Are you bored of snakes and ladders? Some math can help bring back the fun

Have you ever played Snakes and Ladders (also known as Chutes and Ladders)? are you sure

The game has its origins in ancient Indian games in which players roll dice to advance across a board of squares, such as Pachisi. While Pachisi mixes luck and skill, early forms of snakes and ladders used pure chance to teach players a spiritual lesson about accepting their fate. Players climbed the board, freeing the soul from earthly desires to reach the goal of spiritual enlightenment, with versions associated with Hindu, Jain and Sufi philosophies. Along the way, they can display virtues that manifest as ladders that lift them to a higher position, but they must avoid the vices represented by snakes.

The game traveled with families returning from the British Raj to the UK. From 1892, British versions appeared with simpler morals and lacked the spiritual path. Over time, the moral lessons faded away, leaving only snakes and ladders.

I would define playing a game as taking a role in making decisions that affect the outcome. In games like snakes and ladders where you don’t choose, you aren’t really playing a game. If you left the room and someone took your turn while you were gone, would the outcome be different?

Gaming involving pure chance can be studied using probability theory. A Markov chain is a model where each step in the sequence is determined by the transition probabilities to it from previous steps. For snakes and ladders, we can calculate the probability of landing in different places after rolling the dice (taking into account any ladders or snakes). From each of these positions we can find the probabilities after the second roll and so on. In this way, we can get the probable positions of the player after a given number of throws, the expected length of the game and other statistics. Markov chains have applications in almost all areas of applied mathematics, including thermodynamics and population modeling.

Some games, such as chess, involve no chance at all. Many sit in between, combining elements of chance and skill, and their exact balance can affect how invested you feel in the game. This is perhaps why some people prefer a game like Catan, where you decide how to use randomly allocated resources, to Monopoly, where you only make decisions occasionally.

For older kids who are bored with snakes and ladders, try this twist: after rolling, decide whether to move the number of displayed squares up or down the board. This simple change will make you a much more active player and increase engagement.

The next time you play a new board game, see if you’re making decisions that affect the outcome. If not, maybe leave the game to the Markov chain and try to switch to the one that actually applies to you.

These articles are published weekly at
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Peter Rowlett is a mathematics lecturer, podcaster and author based at Sheffield Hallam University in the UK. Follow him @peterrowlett

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