Game Tree

1. Introduction

Getting your game tree right is the most important part of generating GTO solutions. This guide explains what a game tree is and how to build efficient, well-structured ones for optimal solver performance.

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2. What Is a Game Tree?

A game tree represents all possible decisions and outcomes that can occur in a poker hand — from the first action to the final showdown. Think of it as a map of every possible path the hand could take. The primary way to control the size of the game tree is by limiting the number of available bet sizes.

The Basic Idea

At the start of a hand, both players are dealt cards. From there, each betting action, card dealt, or player decision adds a new branch to the tree.

A tree consists of nodes (states) and edges (transitions between states). There are three types of nodes:

• Action Nodes: A player takes an action (bet, call, raise, fold, etc.).
• Chance Nodes: A new board card is dealt.
• Terminal Nodes: The hand ends (either at showdown or when all but one player folds).

Edges represent player actions or cards being drawn.

• The root node is the starting situation (no actions yet).
• Each node represents a game state — who’s to act, pot size, cards on the board, etc.
• Each edge (or branch) represents an action — check, bet, call, fold, raise, etc.
• The leaves (endpoints) are terminal nodes — the hand concludes here.

Why GTO Solvers Use Game Trees

A GTO (Game Theory Optimal) solver aims to find a balanced strategy — one that cannot be exploited. To do this, it must understand every possible situation that could arise. The game tree provides this complete structure.

The solver iterates through the tree, node by node, calculating expected values (EVs) and adjusting strategies until reaching an equilibrium — where each player’s strategy is the best possible response to the other.

Does the Size of the Game Tree Matter?

Absolutely. The size of the game tree is one of the most critical factors when setting up a solve. A tree that’s too large may exceed available memory (RAM) and become unsolvable on most consumer hardware.

Tree size also directly impacts solve time — the more nodes, the longer the solver will take to finish.

What Defines the Size of a Game Tree?

Several factors affect tree size, but two are especially important:

• Stack-to-Pot Ratio (SPR): A lower SPR (large pot, short stacks) means the game is more likely to reach all-in scenarios sooner, resulting in fewer nodes. Conversely, a high SPR (small pot, deep stacks) allows many more bets and raises before reaching all-in, making the tree much larger.

• Number of Bet Sizes: Each additional bet size increases the number of possible branches (action paths). Keeping bet sizes minimal and well-chosen is key to fast, memory-efficient solves.

How to Build the Best Game Tree

Building an effective game tree is about balancing precision with performance. The key is choosing representative bet sizes — ones that capture realistic poker dynamics without overloading the tree.

For example, using only very small bet sizes (e.g., 5%, 10%, 15%) might miss important strategic options that larger bets (e.g., 50%, 100%) reveal. Instead, consider using a small but diverse set, like 25%, 50%, and 100%, to represent a good spread of betting behavior.

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3. Tips for Reducing Tree Size

• 📝 Lower SPR: Reduce the stack-to-pot ratio — smaller effective stacks lead to smaller trees.
• 🧠 Simplify the Tree: Remove unrealistic actions or reduce bet sizes to dramatically cut computation time.
• ⚙️ Increase Merging Threshold: Combine similar bet sizes into one representative size.
• 💾 Raise the All-In Threshold: Larger bets automatically convert to all-ins, reducing unnecessary branches.
• 🔍 Limit Maximum Actions: Cap the number of betting rounds — beyond a certain depth, force all-in actions.

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Need Help?

If you encounter any issues while setting up your game:

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