David said...

Kosteniuk doesn't say that the players are aiming for "one victory and no losses"; she says they're aiming for +1.

I don't see that longer matches would lead to less conservative strategy. Agreed that you can make the match long enough that player A is practically bound to lose a game; but does that knowledge really encourage him to take more risks? Surely not; because in such a match player B is also practically bound to lose games. Playing conservatively is still a good strategy.

(If you believe that you are stronger than your opponent, then in a match you should be looking to minimize the variance. Thus a player who fancies his chances should favour conservative play - and longer matches).

By the way, from a statistical point of view these matches are always far too short to determine who is actually the stronger player. (This is a significant issue in computer chess, where vast numbers of games are required before concluding that some change improves your program). By my back of the envelope calculation, it would take roughly 50 games (+17 -5 =28, or thereabouts) to demonstrate that a 100 point Elo advantage over some opponent was real - and rather more than that to demonstrate the presumably much smaller difference between, say, Topalov and Anand.

Adam Fysh-Foskett said...

I agree with Ehj that the match has been pretty good.

How about encouraging more ambitious play with the black pieces by stating that a drawn match goes to whoever won the most games with Black? It would be similar to the away-goals rule in football. There would be a danger that this could backfire and lead only to players playing less ambitiously with White!

Tom Chivers said...

On this subject, this is definitely worth a read.