Have you ever played Snakes and Ladders (also known as Chutes and Ladders)? If so, are you a serious competitor?

The game traces its roots back to ancient Indian games like Pachisi, where players roll dice to progress on a square board. While Pachisi incorporates elements of luck and skill, the earliest variations of Snakes and Ladders relied solely on chance to impart a spiritual lesson about accepting one’s fate. Players advanced across a board inspired by Hindu, Jain, and Sufi teachings, cultivating virtues represented by ladders while avoiding vices symbolized by snakes.

This game made its way to the UK through families returning from British colonies. Starting in 1892, a British adaptation appeared, focusing more on simplistic morality and minimizing the spiritual aspects. Over time, moral teachings faded, leaving just the snakes and ladders.

I believe that playing a game entails making decisions that influence the outcome. In games devoid of choice, like Snakes and Ladders, the player isn’t truly engaged. If you step out of the room and someone else takes your turn, does the result change?

The randomness of gameplay can be analyzed using probability theory. A Markov chain illustrates how each step in a sequence is dictated by the probability of transitioning from the preceding position. For Snakes and Ladders, it’s possible to calculate the likelihood of landing on different spaces after rolling the dice (factoring in ladders and snakes). By analyzing all possible moves, you can determine a player’s expected position after a specified number of rolls, the estimated game duration, and other valuable statistics. Markov chains find applications across various fields in applied mathematics, including thermodynamics and population modeling.

Some games, like chess, are purely skill-based, while many others blend elements of chance and strategy. This balance significantly impacts player engagement and immersion, explaining why some favor games like Catan, which require strategic resource allocation amidst randomness, over others like Monopoly that demand fewer decisions.

For older kids who might find Snakes and Ladders monotonous, consider adding a twist: after rolling, let players decide whether to navigate up or down the board. This small adjustment enhances player interaction and engagement.

The next time you explore a new board game, ensure you’re making choices that impact the results. If not, consider pivoting to games that incorporate Markov Chains and strategic decision-making.

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Peter Rowlett – A mathematics lecturer, podcaster, and author at Sheffield Hallam University, UK. Follow me on Twitter @peterrowlett