A new chess tie-break system based on directed network analysis
David Smerdon June 30, 2012
The 2011 European Chess Championships saw over 400 of Europe’s top chess players compete for one of 23 qualifying spots for the World Chess Cup, and with it a shot at the world title and the e1.5 million prize fund. With only eleven rounds played in the Swiss-system tournament (where all players play all eleven games), the chances of potential qualiﬁers being tied on the same score were high, and so it transpired: Four players ﬁnished on 8.5 points (out of eleven)1 , eleven players ﬁnished with 8.0, and a further 29 ﬁnished on 7.5. The eventual decision of how to decide the ﬁnal eight available qualifying positions from these 29 players was highly controversial, leading to oﬃcial protests, heated debate in all levels of the chess community from oﬃcial international forums to amateur clubs, and eventually an admission from FIDE2 that the current tie-breaking regulations were woefully inadequate.
At the same time, in South Africa, the 2011 Commonwealth Chess Championships also ended in a tie, on this occasion for ﬁrst place. Despite the employment of the oﬃcial FIDE tie-break procedures in this elevenround event with over 700 players, the gold medal was ultimately decided by the result on board 44 of by a player who ﬁnished 144th. It has become increasingly clear that current tie-break methodologies in large tournaments are proving unsatisfactory in their stated objective of determining the strongest performing player.
Meanwhile, an escalating issue in international chess over the past few years is the high number of draws (and particularly ‘soft’ draws) between top players. With typically several games played each day, each lasting up to ﬁve hours, open tournaments are acutely mentally draining. As a result, many grandmasters employ a strategy of agreeing to quick draws in games against other grandmasters to conserve energy. This helps to ensure they win their games against weaker players, frequently netting a score suﬃcient for a large expected payout from the prize fund. However, the consequences for spectators, sponsors and the sport ∗ 1
Social Network Analysis Research Proposal, Tinbergen Institute In international chess, a win is recorded as one point, a loss as zero, and a draw earns a player 0.5 points. 2 ´ The F´d´ration Internationale des Echecs, or World Chess Federation e e
in general are rather more damaging. In an age when grandmasters are concerned about protecting their livelihood but the general public craves increasing levels of excitement and drama for their entertainment purposes, professional chess is at risk of becoming obsolete. Many radical measures have been suggested to combat the draw problem in chess, but none have found favour with the overarching chess community, traditionalists and liberals alike.
This proposal seeks to address both the inadequacies of current tie-break systems and the issue of everincreasing draws in chess by introducing a new tie-break system for large tournaments. The system uses a measure based on both direct and indirect wins, and is a generalisation of standard centrality values stemming from the directed network of wins throughout an event.
2.1 Chess tie-break systems
The above examples are not unusual in the chess world or indeed in many other sporting and gaming contests. This is particularly the case in large open tournaments in which players typically play against diﬀerent opponents and in which it may be undesirable or impractical for ties to be broken by straight head-to-head playoﬀs. In the majority of chess events held around the world, the so-called Swiss pairing system matches players of a similar score against each other over a ﬁxed number of rounds (usually seven, nine or eleven), with the top ﬁnishers usually facing opponents of increasing diﬃculty over the course of the...