Endless love: On the termination of a playground number game
Iain G. Johnston

TL;DR
This paper analyzes a childhood digit game called 'LOVES', exploring its convergence behavior with different initial conditions, names, and languages, revealing factors influencing whether the game reaches a fixed outcome.
Contribution
It provides a detailed examination of the game's convergence properties, including the impact of names, surnames, and language variations, and offers an estimate for non-convergence likelihood.
Findings
Top UK first names rarely exhibit non-convergence.
Including surnames increases the chance of non-convergence.
Names with intermediate letter counts often perform best.
Abstract
A simple and popular childhood game, `LOVES' or the `Love Calculator', involves an iterated rule applied to a string of digits and gives rise to surprisingly rich behaviour. Traditionally, players' names are used to set the initial conditions for an instance of the game: its behaviour for an exhaustive set of pairings of popular UK childrens' names, and for more general initial conditions, is examined. Convergence to a fixed outcome (the desired result) is not guaranteed, even for some plausible first name pairings. No pairs of top-50 common first names exhibit non-convergence, suggesting that it is rare in the playground; however, including surnames makes non-convergence more likely due to higher letter counts (for example, `Reese Witherspoon LOVES Calvin Harris'). Different game keywords (including from different languages) are also considered. An estimate for non-convergence…
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