What is a Solver?

Welcome!

It’s Michael Lukich here, back with the second issue of the Solver School newsletter. I’m excited you’re along for the ride.

Last time, we explored the inspiration behind starting this publication. Today, we tackle a basic and foundational question that’s often misunderstood: What exactly is a poker solver?

In short, solvers are calculators. They are software tools that estimate game theoretic solutions for a well-defined poker scenario.

But calling them calculators undersells their immense value if utilized properly. Solvers crunch algorithms to provide mathematical insights into optimal play. Their outputs help unravel poker's inherent complexities and point toward winning strategies.

Debunking Myths

Before I dive into what solvers are, I’m going to tell you what they’re not:

• Solvers don't provide a catch-all solution for playing poker

• Solvers won’t “spit out a GTO solution” that can be followed blindly to make money

• Solvers haven’t solved the game of poker entirely

• Solvers haven’t “ruined the game” by creating a bunch of unbeatable GTO robots

This is important to note because there may be misconceptions or exaggerated claims about the capabilities of solvers. They are not magic wands that will turn you into an unbeatable player. Instead, they should be seen as what they are — tools for better understanding the mathematical components of poker strategy.

Demystifying the Magical Black Box

When I first discovered solvers, I thought they were these magical black boxes that would spit out unbeatable “GTO” solutions. But in reality, they calculate equilibrium estimates based on the inputs you feed them.

Solvers take strategic scenarios encoded into inputs, run calculations, and output a solution based on math. To fully tap into their power, you need a grasp of game theory, the skill of translating poker scenarios into reasonable inputs, and the ability to interpret the outputs.

Solver = Function Machine

You can think of a solver in a similar way. But instead of x's and y's, you're inputting a poker situation. As an output, you get an approximation of an equilibrium solution for that scenario. But what is an equilibrium solution?

An Equilibrium Solution

Solvers use mathematical algorithms that are admittedly complex. But those algorithms generate an output solution that maximizes the expectation value (the amount of money or chips a player makes) for both players based on the inputs entered.

So, the solver iterates the strategies between players, trying to find the one that can make the most EV against the other. When it reaches a strategy for both players that meets the required accuracy (something that you enter), the solver stops and displays the solution.

So, you will enter the variables from the hand you want to analyze, like player positions, ranges, bet size options, and the stack and pot size. The solver will then churn those parameters through its enigmatic internal mechanism, and—voila!—out comes the equilibrium solution based on the game situation within a predetermined margin of error.

But remember, what comes out is entirely based on what you put in. So if you put garbage in, you're gonna get garbage out.

Garbage In, Garbage Out

A solver is only as good as what you put into it. Without thoughtful configuration of the inputs, the outputs mean very little. Mastering solvers requires skill in translating aspects of poker into parameters the algorithms can process.

This analogizes to any forecast. The models used to predict something are fixed. The actual forecast, or the model output, will only be as good as the relevant data that goes into it. Similarly, solvers reveal the equilibrium solution for the game scenario the inputs represent. If your inputs do not accurately reflect the actual game scenario, your output won’t be worth a lot in terms of answering your questions.

Changing the inputs changes the game state and, thus, the corresponding outputs. Sometimes, seemingly small changes in the inputs can yield significant variations in the output.

The Value Lies in Making Connections

We can't see inside the solver to fully grasp their inner workings. But we can better understand how the game works by observing how tweaking inputs changes outputs. This allows for the interpretation of results through a game theory lens.

Solvers have no magical "solve poker" button. Their power emerges from your ability to encode, run, and comprehend strategic scenarios. With practice, you gain a deeper understanding of optimally navigating common situations.

What's the Real Value?

So why are solvers such a big deal? They allow you to experiment with different game variables and test the sensitivity to changes with each one. This knowledge can be transformative in helping you strengthen your intuition at the table. And that, my friends, is invaluable. You can adapt your strategy based on solid, mathematical insights rather than gut feeling or flimsy advice from your poker buddy, Dave. (No offense, Dave.)

Excited to Learn More?

While solvers can initially seem intimidating, learning to use them effectively is achievable with the right guidance.

If you want to dive deeper into leveraging solvers to improve your poker skills, check out my full back-library library of long-form writing on the Solver School website.

For the best solver training content available, check out my course catalog. It contains all my training material, including my flagship course, The Solver Masterclass. This 9-module course will transform you from Beginner to Expert with a comprehensive walkthrough of using these tools effectively.

I'm also on Twitter and YouTube, where I share more solver-focused and poker strategy insights.

What's Next?

I’ll explore foundational game theory concepts, such as Nash Equilibrium, in the next newsletter at the end of this month. Understanding game theory provides context for interpreting the equilibrium estimates solvers generate and understanding how to manipulate them to answer specific questions.

Until then, thanks for reading! I appreciate you joining me on this journey toward poker excellence aided by the power of solvers.

Best,
Mike Lukich