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TechGames = Games x Maths x Startups.

This newsletter is about empowering brains AND hearts

Startups aren’t just like games — they are games. And the maths of how to win them is already written.

Today, we’re proving it. 😎

Let’s dive in!

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🧮 GTO Moves - “The Fundamental Game of Startups”

By being a founder, you signed up to play a game (or in reality, multiple games).

But what does “founding a startup” mathematically mean? 🤔

1. Defining What We Mean by Games

We define some quintessential notions here.

💡 Dumbifying this:

Basically, a game is anything that involves the following 4 ingredients:

Players - folks who play the game
Action spaces A_i - the possible moves each player can make
State spaces S_i - the information available to each player at a given moment
Payoff function u_i - how we measure success or winning.

Example: chess

Players - you and me
Action space A_i - all legal moves according to chess rules (same in theory, but constrained by position)
State space S_i - the board configuration, fully visible to both of us
Payoff functions u_i - we both share the same win condition (checkmate). Along the way, pieces carry values (pawn = 1, knight/bishop = 3, rook = 5, queen = 8), so capturing a queen gives increases the u_i by +8. In practice, payoff functions are often approximated computationally (e.g., Monte Carlo simulations in AI).

2. Listing Some Important Families of Games

Not all games are created equal.

Mathematicians group them into families — each family comes with its own playbook & properties.

💡 Spot the family, and you instantly have an idea of what the optimal moves should look like.

i) Zero-sum vs Positive-sum vs Negative-sum

The least obvious (but arguably the most important) part of the definition of a game is the payoff functions.

These are SO important that mathematicians split games in different ways based on how these functions behave.

💡 Dumbifying this:

The sum-property just tells you what happens if someone wins or loses with respect to competitors.

Zero-sum = “if one of your win gets someone else to lose by the same amount, reciprocally & inversally”
- Example: poker cash game (you win $10, I lose $10).
Positive-sum = “if one of your win causes someone to lose by by less than how much you won, reciprocally & inversally”
- Example: Huel vs Soylent. Both are competing to be the meal-substitute in the liquid form. If say Huel decides to deploy $100M of marketing capital this month with the goal of opening the average Joe’s mentality regarding consuming a fluid for lunch instead of a burger, Soylent also wins from it as this marketing operation will not only increase the total number of people in the market for liquid food, but some of them will also get to become aware of Soylent through Huel when making their own mind about the solutions that exist.
Negative-sum = “if one of your win causes someone to lose by MUCH more than how much you won, reciprocally & inversally”
- Example: world war. A country must sacrifice a lot to win a war but at the cost of uncountable loses from the “losers”.

Beyond the zero-sum property, there are other important qualities that mathematicians look at when classifying games.

ii) Cooperative vs Non-Cooperative

iii) Symmetric vs Asymmetric

iv) Perfect vs Imperfect Information

💡 Summerising it:

It’s pretty important to split up games in families. Why? Because similar families share similar results and properties.

Zero-sum, Positive-sum, or Negative-sum games - i.e., games where “if someone wins, how much does some else lose?”
Cooperative/non-cooperative games - i.e., games where “you can team up with other people & restrict their actions based on a contract/agreement”
Symmetric/asymmetric games - i.e., games where everybody has the same winning conditions, sees the same information, and can act the same way.
Perfect/imperfect information games - i.e., games where you see everything that everybody has done so far.

Examples:

♟️ Chess:
1. Zero-sum
2. Non-cooperative
3. Symmetric
4. Perfect information
♥️ Poker:
1. Zero-sum (without a rake), non-zero sum (if rake at the casino)
2. Non-cooperative (you’re alone in this)
3. Symmetric
4. Imperfect information (hidden cards)
🐑 Catan
1. Non-zero-sum (resources + points don’t cancel out)
2. Cooperative (alliances/trades)
3. Symmetric (victory points)
4. Imperfect information (hidden cards)
👾 Online 2v2 game of “Age of Empires”/Starcraft 2:
1. Zero-sum (limited resources/units)
2. Cooperative (allies can’t attack each other)
3. Asymmetric (different races/civilisations)
4. Imperfect information (fog of war)

3. The Fundamental Game of Startups - G*

We now define a fundamental game that every founder is playing, the “Fundamental game of startups”.

This game is characterised as follows:

Summability property: it depends on C. Under the assumption that a prospect uses one (and only one) solution to fix their problem, the game can be zero-sum. For example, in saturated markets, when a prospect switch to a new solution, say from player Pi, the user count of the previous solution’s owner (say player Pj) is reduced by 1. It can also be positive-sum (examples in markets where people need to be educated) or negative-sum (in markets where people are massively competing on price).
Imperfect information: players rarely know the full state of the market, competition, or future shocks.
Asymmetric: players have different roles, resources, and payoff structures.

💡 Takeaway:

This game is a huge deal.

Why?

All of you, founders, are playing MULTIPLE games at the same time.

While you, founders in the community, might not play the same games, every single one of you shares in common 1 game - the fundamental game of startups.

It’s so fundamental that it is how you, me, us founders, are defined mathematically.

4. Founders are playing multiple games at the same time

This is where it all starts becoming EXTREMELY interesting & rich. We’ll touch on that in other editions.

But TLDR: by being a founder, you’re playing many games.

For example:

The fundamental game of startups
The game of hiring
The game of PMF
The game of acquisition
The game of fundraising
The game of pricing
The game of customer research
The game of geographic expansion
And so many others…

And each of them can be classified. And each classification enjoys many really powerful theorems and results that we can leverage.

Which "Startup Game Theory" piece do you want us to write about next? 🤔

🚀 The Network at Your Service

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⚡️ Let the Community Help You

💌 Your Move

Got 10 seconds? Reply and tell me: what’s the most important game you’re playing this week? Hiring? Product iteration? I read every answer. 😎

And don’t just play solo — forward this to one sharp friend. The bigger the network, the faster we crush bottlenecks, the faster we win. ⚡

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