Nash equilibrium in poker, and when best response earns more
Equilibrium is the reference. The profitable play against a specific opponent is a best response to how that opponent actually plays. This page explains the difference and how Poker Shark's Best Response Engine puts it to work.
Get first accessEquilibrium
- Balanced against every opponent
- Mixes: bet 40% / check 60%
- Wins from mistakes without targeting them
Best response
- Built against this opponent
- One action: bet
- Collects the mistakes
01
What a Nash equilibrium guarantees
A Nash equilibrium is a pair of strategies where neither player can do better by changing only their own play. In poker, a strategy covers every hand you can hold at every point in the hand, and it can mix between actions. Solvers reach it with counterfactual regret minimization, or CFR. The solver plays the game against itself, keeps track of which actions would have earned more, and shifts toward them until neither side can gain. Balance shows up on its own from the two players pushing against each other. In a two-player zero-sum game the guarantee is simple: an equilibrium strategy earns at least the value of the game, whatever the opponent does. With more players that guarantee is gone, and in practice it has other limits:
- 1
Fixed bet sizes
Solvers work from a menu of bet sizes. The answer is balanced for that menu, not for every size a real player can choose.
- 2
Nobody plays it
Real players drift from equilibrium in ways that repeat, and those repeats are what you can read.
- 3
Needs the full strategy
A solver computes its answer against the opponent's whole strategy, every hand in every spot. At the table you only see the hands that reach showdown, so a read has to be built from bets, folds and the few cards you see.
- 4
Money left behind
An equilibrium strategy wins from many mistakes, but it does not go out of its way to collect them. Against a weak opponent, the money a targeted adjustment adds is often the bigger number. Node locking is the proposed fix, but reaching a maximally exploitative strategy that way means locking a very large number of nodes across the game tree.
As Daniel Negreanu put it after years of solver study, no human being plays perfectly balanced.
02
What a best response is
In game theory, a best response is the strategy with the highest expected value against one specified opponent, using only the information you actually have. The opponent's behavior is held fixed while your decisions are optimized, and there is no requirement to stay balanced, because the model does not counter-adjust. Game theory also calls this a maximally exploitative strategy. Poker Shark's goal with best response is to find a single action with the highest expected payoff.
03
Why a mixed frequency stops being right
When a solver tells you to bet 40% and check 60% with a hand, both actions earn the same against the equilibrium opponent. That is the only reason mixing is allowed. Put a real opponent across the table and the tie breaks. One of the two actions now earns more, and mixing means giving up part of that edge on purpose. Negreanu's rock-paper-scissors example is the whole idea in one line: if someone throws rock too often, you throw paper more, because you are playing them and not a textbook. Poker just makes the read harder to get. You see bets and folds and rarely the cards behind them, so the adjustment has to come from ranges and patterns instead of one showdown.
Solver, against the equilibrium opponent
Best response, against this player
04
What the read was worth: 25,001 hands
We dealt 25,001 heads-up hands against the Loose Passive and played each one twice: once with the GTO baseline from our CFR solver, once with the Best Response Engine. Same cards, same opponent, no rake. Playing the same hands both ways takes the luck of the deal out of the comparison.
The opponent played the same fixed strategy for all 25,001 hands, so this is what the read is worth when it is exactly right. A real player who only partly fits the type will pay less, and one who adjusts to you will pay less again.
| Strategy | Won, bb/100 |
|---|---|
| Best Response Engine | 237.01 |
| GTO baseline (our CFR solver) | 26.03 |
| Difference | +210.97 |
The difference is taken from the unrounded results.
05
Where the opponents come from
Poker Shark's five player types are each written to play the way that kind of cash-game player plays, street by street, from published research and our own hand analysis. Each represents a cohesive, logical way of playing poker, not a label or a single stat. Dan Cates groups opponents from experience into recognizable categories and notes that with enough data you can have population reads. You face these styles in the training arena.
-
Loose Passive -
Loose Aggressive -
Tight Passive -
Regular -
GTO -
Adaptive
06
How a read updates during a hand
Before an opponent acts, they can have any two hole cards. As the action develops, Shark Vision, our range analysis tool, narrows the hands the villain can still hold given the configuration and action history of that hand.
Each cell fills to how often that hand takes the action.
-
01
Before they act
Any two cards. Nothing is ruled out yet.
All 169 starting hands.
-
02
Facing a raise, they continue
They continue with 108 of 169 hands and fold the rest.
