15 Solvers: How They Work and How to Study With Them

For most of poker’s history, “good strategy” was a matter of opinion backed by results. Then came the solvers. A solver is a piece of software that takes a precisely defined poker situation and computes a strategy that cannot be exploited — a strategy that, played correctly, guarantees you at least a break-even result against any opponent, no matter how cleverly they play. That is a remarkable mathematical object, and learning to study with one is one of the highest-leverage things a modern player can do.

But solvers are also widely misused. Players memorize outputs they don’t understand, chase precision that doesn’t matter, and forget that the solver is answering a question — “what is unexploitable against a perfect opponent?” — that is often not the question you actually face at the table. This chapter explains what solvers do under the hood, what you feed them and what they give back, which tools exist, and, most importantly, a disciplined workflow for turning solver output into transferable poker skill.

15.1 What a solver actually computes

A solver finds (an approximation of) a Nash equilibrium for the specific spot you define. In a two-player zero-sum game like heads-up postflop poker, a Nash equilibrium is a pair of strategies — one for each player — such that neither player can improve their expected value (EV) by unilaterally changing their own strategy. Both players are simultaneously playing the best possible response to the other. That is the meaning of “GTO,” game-theory-optimal: it is the strategy at the equilibrium.

The key property is unexploitability. If you play your half of the equilibrium, the worst any opponent can do to you is tie; their mistakes only help you. This is defensive by nature. The solver is not trying to maximally punish a specific bad player — it is trying to be impossible to punish. That distinction will matter enormously when we discuss limitations.

Counterfactual regret minimization (CFR)

Solvers don’t compute the equilibrium with a closed-form equation; the game tree is far too large. Instead they use an iterative self-play algorithm, almost always a variant of counterfactual regret minimization (CFR).

The intuition is simpler than the name. Imagine two copies of the program playing the same spot against each other thousands of times. On each iteration, at every decision point, the program asks a “what if” question: for each action I could have taken (check, bet small, bet big, fold), how much better or worse would I have done than the action I actually took, weighted by how likely I was to even reach this point? That weighted difference is called regret. Actions that would have done better accumulate positive regret; actions that would have done worse accumulate negative regret.

The algorithm then adjusts: on the next iteration, it shifts its mix of actions proportionally to accumulated positive regret. Actions it “regrets not taking” get played more often; actions it regrets taking get played less. Crucially, the strategy the solver reports is not the strategy on any single iteration — it is the average strategy over all iterations. A deep theorem of CFR guarantees that this time-averaged strategy converges toward a Nash equilibrium as the number of iterations grows.

A few practical consequences fall directly out of this:

Solutions are approximate. You never reach the exact equilibrium; you get progressively closer. The remaining error is measured by exploitability, usually reported as a fraction of the pot.
That error metric matters. Most software lets you set a target accuracy — often expressed as a percentage of the pot. A solve to 0.5% of the pot is good enough for nearly all study; chasing 0.1% can multiply your solve time for differences you will never perceive at the table.
Mixed strategies are normal, not noise. Because the solver is balancing actions to remain unexploitable, it frequently splits a single hand across multiple actions — e.g., betting A♠Q♠ 60% and checking it 40%. This is not the solver being indecisive; it is the equilibrium genuinely requiring a mix.

Key idea

A solver answers exactly one question: “What strategy cannot be exploited if my opponent also plays perfectly?” Every strength and every limitation of solver study flows from that single sentence. Keep it taped to your monitor.

15.2 Inputs: garbage in, garbage out

A solver’s answer is only as meaningful as the situation you define. Defining that situation — building the game tree — is where most of the skill (and most of the mistakes) live. The core inputs are:

Ranges. You must specify the full range of hands each player can hold at the start of the solve. For a single-raised pot, this might be “BTN opens to 2.5bb with roughly the top 45% of hands; BB calls with a defending range” — and you specify those ranges hand-by-hand, often with frequencies (e.g., calls A5s 100%, calls K9o 50%). The output is exquisitely sensitive to these ranges. If you put hands in a range that a real opponent would never have, the solution is “correct” for a fantasy game.
Board. The specific flop (and optionally the turn/river runout you want to study), e.g., Q♥7♦2♣ rainbow.
Stack depth and pot size. Effective stacks and the starting pot, both in big blinds. A spot at 40bb deep is a different game from the same board at 150bb deep.
The bet-size tree. This is the menu of allowed actions. You decide which bet sizes each player may use on each street — for example, “flop: check, bet 33% pot, bet 75% pot; turn: check, bet 50%, bet 125%, all-in.” The solver can only choose among the sizes you offer. Offer too few and you may miss the best strategy; offer too many and solve times explode while the EV gain becomes trivial.
Rake (for cash games). Online rake meaningfully changes marginal decisions, especially preflop and in small pots. A no-rake solve overstates how much you should play.

