Solver Outputs Decoded

Hello, and welcome back to the November 30th issue of the Solver School Newsletter!

Before I jump into the content today, I want to share two quick updates:

• I’m adding some variety to future newsletters with different issue themes. The first of which I plan to introduce in an upcoming issue is a quick analysis of a hand via video, text, or a combination of both. If you have a hand or scenario you’d like me to examine using solvers within a newsletter, email me the details at [email protected].

• I’m working on a major update to my Solver Masterclass course that focuses entirely on using GTO Wizard within your studies. More to come in the December 15 newsletter issue!

Now that I’ve gotten the updates out of the way, let’s jump into today’s newsletter topic.

Last month, I explored the input side of configuring poker solvers. Inputs set the stage - they establish the scenario and possibilities to be analyzed.

Today, I’ll examine the outputs that result from this process. Fluently interpreting solver outputs is crucial for accurately translating solutions into strategic takeaways.

Revisiting How Solvers Operate

First, let’s quickly recap how solvers function...

Solvers take user inputs that model a poker situation and attempt to calculate an optimal strategy. This outputs an equilibrium solution in the form of frequencies, metrics, and data points. We can then analyze these outputs to derive insights and adjust our play.

“Garbage in, garbage out” still applies. Poorly configured inputs will produce meaningless outputs. But today, we’ll assume reasonable inputs have been entered and focus completely on unpacking what comes out the other end of a solver.

The Core Solver Outputs

After performing its complex calculations on our modeled scenario, the solver produces outputs to quantify the balanced optimal strategy. The primary metrics include:

• Equity — Equities are dependent on range interactions and represent the frequency at which the specified player would win the pot if there were no more action throughout the rest of the hand.

• EV — EV is the primary measure of success in poker as it represents the amount we expect to win (or lose) through gameplay. EV is a function of many things, including position, equity differentials, and range composition.

• Strategic Frequencies — Solvers vary the set of strategic actions available (e.g. raise, call, or fold) within a range in order to reach a final state of equilibrium. The specific values of these strategic actions are an output of the solution.

These three metrics form the foundation of almost all solver analysis. Equity gives the inherent baseline strength of our holding or range at that moment. EV guides decision-making by estimating profitability. Strategic frequencies suggest how to construct theoretically sound ranges by mixing actions. I dove way deeper into these success metrics in an earlier post several years ago.

Supplemental metrics like EV% (EV divided by pot size at the node) and EQR (Equity Realization) help assess if a range is under or over-realizing relative to its equity. But most core solver work revolves around equity, EV, and strategic frequencies.

Below are some output screens from several popular commercial solvers:

Applying Context to Interpret Data

Here is a critical contextual point about solver outputs — they are specific to the precise node (decision point) currently being examined in the game tree.

The equity, EV, and frequencies apply only to that singular point and are calculated only using the available information. As an example, let’s look at facing a flop bet after calling preflop.

At this node, equity is calculated using our range against only our opponent's assumed betting range. The EV incorporates the flop pot size and potential future actions. The frequencies relate specifically to the equilibrium response facing the flop bet.

The node context is essential because these output values differ across the full game tree as play progresses. You cannot naively compare metrics from the preflop opening stage to the postflop action on later streets. The scenario state has evolved as ranges have evolved throughout the hand.

This context needs highlighting because it causes many pitfalls when working with solvers if ignored.

Common Solver Analysis Pitfalls

Forgetting node context leads to several missteps:

• Blindly assuming flop EV applies the whole way — EV changes street by street, and even node by node, based on the action.

• Directly comparing metrics from different solver configurations — Outputs rely heavily on input differences.

• Overvaluing magnitudes rather than comparative differences — Focus on relative gaps in these output metrics, not absolute values.

The key is avoiding taking metrics out of context because they are snapshots applying only to that particular node. Solver outputs require qualitative evaluation anchored in poker fundamentals, not just number crunching. Their value comes from assessing directional differences to identify improvement areas - not just figuring out if a number is big or small based on magnitude alone.

Conducting Goal-Oriented Analysis

Approaching your solver work with a goal-oriented process helps cut through noise. Outline the strategic question, hypothesis, or theory you want to test first in an issue → solution format:

Issue - “I face 3-bets too often from the blinds and struggle playing postflop against them.”

Hypothesis - “Slowplaying strong hands preflop might help protect my postflop range.”

Experiment - “I’ll include some stronger hands as calls in my 3-bet defense range.”

Analysis - “My overall EV has increased...let's refine my 3-bet defense range.”

Takeaway - "I will update my 3-bet defense range based on my analysis. I will also account for this when studying my 4-betting range to see how this strategy change affects other parts of the game tree."

Clearly defining the issue focuses your analysis. Framing a hypothesis grounds your testing. Configuring targeted experiments isolates the impact of specific ideas. Assessing comparative EV differences reveals if you are on the right track. Finally, developing clear, concise strategic takeaways creates actionable next steps for your learning.

This overall framework keeps your analysis focused, your hypotheses grounded in fundamentals, and your findings actionable - helping avoid the common context pitfalls we just discussed.

Continuing Your Solver Journey

With a more solid grasp of solver inputs and outputs, you have a strong foundation for applying these tools correctly.

As we close out 2023, I suggest picking one current leak in your poker game or area of confusion to model and improve.

See if you can translate it into a simplified solver scenario:

• Define roles and contexts (game type, positions, etc.)

• Estimate reasonable ranges or utilize the ranges within the Solver School Starter Pack

• Configure a baseline model and start tweaking inputs to see how small changes affect the outputs

Use the goal-oriented process above to guide your investigation and analysis. Challenge some of your current assumptions. See if the solver outputs align with your intuition or if you disagree with them. Look for EV-based tipping points that might indicate beneficial adjustments.

Looking Ahead

In an upcoming newsletter, I’m going to dive into inputs and outputs a bit more. Now that I’ve defined the two sides of the equation, it’s time to dig into the relationship between them. This is where the value of using solvers is realized.

Again, please email me at [email protected] with any hands you’d like me to analyze. I plan to have more example-based newsletters.

For more free solver content, check out the rest of the Solver School website. It is filled with video and written content about solvers and analyzing poker with data.

I have several courses for sale. If you want to take the next step in using solvers, check out my flagship product, The Solver Masterclass. It contains everything you need to know to become an expert at using solvers to analyze poker data.

You can also follow me on Twitter and YouTube, where I share more solver-focused and poker strategy insights.

I appreciate you following along and reading the newsletter today.

Until next time.
Michael Lukich