Did the Soviets collude? A statistical analysis of championship chess 1940-1978

We expand the set of outcomes considered by the tournament literature to include draws and use games from post-war chess tournaments to see whether strategic behavior can be important in such scenarios. In particular, we examine whether players from the former Soviet Union acted as a cartel in international all-play-all tournaments - intentionally drawing against one another in order to focus effort on non-Soviet opponents - to maximize the chance of some Soviet winning. Using data from international qualifying tournaments as well as USSR national tournaments, we consider several tests for collusion. Our results are inconsistent with Soviet competition but consistent with Soviet draw-collusion that yielded substantial benefits to the cartel. Simulations of the period's five premier international competitions (the FIDE Candidates tournaments) suggest that the observed Soviet sweep was a 60%-probability event under collusion but only a 25%-probability event had the Soviet players not colluded.