Common mistake

The single most common solver error is feeding it unrealistic ranges and then trusting the precise output. If you assume your opponent 3-bets a perfectly balanced, polarized range and they actually 3-bet only premiums, the solver’s beautiful bluff-catching frequencies are answers to a question you will never be asked. Spend more time on your range assumptions than on reading the third decimal place of the output.

15.3 Outputs: reading the matrix

Once solved, the software hands back a strategy at every node of the tree. The outputs you’ll actually use:

Action frequencies. For each hand in the range, how often it takes each action. Usually shown as a 13×13 hand grid colored by action — a quick glance tells you the shape of the strategy (which hands bet, which check, how polarized it is).
Overall strategy at a node. The aggregate: “this range bets 75% pot 28% of the time, bets 33% pot 22%, checks 50%.” This is the betting frequency for the whole range, which is what governs your meta-strategy.
EV. The expected value of each hand, and of each action with that hand, typically in big blinds or chips. Comparing the EV of two actions tells you whether a decision is high-stakes (big EV gap) or nearly indifferent (tiny gap — meaning the mix barely matters).
Equity vs. EV. Equity is your raw share of the pot if all cards ran out; EV folds in the strategic value of position, initiative, and future betting. They often diverge sharply, and the gap is itself instructive.
Range breakdowns / made-hand categories. How much of a range is value, top pair, draws, air, etc., after a given line.

Two higher-level tools deserve their own treatment.

Aggregate (range) reports

Instead of solving one flop, you solve the same preflop spot across many flops at once — often a representative sample of all 1,755 strategically distinct flops, or a chosen subset — and view a summary table: for each board, the c-bet frequency, the average bet size, the overall EV, and so on. This is where principles come from. You stop asking “what do I do on Q♥7♦2♣?” and start asking “across all ace-high disconnected boards, how does the in-position raiser’s c-bet frequency change?” Patterns leap out: high, dry, ace- or king-high boards favor a high-frequency small c-bet; low, connected, two-tone boards favor a more checked, polarized strategy. Those patterns are what you carry to the table — you cannot recall 1,755 board-specific strategies, but you can recall a dozen board-texture principles.

Node-locking

By default both players play the equilibrium. Node-locking lets you override one player’s strategy at a chosen node and re-solve for the best response against that fixed (usually deliberately flawed) behavior. This is how you convert a solver from a GTO machine into an exploitative one.

Example: lock the river so that the opponent never bluffs when they bet — fix their betting range to value only. Re-solve, and the solver will show you the maximally exploitative counter: you should fold all your bluff-catchers, because there is nothing to catch. Conversely, lock them to over-fold to river raises and watch the solver start raising thin value and even pure air. Node-locking is the bridge between this chapter’s pure theory and the “play the player” material elsewhere in the book: you encode a population read as a locked node, and the solver tells you exactly how to attack it.

Key idea

The equilibrium output tells you how to be unbeatable. Node-locking tells you how to be maximally profitable against a specific flaw. Strong players use the first to understand the game’s structure and the second to print money against real humans.

15.4 The tools

You don’t need all of these; pick one or two and go deep. As of this writing the landscape looks like:

PioSOLVER. The long-standing professional standard for heads-up postflop spots. Extremely fast and configurable; runs locally on your own machine (RAM is the main constraint for deep, wide trees). Steep learning curve, but it is the reference tool for serious cash-game study.
GTO Wizard. A cloud/browser-based platform with enormous libraries of precomputed solutions for common formats (cash, MTT with ICM, spin-and-gos), plus its own solving, aggregate reports, drilling, and hand-history analysis. Far lower friction than Pio — you can browse equilibria in seconds — at the cost of less control over fully custom trees. Excellent for volume study and for tournament players.
Simple Postflop. An older, more approachable postflop solver; lighter on features than Pio but historically a gentler on-ramp and cheaper.
MonkerSolver. The go-to for multiway pots (3+ players) and complex preflop/tournament trees. Multiway solving is dramatically harder — the game tree and memory requirements balloon, and equilibria in 3+ player games carry theoretical caveats — but Monker is the practical tool when you must study a limped four-way pot or a multiway all-in.

