Chess can be significantly enhanced by rearranging the starting pieces, creating a more challenging or equitable game, as discovered by physicists.

In traditional chess, the pieces initiate the game symmetrically, with rooks, knights, and bishops positioned on the board’s edges, while kings and queens are centrally located. This fixed setup enables elite players to memorize optimal opening moves, potentially leading to predictable and uninspiring matches.

In the 1990s, the renowned chess grandmaster Bobby Fischer proposed an innovative variation to mitigate this reliance on memory. This variation, which effectively randomizes the starting positions of the seven pieces behind the board, allows for a fair arrangement between the white and black pieces, under the rule that bishops, rooks, and kings maintain relative positions. Known as Chess960 due to its 960 possible starting positions, this format has recently gained immense popularity, drawing players like former world champion Magnus Carlsen to competitive events.

Although Chess960 appears equitable due to its randomness, Marc Barthelemy from The University of Paris-Saclay has revealed that this perceived fairness is deceptive after analyzing all possible configurations.

Typically, the white pieces, who commence the game, hold a slight edge in standard chess. Barthelemy’s analysis indicates that while certain Chess960 setups may greatly favor white, others could advantage black. “Not all positions are equal,” he explains.

To arrive at these findings, Barthelemy utilized Stockfish, an open-source chess engine, to evaluate each starting position’s complexity based on how challenging it was for both players to determine their next moves. By comparing the ease with which the best move could be identified, he assessed the complexity of each configuration. If finding the best move was straightforward, the player encountered minimal decision-making challenges. However, if both players faced comparable difficulties, the decision-making process became increasingly complex.

His research identified the starting position BNRQKBNR as the most complex, while QNBRKBNR offered a balanced challenge for both players. Such insights could assist tournament organizers in ensuring fairer matchups, Barthelemy notes.

Conversely, Vito Servedio from Austria’s Complexity Science Hub argues that randomness inherently provides fairness, and favoring specific Chess960 arrangements over others may lead players to prepare excessively. “It’s more equitable as players start on an equal footing,” Servedio asserts. “Grandmasters have deep knowledge of standard chess openings, but cannot prepare for every potential Chess960 setup.”

Barthelemy also discovered that the standard chess setup is relatively unremarkable regarding fairness and complexity in comparison to many of the other existing positions. “Surprisingly, the standard chess arrangement is not particularly striking,” Barthelemy observes. “It lacks balance and asymmetry, sitting rather centrally in the spectrum of positions. The reasoning for this historical choice remains unclear.”

“In a vast array of positions, it stands in the middle,” Servedio remarks. “Is it purely coincidental? I cannot say.”

Barthelemy notes that measuring complexity is not the sole method for evaluating chess game difficulty. Giordano De Marso from the University of Konstanz comments that the true challenge of a position often lies in having a singular move to identify, rather than choosing the best among several options.

De Marso expresses uncertainty regarding whether Barthelemy’s higher complexity scores correlate with players perceiving games as more difficult but suspects they do. “If increased positional complexity leads to longer deliberation times, it strengthens the case for this measurement,” he concludes.