🔢 Discover how math provides a strategic advantage in games and how the rules reveal fascinating mathematical principles.
Games and mathematics
Marcus du Sautoy, the famous British mathematician and author, opens the doors to the fabulous world of board games in his latest work released last November: Around the World in Eighty Games: From Tarot to Tic-Tac-Toe, Catan to Chutes and Ladders, a Mathematician Unlocks the Secrets of the World’s Greatest Gameswhich could be translated (unofficially) Around the World in Eighty Games.
From the subtle game of chess to the fun games of Tic-Tac-Toes, the math teacher gives us a unique look at how these games are much more than just entertainment. They represent incredible constructs woven into the fundamental principles of mathematics.
Why math?
Why would a mathematician be interested in games? Games, like mathematics, are based on precise rules, similar to mathematical axioms. To play is to discover the ramifications of these rules, to prove theorems. Understanding the math behind a game can provide a huge strategic advantage.
For example, in Monopoly, knowing the most visited properties can transform your approach to the game. Du Sautoy reveals that the prison space is the most visited, thus increasing the value of orange properties after being released from prison. (Be careful, don’t tell your opponents!)
Knowledge as a strategic advantage
Games have always been a central part of human culture, creating connections and shared stories. Unlike a book or a film which awakens our emotions, a game fully engages us in a story whose unfolding we influence through our choices. It’s this mix of chance and strategy that makes each game unique.
Understanding the mathematical workings of a game can give you a decisive advantage. For example, in Monopoly, knowing which properties are most likely to be visited can change your strategy.
The illustrious history of Indian games
India gave us two fabulous games: chess and Snakes and Ladders. Originally, a game of chess brought together four people, far from the two-player version we know. The Snakes and Ladders game was a philosophical tool representing the journey to enlightenment, very different from today’s children’s game.
According to du Sautoy, a great game has a balance of chance and skill, simple but profound rules, and the ability to keep players focused until the end. Even in a seemingly unequal game, like a novice against a master in chess, a surprise must always be possible.
The evolution of chess from a game of dice to a strategic battle reflects our growing appreciation for thinking about chance. Likewise, the transition of snakes and ladders from a spiritual tool to simple entertainment illustrates the transformation of our relationship to play.
The criteria of a great game according to du Sautoy
A good game must above all be:
- Strategic
- Entertaining
- Accessible
- Original
A good game skillfully balances chance and tactics. Even bad dice rolls in backgammon can be made up for with wise strategy. This is what makes the depth and richness of this 5000 year old game, a model of perfect design according to du Sautoy.
First, a game should never be finished before it has started. Even if you are not as good as your opponent, you must have a chance of winning. A good game should not be punitive: a bad move should not ruin the game. In Lorcana, you are never sure of having lost until you have… lost (well, 1 to 18 still smells like a tree 🌲). A good game should not be punitive: one bad shot, and we lose the game.
Second, it is essential that the game does not end before its end. The best games are the ones where everyone has a chance to win in the end. This is probably why Monopoly is often criticized: it quickly becomes obvious who owns most of the properties, and the game then becomes about ruining everyone else.
Third, if a game is to have an element of chance, it must also be based on strategy and decision-making. If there is no strategy, the player is nothing more than a machine that follows the rules of the game. In Snakes and Ladders for example, everything is based on the rolling of the dice, which which strongly limits strategic interest.
The fourth characteristic is that a game needs basic rules, but these must lead to interesting variability in the way the game is played. The basic rules should get you started quickly, but the variety offered by the expanded options should keep you coming back to play.
Finally, the fifth characteristic of the game is that it requires a story, a narrative, a captivating theme. It doesn’t have to be about castles and goblins, but a good game, like a good math book, needs to have a compelling story arc.
Take the example of backgammon: it combines these five characteristics. Backgammon, one of the oldest games invented by humans, combines uncertainty and unpredictability due to dice, but even if the dice are not good, it is possible to use strategy to win.
The psychological benefits of gaming
Modern board games take inspiration from their ancestors, gaining in complexity and sophistication while retaining the soul of the classics. Technology opens up new horizons, but the essence of gaming endures.
Playing has many benefits. Chess and Snakes and Ladders were used for education, teaching strategy, probability and life lessons. Today, gaming brings us relaxation, social connection, intellectual stimulation, and a healthy dose of adrenaline!
Conclusion
At the end of this mathematical journey through the world of games with Marcus du Sautoy, one thing is clear: games are much more than just a pastime. Behind each board, each card, lie mathematical, psychological and cultural treasures. Their apparent simplicity conceals a fascinating complexity.
As technology opens new horizons, the essence of play endures, fulfilling our deep need to face challenges and find meaning in our quest. Games are not just games: they are an invitation to explore the infinite potential of our humanity. It’s up to us to continue to invent, together, the greatest game of all: life.
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