A critical distinction for tournament players: ICM. In tournaments, chips are not worth a linear amount of money — the Independent Chip Model translates a chip stack into real-money equity, and near pay jumps this radically changes correct play (you fold hands you’d happily stack off with in a cash game). Solvers that support ICM (GTO Wizard, MonkerSolver, ICMIZER for preflop push/fold) bake this into the EV calculation. A cash-game (chip-EV) solve will badly misadvise you on a final-table bubble. The mechanics of ICM belong to the tournament chapters; here, just know your solver must be told you’re playing for ICM, or its numbers are wrong for that context.

15.5 A worked example: reading a single output

Let’s make this concrete. Single-raised pot, 100bb effective, online 6-max. BTN opens to 2.5bb, BB calls. Flop comes Q♥7♦2♣ (rainbow, dry, queen-high). Pot is roughly 5.5bb. BB checks. We’re studying BTN’s c-bet, with a size tree of {check, bet 33%, bet 75%}.

A typical equilibrium output looks like this:

Overall: BTN bets ~75–85% of the time, almost entirely using the small 33% size. The large size is used rarely or not at all.
Why: Q72r is a board that hugely favors the preflop raiser. BTN’s opening range contains far more strong queens, overpairs, and ace-high than BB’s calling range, which is missing many of the best queens (those got 3-bet) and is weighted toward suited connectors and broadways that mostly missed. This range advantage plus a flat, low board (few turn cards scare BTN, few draws exist) is the textbook condition for a high-frequency, small-sized “range bet.” BTN can bet almost everything cheaply because BB simply cannot fight back hard.
Hand by hand: A♠Q♠ bets near 100% (value, wants to build a pot). 8♠8♦ (an underpair to the queen) bets often for thin value/protection. K♣J♣ (overcards + backdoors) bets as a semi-bluff at high frequency. 5♦4♦ bets sometimes as a pure bluff with a backdoor straight draw and gives up otherwise. A genuine air hand like J♥9♥ with no backdoors might mix bet/check — and here the EV gap between betting and checking is tiny, which is the solver’s way of telling you the exact frequency is nearly irrelevant.

The transferable lesson is not “bet J9hh 41% of the time.” It is: on dry, high, range-advantaged boards, the in-position preflop raiser should bet a very high frequency for a small size, and the precise hand-by-hand mixes barely matter because the decisions are nearly indifferent. That one sentence applies to hundreds of boards. The specific percentage applies to exactly one, against an opponent you’ll never meet.

Drill

Take three flops of contrasting texture — A♣8♦3♥ (dry, ace-high), 9♥8♥7♣ (wet, connected), and K♦K♠4♣ (paired) — for the same BTN-vs-BB single-raised pot. Before you open the solver, write down a prediction: high or low c-bet frequency, small or large size, polarized or condensed. Then check the aggregate report. Grade your predictions. The gap between your guess and the solution is your actual study list.

15.6 How to study — extracting principles, not memorizing outputs

The difference between players who improve with solvers and players who waste years on them comes down to one habit: studying for understanding, not for recall. You cannot memorize the solver. There are too many board, range, stack, and size combinations, and at the table you have seconds, not a database lookup. What you can do is internalize the underlying logic so you reconstruct the right strategy on the fly.

Work in this order of questions, every time:

Who has the range advantage? Whose range has more equity on this texture overall?
Who has the nut advantage? Even with equal overall equity, whoever holds more of the absolute nuts (sets, straights, the top overpairs) gets to use big sizes and apply real pressure.
What does the texture do to draws and future streets? Dry boards favor small, high-frequency betting; dynamic boards favor polarization and bigger sizes because equities shift hard on later cards.
What is the EV gap on the marginal hands? Big gap = a real decision worth learning. Tiny gap = the solver is indifferent and you should not waste a single neuron memorizing the exact split.

