Equiprobable and attacked-square chess entropies by phases, levels of play and game outcomes

J. D. A. Islas-García (), M. del Castillo-Escribano () and M. del Castillo-Mussot
Additional contact information
J. D. A. Islas-García: Facultad de Ciencias, Universidad Nacional Autónoma de México, México City 04510, Mexico
M. del Castillo-Escribano: Escuela Nacional de Estudios Superiores, Universidad Nacional Autónoma de México, Morelia 58190, Mexico
M. del Castillo-Mussot: Instituto de Física, Universidad Nacional Autónoma de México, México City 04510, Mexico

International Journal of Modern Physics C (IJMPC), 2022, vol. 33, issue 02, 1-18

Abstract: In any legal chess position, we define an attacked-square entropy S for either Black or White pieces in terms of the square occupation probability pi=mi∕M, where m is the number of all possible movements to square i (free or occupied by an opponent’s piece) and M is the total mobility defined as the sum of all possible movements. Thus, each attacked square contributes to the entropy according to its received “firepower†concentration. A simpler nonsquare-dependant equiprobable entropy Se in terms of equal probabilities pe=1∕M always yields Se−S≥0. On average, the difference Se−S is very large in the Opening phase and S decreases faster for lower ranked players after move 25. A major cause of the reduction of S during a game is material loss, which is an irreversible process. By game outcome, gaps in average 〈S〉 among winners, draws and losers are larger for Amateur players than for Elite players, both in the Middlegame and Endgame. Statistically, Elite players exhibit narrower dispersions in S. Also, the entropy rates of the Elite level fluctuate much less than the entropies of other levels. Density of attacks in the four-square central zone is very high in the Opening, specially for Elite players.

Keywords: Chess; statistics; level of play (search for similar items in EconPapers)
Date: 2022
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S0129183122500279
Access to full text is restricted to subscribers

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wsi:ijmpcx:v:33:y:2022:i:02:n:s0129183122500279

Ordering information: This journal article can be ordered from

DOI: 10.1142/S0129183122500279

Access Statistics for this article

International Journal of Modern Physics C (IJMPC) is currently edited by H. J. Herrmann

More articles in International Journal of Modern Physics C (IJMPC) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().