GTO Foundations

advanced

Game theory for poker players: equilibrium, MDF and alpha, indifference, mixed strategies, range construction, and how to read and apply solver outputs without worshipping them.

7 modules55 lessons12h 50m

Game Theory Basics

What strategies and equilibria actually are, built up through toy games you can solve by hand before touching a solver.

Strategies, Nash Equilibrium, and UnexploitabilityDefines a strategy as a complete action plan covering every decision node and information state, then defines Nash equilibrium as a strategy pair where neither player gains by unilaterally deviating, and shows why equilibrium play.14m Zero-Sum Games and Rock-Paper-ScissorsCovers zero-sum game structure, why one player's EV gain is exactly the other's loss, and why some games admit only mixed-strategy equilibria.14m The Clairvoyance Game Solved by HandSets up the clairvoyance toy game: a $100 pot on the river where the bettor holds the nuts 60% of the time and pure air 40%, the defender holds only bluff-catchers, and the bettor may bet $100 or check.14m The AKQ Game Part 1: Roles Emerge from the RulesIntroduces the half-street AKQ game: each player antes into a 2-unit pot, each is dealt one card from {A, K, Q}, player 1 may bet 1 unit or check, player 2 may call or fold.14m The AKQ Game Part 2: Frequencies and PayoffsCompletes the AKQ game with a pot-sized bet of 1 into a pot of 2 (after antes), deriving that the Q bluffs at the frequency that makes the K indifferent between calling and folding, and the K calls at the frequency that makes the .14m EV at Equilibrium: Why Position Earns MoneyEstablishes that equilibrium does not mean zero EV for both players: the structure of a game assigns value, and acting last is structurally valuable because the in-position player realizes more equity.14m Exploitability: Measuring EV Loss vs Best ResponseDefines exploitability as the EV a perfect counter-strategy (best response or 'nemesis') gains against your strategy, measured in bb/100 or fraction of the pot, and explains why equilibrium is exactly the strategy with zero exploi.14m GTO vs Exploitative: A Spectrum, Not a ReligionFrames equilibrium play and exploitative play as endpoints of one spectrum governed by information: with zero reads you default toward baseline, and every reliable read justifies a measured deviation that itself opens you to count.14m

MDF & Alpha

The frequency mathematics of betting and defending: breakeven bluff thresholds, minimum defense, where the formulas break, and drilling the numbers until they are automatic.

Alpha: The Breakeven Folding Frequency a Bluff NeedsDerives alpha = risk / (risk + reward) as the fold frequency at which a zero-equity bluff breaks even, walking through the algebra from the EV equation of a bluff.14m MDF Derived: What 1 Minus Alpha Actually ProtectsDerives minimum defense frequency as MDF = 1 − alpha = pot / (pot + bet) and shows it is precisely the continuing frequency that denies automatic profit to an any-two-cards zero-equity bluff.14m

Indifference & Mixed Strategies

Why equilibrium strategies mix, what indifference actually buys you, and how to derive and implement mixed frequencies yourself.

The Indifference Principle: What Zero-EV Really MeansStates the indifference principle: at equilibrium, a polarized bettor's bluff frequency makes the opponent's bluff-catchers exactly zero-EV between calling and folding, and the defender's calling frequency makes the bettor's bluff.14m Value-to-Bluff Ratios by Street and SizingDerives the river bluffing ratio from indifference — at pot sizing the betting range is 2:1 value to bluffs, at half pot 3:1, at 2x pot roughly 1.14m

Range Construction & Polarity

How ranges take shape through actions: polarity, capping, coverage, advantages, sizing semantics, and blockers, ending in a full two-sided hand build.

Polarized, Linear, Condensed, and Capped RangesDefines the four core range shapes with equity-distribution diagrams: polarized (nuts and air, e.14m How Actions Filter Ranges Street by StreetTracks range morphology through a complete bet-call line: BTN opens 2.14m

Solver Fundamentals

What solvers compute, how to set up and read solves without fooling yourself, and how to turn outputs into study material.

What a Solver Actually ComputesExplains that a solver takes a fully specified game — both players' exact preflop ranges, an allowed menu of bet sizes, stack depth, and rake — and iterates (CFR-style self-play) toward a Nash equilibrium of THAT game tree, report.14m Game-Tree Abstraction: Garbage In, Garbage OutCovers abstraction: real no-limit allows any bet size at every node, but solvers work with a finite menu, so the chosen sizings define the game being solved and missing options distort the answer.14m

Solver Lessons by Spot

Human-usable heuristics extracted from solver outputs, one common spot family at a time.

SRP BTN vs BB: Dry A-High and K-High BoardsExtracts the range-bet heuristic for single-raised pots on dry high boards: on textures like Ah7d2c and Kh7c2d, BTN c-bets 33% pot at near-100% frequency because BTN's range advantage is overwhelming, BB cannot raise profitably wi.14m SRP BTN vs BB: Low Connected BoardsCovers the opposite texture family: on boards like 6h5h4c and 7c6d5d, BB's defend range holds the nut advantage (two-pairs, straights, sets from 65s, 87s, small pairs), so solver BTN checks back roughly half its range and splits i.14m

Applying GTO at the Table

Turning theory into an executable baseline: simplification, self-measurement, principled deviation, myth-busting, rake adjustments, and a complete session plan.

Simplification: Collapsing Mixes into Pure RulesTeaches the simplification discipline: replace solver mixes with pure, memorable rules wherever the EV loss is small, targeting the 20% of decisions that occur 80% of the time.14m Building a Baseline Strategy You Can ExecuteAssembles a complete playable baseline: one opening size per position, one 3-bet size IP and one OOP, a default c-bet plan per texture family (range-bet 33% on dry-high, check-half on low-connected, polar 75% where applicable), on.14m