When you find a pattern, articulate it in a sentence you could teach to someone else. “The defender check-raises more on low connected boards because they hold the range’s nutted hands there and the raiser’s overpairs are vulnerable.” If you can say it, you own it. If you can only point at a colored grid, you don’t.

Common mistake

Memorizing frequencies on indifferent hands. Players spend hours drilling that some hand bluffs 33% versus 38% — a distinction with essentially zero EV consequence. Meanwhile they miss the high-leverage structural facts: which size, what overall frequency, and why. Always check the EV difference between actions before you decide a mix is worth learning. If the EVs are within a sliver, the solver is telling you the decision doesn’t matter — believe it and move on.

15.7 Limitations: the perfect opponent who never shows up

Everything a solver tells you is conditioned on the assumption that your opponent also plays the equilibrium. Real opponents do not. They c-bet too much, fold too often to river bets, never check-raise bluff, call down too light. Against these players, the GTO strategy is merely break-even-proof — it leaves a lot of money on the table. The equilibrium will not punish your opponent’s specific leaks; it only declines to be punished itself.

Concretely, the limitations to keep front of mind:

It assumes perfect opposition. Against a fish who never bluffs, GTO has you correctly bluff-catching at equilibrium frequency — and losing money doing it, when folding would be free. Maximum exploitation (via reads and node-locking) beats GTO against anyone who isn’t also perfect.
It is only as good as your tree. Wrong ranges, a too-thin bet-size menu, or omitting rake all produce confident, precise, wrong answers.
Heads-up and chip-EV by default. Multiway equilibria are theoretically thorny and computationally brutal; tournament ICM must be explicitly modeled. Don’t apply a heads-up cash solve to a four-way ICM spot.
No exploits, no dynamics, no soul-reads. The solver doesn’t know this villain tilts, that one is a nit, or that the table just turned over. It has no timing tells, no bet-sizing reads, no history. Those live in the psychology and hand-reading chapters — and against weak fields, they out-earn pure GTO handily.
The table is not a study room. You have seconds and no grid. Solvers build the library of principles you draw on; they cannot make the decision for you live.

Key idea

Use GTO as your default and your baseline: a sound, unexploitable strategy you fall back on when you have no read, and the reference point you deviate from. Then deviate deliberately, in the direction your reads justify, to exploit. GTO is where you start; exploitation is where you profit. A great player fluidly moves between the two.

15.8 A practical solver study workflow

Bring it together into a repeatable routine. A focused 60–90 minute session beats hours of aimless clicking.

Start from your own hands, not random spots. Pull 5–10 hands from your recent sessions where you were genuinely unsure or got a bad result. Real confusion is the best curriculum. Tag spots during play so you can find them later.
Define the tree honestly. Set the ranges to what your actual pool does, not idealized ranges. Use a realistic bet-size menu (2–3 sizes per street is plenty for study), correct stacks, and include rake for cash. Garbage in, garbage out.
Solve to a sane accuracy and zoom out first. Target ~0.5% of pot. Before diving into one flop, run the aggregate report across many boards to see the big-picture pattern. Identify the structural strategy — overall frequency and size — before any single hand.
Interrogate the spot with the four questions. Range advantage? Nut advantage? Texture/dynamism? EV gaps on marginal hands? Write the answers down in plain language.
Node-lock to exploit. Now encode your population read — “this pool under-bluffs rivers,” “they over-fold to check-raises,” “they never barrel turn after checking flop” — as a locked node, and re-solve for the best response. This is where you turn theory into a concrete, profitable adjustment you can actually use tomorrow.
Write one transferable principle per spot. End every spot with a single teachable sentence. Keep a running document of these. Over months it becomes your strategy book — far more valuable than any saved solve file, because it lives in language you can recall at the table.
Drill, then test under time pressure. Use a trainer (GTO Wizard’s drills, or self-made flashcards from your principle list) to rehearse, but always grade against understanding: can you explain why, not just click the green box? Then deliberately apply the principle in your next session and review whether it held.

The goal is not to become a worse, slower copy of the solver. It is to absorb the structure of correct play so deeply that your instincts at the table are sound — and then to layer your human reads on top, departing from the baseline exactly when, and only when, you have a reason to. The solver builds the foundation. You build the house.