The bishop and knight checkmate on a large chessboard

TL;DR

This paper details a precise method for a king, bishop, and knight to checkmate a lone king on arbitrarily large chessboards, addressing gaps in previous descriptions and analyzing the problem's asymptotic aspects.

Contribution

It provides a complete, rigorous description of the Telesin checkmating procedure and proves its effectiveness against all defenses on large boards.

Findings

The checkmating method works universally on large boards.

The paper clarifies the previously incomplete description of the procedure.

Open questions remain about the maximum distance to mate as board size increases.

Abstract

In 1983 the chess periodical EG published a summary of a letter from Julius Telesin outlining how a king, a bishop and a knight can checkmate a lonely king on an arbitrarily large chessboard. The Telesin checkmating procedure doesn't seem to be widely known, and the published account left out a number of details. We describe the method precisely and show that it works against every defense. We also discuss the open question of the asymptotics of the largest distance to mate on a large square board.