Why the game of Go defies the universe

When we think of strategically complex board games, Chess is usually the first name that comes to mind for most people. However, if we look strictly at the mathematics behind the gameplay possibilities, the Western classic looks almost simple compared to the ancient Eastern game of Go.



A fascinating trivia piece from the Brazilian book "A descoberta dos números: uma aventura matemática" (The discovery of numbers: a mathematical adventure), by mathematician Marcelo Viana, helps us put this scale into a cosmic perspective.

Numbers That Defy the Universe

In Chess, it is estimated that there are "only" 10⁴⁰ (the number 1 followed by 40 zeros) possible positions on the board. That is an enormous amount, without a doubt.

Yet, when we move to the Go board, the simple rules of surrounding territories generate an unbelievable combinatorial explosion: the number of possible positions is greater than 10¹⁷⁰ (the number 1 followed by 170 zeros).

To give you an idea of what this actually means:

• 10⁴⁰: Estimated possible positions in Chess.
• 10⁸⁰: Estimated number of atoms in the entire known universe.
• 10¹⁷⁰: Possible positions in Go.

The Game Design and A.I. Nightmare

In other words, there are drastically more possible configurations in a single game of Go than there are grains of sand on Earth, stars in the sky, or atoms scattered across the entire observable cosmos.

For anyone who studies or works with game design, this brutal difference explains why computers took so long to defeat human masters at Go. While "brute force" calculation managed to beat world Chess champion Garry Kasparov back in 1997 (with Deep Blue), a purely mathematical approach was physically impossible for Go. No machine could ever compute 10¹⁷⁰ paths.

It required the development of deep neural networks and artificial intelligence based on intuition and continuous learning (like DeepMind's AlphaGo) to finally break through the barrier of this infinite tangle of nodes and branches in 2016.

Go proves that, sometimes, the most minimalist rules yield the most vast and unpredictable systems that the human mind—and the universe itself—can fathom.

#GoGamers  

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Reference:

VIANA, Marcelo. A descoberta dos números: Uma aventura matemática. Rio de Janeiro: Tinta da China, 2025.

From ancient games to modern mathematics: the birth of probability theory

The seeds of probability theory were sown in the fertile ground of games of chance. Archaeological evidence suggests that dice and other rudimentary games employing randomness date back to ancient civilizations, possibly even predating written records. Early references to such games can be found in historical and mythological accounts, hinting at their deep integration into various cultures.



It was the desire to quantify the uncertainty inherent in these games that spurred the development of probabilistic concepts. A pivotal moment occurred in the 17th century when a gambling dispute between French mathematicians ignited a correspondence that laid the groundwork for modern probability theory. This exchange, primarily between Blaise Pascal and Pierre de Fermat, addressed the fair division of stakes in an interrupted game, prompting them to formalize ideas of expected value and chance outcomes.

Following these initial explorations, mathematicians like Christiaan Huygens built upon this foundation, establishing frameworks for analyzing games of chance and laying the groundwork for the wider application of probability in various scientific disciplines. The journey from rudimentary games to sophisticated mathematical concepts highlights the enduring human fascination with both chance and the quest to understand it.

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Source: JOHNSON, Steven. How We Got to Now: Six Innovations That Made the Modern World. New York: Riverhead Books, 2016.

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The Counting Kingdom: learning math could be fun

What an excellent surprise one student brought in the last “gaming analysis” class. The Counting Kingdom is an educational game for kids (6 to 8 years), that teaches basics concepts of sum and equations using a tower defense mechanics. It’s very easy: you need to cast a spell using some magic scrolls to stop the monsters. Each monster has a number of strength and the player needs to sum the scrolls to make an equal number and eliminate the enemy. Check the gameplay:



That’s a great example of how we can use a game-based learning strategy. It’s important to mention that a game like this one does not replace a math class, but it helps to complement and reinforce the studied ideas.

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