Maximum length of a terminating Beggar-My-Neighbor game

Ascertain the maximal length of a terminating Beggar-My-Neighbor game played with a standard 52-card deck under the 1911 Encyclopaedia Britannica rules, measured either in number of tricks or in total cards played.

Background

The authors recount decades of computational searches that progressively extended records for the longest known terminating games, measured both in tricks and cards played, and show that the distribution of random game lengths has an approximately exponential tail.

Despite extensive computation (exceeding 10^15 simulated games) and steady record improvements, the absolute maximum length of a terminating game remains unknown. The question persists even after the discovery of a non-terminating cycle, and relates to extremal behavior in the game's deterministic dynamics.