Hmmmm...Ajedrecista wrote: ↑Thu Jan 29, 2026 9:05 pm...But the OP asked about winning more game pairs, which introduces a subtle difference: an engine can win more engine pairs while losing more games than wins. How can be possible? It is very unlikely to be fair, but mathematically possible: please imagine that the engine A is only able to win game pairs 1.5-0.5 against the engine B, while the engine B only wins game pairs 2-0 against the engine A, with A winning 1.5-0.5 more frequently than B wins 2-0, but not far more:
If this actually happened over a large number of games, then there would be a problem with the Elo rating system!
The Elo rating system is a statistical distribution, and thus requires independence between events. If this was happening over a large number of games, then that independence would appear to be lacking. There could be reasonable explanations why this anomaly was happening - but none of these would be compatible with independence between games.
If you were seeing this kind of anomaly, then maybe probability theory might provide a better model than one based on statistics: this could provide insight into where the dependence (or "lack of independence") might be coming from. Maybe the players were somehow adapting to each other as they played?