AA: 3-bet 50%, call 50%; AKs: 3-bet 100%; AQs: 3-bet 85%, call 15%; AJs: call 100%; ATs: call 100%; A9s: call 100%; A8s: call 100%; A7s: call 95%; A6s: call 90%; A5s: call 90%; A4s: call 90%; A3s: call 85%; A2s: call 85%; AKo: 3-bet 100%; KK: 3-bet 50%, call 50%; KQs: call 100%; KJs: call 100%; KTs: call 100%; K9s: call 95%; K8s: call 85%; K7s: call 70%; K6s: call 65%; K5s: call 45%; K4s: call 45%; K3s: call 45%; K2s: call 45%; AQo: 3-bet 65%, call 35%; KQo: call 100%; QQ: 3-bet 50%, call 50%; QJs: call 100%; QTs: call 100%; Q9s: call 100%; Q8s: call 100%; Q7s: call 100%; Q6s: call 100%; Q5s: call 100%; Q4s: call 50%; Q3s: call 50%; Q2s: call 50%; AJo: call 100%; KJo: call 95%; QJo: call 95%; JJ: 3-bet 42%, call 58%; JTs: call 100%; J9s: call 100%; J8s: call 100%; J7s: call 100%; J6s: call 100%; J5s: call 50%; J4s: call 50%; J3s: call 50%; J2s: call 50%; ATo: call 100%; KTo: call 85%; QTo: call 80%; JTo: call 85%; TT: 3-bet 32%, call 68%; T9s: call 100%; T8s: call 90%; T7s: call 65%; T6s: call 50%; T5s: call 50%; T4s: call 50%; T3s: call 50%; T2s: call 50%; A9o: call 85%; K9o: call 60%; Q9o: call 100%; J9o: call 100%; T9o: call 45%; 99: call 100%; 98s: call 95%; 97s: call 65%; 96s: call 50%; 95s: call 50%; 94s: call 50%; 93s: call 50%; 92s: call 50%; A8o: call 80%; 98o: call 45%; 88: call 100%; 87s: call 95%; 86s: call 100%; 85s: call 50%; 84s: call 50%; 83s: call 50%; 82s: call 50%; A7o: call 65%; 87o: call 45%; 77: call 100%; 76s: call 90%; 75s: call 60%; A6o: call 45%; 76o: call 45%; 66: call 100%; 65s: call 85%; 64s: call 45%; A5o: call 45%; 55: call 95%; 54s: call 80%; 53s: call 45%; A4o: call 45%; 44: call 90%; 43s: call 60%; A3o: call 45%; 33: call 85%; A2o: call 45%; 22: call 80%.
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03
Facing a raise, they 3-bet
Only 9 hands ever 3-bet. The green shows how often.
AA: 3-bet 50%, call 50%; AKs: 3-bet 100%; AQs: 3-bet 85%, call 15%; AKo: 3-bet 100%; KK: 3-bet 50%, call 50%; AQo: 3-bet 65%, call 35%; QQ: 3-bet 50%, call 50%; JJ: 3-bet 42%, call 58%; TT: 3-bet 32%, call 68%.
Get first access to Hand Lab, Shark Vision, the Best Response Engine and the GTO solver.
07
When the opponent changes, the answer changes
Every exploit opens you up to being counter-exploited. Bluff more against a player who folds too much and you will be exploited the moment that player starts calling. Fold more against a player who never bluffs and you will be exploited the moment they add bluffs to their range. Poker Shark's solutions are separated by playstyle, so you need to identify the archetype across the table before you can execute the best response profitably.
- Read: folds too much
- Exploit: bluff more
- Counter: they start calling
08
Why a few node locks answer the wrong question
Most solvers let you lock part of an opponent's strategy and solve again. It is a useful way to study one mistake at a time, and it is also where most exploit analysis goes wrong. One locked node does not express a complete playstyle. Lock a loose flop call and the solver still assumes that player defends the turn and river perfectly, so it can throw out a bluff that would work against the real player. A small combo configuration error in an assumed fold rate turns a winning river bluff into a losing one, and no amount of solving fixes a bad input. Locking a complete opponent by hand will take hundreds of hours. Poker Shark starts from complete opponent styles instead, so the whole opponent is in place before the best response is computed.
One locked node
- Flop: calls too wide
- Turn: assumed perfect
- River: assumed perfect
Answers the wrong question
Complete style
- Flop: calls too wide
- Turn: keeps some draws
- River: raises a narrow set
The whole opponent
09
When to use it
Poker Shark is a study tool for before your session and a review tool for after it. Card rooms and online operators forbid real-time assistance, and we agree with them. Using it, or any tool like it, while you play breaks the rules of every site and card room.
What top players say about adjusting to opponents
The players who run the biggest games say the same thing in their own words. None of these players are affiliated with Poker Shark.
And with enough experience or the right data you can have population reads on how people play.
No human being plays perfectly balanced.
I’m playing against you, so I have to adjust.
Not the approach that wins the most amount of $$.
Bart Hanson on a GTO approach to mid-stakes live games, Crush Live Poker Podcast #184
Know the fundamentals, but run exploit scripts like you can’t get enough of them.
Phil Laak describing Pete Clarke’s coaching, Late Reg Podcast episode 5
They misreact in some way.
Jason Somerville on an unfamiliar lead, Late Reg Podcast episode 5
Frequently asked questions
What is a Nash equilibrium in poker? +
A pair of strategies where neither player can do better by changing only their own play. Solvers find it with CFR. In two-player zero-sum poker, an equilibrium strategy guarantees at least the game's equilibrium value against any opponent; it does not adjust to target their mistakes.
Is GTO the same as Nash equilibrium? +
In poker talk, yes. GTO means the equilibrium strategy for the game as the solver modeled it, including its fixed bet sizes and ranges. Change the sizes or the ranges and you get a different equilibrium.
What is a best response in poker? +
The strategy that earns the most against one specific opponent, using only what you can see. Hold the opponent's play fixed, then pick the line that wins the most against it. Game theory also calls it a maximally exploitative strategy.
What is a maximally exploitative strategy? +
Another name for a best response. It takes every profitable deviation the opponent allows and gives up balance to do it, which is why it only pays against the opponent it was built for.
Does Poker Shark use a solver? +
Yes, two. A CFR solver produces the GTO baseline, and the Best Response Engine finds the highest-EV action against each opponent type except the Adaptive. In Hand Lab you can compare heads-up decisions after the flop with either one. The GTO opponent in the Arena is not solver output: it plays hand-written rules modeled on solver play.