Fairer Chess: A Reversal of Two Opening Moves in Chess Creates Balance Between White and Black

Brams, Steven J. and Ismail, Mehmet S. (2021): Fairer Chess: A Reversal of Two Opening Moves in Chess Creates Balance Between White and Black. Published in: 2021 IEEE Conference on Games (CoG)

Abstract

Unlike tic-tac-toe or checkers, in which optimal play leads to a draw, it is not known whether optimal play in chess ends in a win for White, a win for Black, or a draw. But after White moves first in chess, if Black has a double move followed by a double move of White and then alternating play, play is more balanced because White does not always tie or lead in moves. Symbolically, Balanced Alternation gives the following move sequence: After White’s (W) initial move, first Black (B) and then White each have two moves in a row (BBWW), followed by the alternating sequence, beginning with W, which altogether can be written as WB/BW/WB/WB/WB… (the slashes separate alternating pairs of moves). Except for reversal of the 3rd and 4th moves from WB to BW, this is the standard chess sequence. Because Balanced Alternation lies between the standard sequence, which favors White, and a comparable sequence that favors Black, it is highly likely to produce a draw with optimal play, rendering chess fairer. This conclusion is supported by a computer analysis of chess openings and how they would play out under Balanced Alternation.

• Item Type: MPRA Paper
• Language: English
• Keywords: combinatorial games, chess, fairness, sequencing
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory

References

Adorján, A. (2004). Black is Still OK! London: Batsford.

Brams, S. J., and A. D. Taylor (1999). The Win-Win Solution: Guaranteeing Fair Shares to Everybody. New York: W. W. Norton.

González-Díaz, J., and Palacios-Huerta, I. (2016). “Cognitive Performance in Competitive Environments: Evidence from a Natural Experiment.” Journal of Public Economics, 139 (July): 40-52.

Schaeffer, J., N. Burch, Y. Björnsson, et al. (2007). “Checkers Is Solved.” Science, 317(5844): 1518-1522.

Schwalbe, U., and Walker, P. (2001). “Zermelo and the Early History of Game Theory.” Games and Economic Behavior, 34(1): 123-137.

Tomašev, N., U. Paquet, D. Hassabis, and V. Kramnik, “Assessing Game Balance with AlphaZero: Exploring Alternative Rule Sets in Chess.” Unpublished, https://arxiv.org/abs/2009.04374

Zermelo, E. (1913). “Über eine Anwendung der Mengenlehre auf die Theorie des Schachspiels,” Proceedings of the Fifth International Congress of Mathematicians 2: 501-504.