The familiar game of Snakes and Ladders, also known in some regions as Chutes and Ladders, begs a simple question: have you truly played it? This question arises when one considers the fundamental mechanics of gameplay itself.
Its roots trace back to ancient Indian pastimes, games like Pachisi that involved rolling dice to advance across a board of marked squares. Unlike Pachisi, which blended luck with strategic decision-making, early iterations of Snakes and Ladders relied solely on chance. The intent was to impart a spiritual lesson, encouraging players to accept their destiny. Through the ascent of the board, players could symbolically liberate their souls from worldly desires, moving towards spiritual enlightenment. Certain versions aligned with Hindu, Jain, and Sufi philosophies. Along this journey, virtuous actions were represented by ladders, elevating players to a superior position, while vices, depicted as snakes, demanded avoidance.
As families returned to the United Kingdom from the British Raj, the game journeyed with them. By 1892, versions began appearing in the UK. These adaptations featured simpler moral lessons and had largely shed the spiritual narrative. Over time, these moral undertones faded entirely, leaving only the mechanics of snakes and ladders.
A core definition of playing a game involves making choices that influence the ultimate result. In a game like Snakes and Ladders, where no player-driven decisions are part of the process, the act of playing is debatable. If you were to leave the room during a game and someone else took your turn, the outcome would remain unaffected. This highlights a critical distinction in game design.
Activities governed purely by chance can be meticulously analyzed through the lens of probability. A Markov chain serves as a mathematical model where each transition in a sequence is dictated by the probabilities stemming from the preceding states. For Snakes and Ladders, this allows for the calculation of probabilities concerning which squares a player might land on after a dice roll, factoring in the effects of ladders and snakes.
From each potential position, one can determine the probabilities after a subsequent roll, and so on. By extending this analysis across the entire board, it becomes possible to ascertain a player’s likely positions after a specified number of turns, estimate the game’s expected duration, and derive other relevant statistics. The principles of Markov chains find application across nearly every domain of applied mathematics, including thermodynamics and population dynamics.
Certain games, such as chess, contain no element of chance whatsoever. Many others occupy a middle ground, integrating both chance and skill. The precise equilibrium between these elements can significantly influence a player’s sense of investment in the gameplay. This might explain why some individuals gravitate towards games like Catan, where they strategically deploy resources allocated by chance, rather than to Monopoly, where decision-making opportunities are infrequent.
For older children who have grown weary of the standard Snakes and Ladders, consider this variation: after rolling the dice, the player chooses whether to move the indicated number of spaces forward or backward on the board. This straightforward alteration transforms the player into a far more active participant, thereby enhancing engagement.
The next time you encounter a new board game, observe whether you are actively making decisions that shape the outcome. If the gameplay relies solely on chance, perhaps you could leave it to a computational model like a Markov chain and opt for a game that genuinely involves your participation.
These articles are published weekly at newscientist.com/maker.
Peter Rowlett is a mathematics lecturer, podcaster, and author based at Sheffield Hallam University in the UK. You can follow him on Twitter @peterrowlett.