Chess is a relatively simple game to learn but a very difficult one to master. Because the starting positions of the pieces are fixed, top players have relied on memorizing the “best” opening moves, which can sometimes result in boring, predictable games. To encourage more creative play and move away from pure memory, former world champion Bobby Fischer proposed Chess960 in the 1990s.
This variant of the game is so called because there are exactly 960 starting positions. It randomizes where the pieces at the back of the board (such as the knights, bishops and the queen) are placed at the start while keeping the rest of the rules the same. Although it was thought that this would make starting the game equally fair and complex for both players, new research suggests otherwise.
Putting chess to the test
In a study available on the preprint server arXiv, Marc Barthelemy at Paris-Saclay University used the open-source chess program Stockfish to analyze each of the 960 starting positions. He also developed a statistical method to measure decision-making complexity by calculating how much “information” a player needs to identify the best moves.
He found that, rather than a level playing field or level playing board, white starts with a clear lead in 99.6% of all 960 positions. This demonstrates that moving first (white pieces always start a match) is a permanent advantage built into the game’s mechanics, irrespective of any memorized move.
Another surprising conclusion from the research was that the standard chess setup (position #518 in Chess960) we have used for more than 500 years is average in terms of the amount of thinking required.
Historical accident
“Standard chess, despite centuries of cultural evolution, does not occupy an exceptional location in this landscape: it exhibits a typical initial advantage and moderate total complexity, while displaying above-average asymmetry in decision difficulty,” wrote Barthelemy in his paper. He suggests that this starting setup is a historical accident and became the standard because it is easy to remember and visually symmetrical.
The research also reveals that the standard game can be a one-sided affair, as players with black pieces have to put in more mental effort than those with white pieces just to stay equal. For a truly fair and balanced match, Barthelemy says we should play position #198, while position #226 is the most complex setup of all 960 starting positions.
The paper concludes with a suggestion that organizers adopt these findings to help them select fair starting positions at Chess960 tournaments. Beyond chess, Barthelemy’s statistical framework can be used to analyze other board games for balance and complexity.
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More information:
Marc Barthelemy, Not all Chess960 positions are equally complex, arXiv (2025). DOI: 10.48550/arxiv.2512.14319
Journal information:
arXiv
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