Overview

Objective: Implement a Rust program that uses CFR to approximate a Nash equilibrium in NLTH, including all game stages and player actions, while managing computational resources effectively.
Key Components

    Game Representation
        Cards and Deck
        Hand Evaluation
        Game State

    Information Sets and Game Tree Nodes

    Player Actions and Betting Abstractions

    Counterfactual Regret Minimization Algorithm

    Data Structures for Regret and Strategy Tracking

    Main Training Loop

1. Game Representation
Cards and Deck

You'll need to represent a standard deck of 52 cards.

// Define suits and ranks
#[derive(Clone, Copy, PartialEq, Eq, Hash, Debug)]
enum Suit {
    Clubs,
    Diamonds,
    Hearts,
    Spades,
}

#[derive(Clone, Copy, PartialEq, Eq, PartialOrd, Ord, Hash, Debug)]
enum Rank {
    Two,
    Three,
    Four,
    Five,
    Six,
    Seven,
    Eight,
    Nine,
    Ten,
    Jack,
    Queen,
    King,
    Ace,
}

// Define a card
#[derive(Clone, Copy, PartialEq, Eq, Hash, Debug)]
struct Card {
    rank: Rank,
    suit: Suit,
}

// Implement methods to create and manage a deck

Hand Evaluation

Use or implement a hand evaluator to assess the strength of poker hands.

    Option 1: Use an existing crate like rust-poker for efficient hand evaluation.
    Option 2: Implement your own hand evaluator (more complex and time-consuming).

Game State

Define the game state to include:

    Player Hands
    Community Cards
    Betting State
    Pot Size
    Current Player

struct GameState {
    player_hands: [Vec<Card>; 2],
    community_cards: Vec<Card>,
    pot: u32,
    bets: [u32; 2],
    current_player: usize,
    // Other necessary fields
}

2. Information Sets and Game Tree Nodes

In CFR, decision-making is based on information sets, which represent the game state from a player's perspective, considering only the information available to them.

Define a struct for information sets:

struct InfoSet {
    // Include relevant information such as:
    // - Player's private cards
    // - Public community cards
    // - Betting history (abstracted)
    // - Position (dealer or small blind)
}

Use hashing or a unique identifier to map information sets to their corresponding strategy data.
3. Player Actions and Betting Abstractions
Action Space

Include the possible actions:

    Fold
    Call/Check
    Bet/Raise

Betting Abstractions

Due to the infinite number of possible bet sizes in NLTH, abstract the betting amounts to a manageable set.

    Discrete Bet Sizes: Define a fixed set of allowable bet sizes (e.g., half-pot, pot-sized bets).
    Buckets: Group hands into strength buckets to reduce the number of hand categories.

enum Action {
    Fold,
    Call,
    Bet(f32), // e.g., multiples of the pot size
}

4. Counterfactual Regret Minimization Algorithm

Implement the CFR algorithm to traverse the game tree and update strategies based on regret minimization.
Recursive CFR Function

fn cfr(
    state: &GameState,
    player: usize,
    history: &Vec<Action>,
    pi: [f64; 2], // Probability of players reaching this node
    regrets: &mut RegretTable,
    strategies: &mut StrategyTable,
    // Other necessary parameters
) -> f64 {
    // Base case: terminal state (showdown or someone folded)
    // Recursive case: update regrets and strategies
}

Regret and Strategy Updates

    Immediate Regret: Difference between the utility of an action and the average utility.
    Cumulative Regret: Sum of immediate regrets over iterations.
    Strategy Update: Normalize positive cumulative regrets to form a probability distribution.

5. Data Structures for Regret and Strategy Tracking

Use hash maps or custom data structures to keep track of cumulative regrets and strategies for each information set.

use std::collections::HashMap;

struct RegretTable {
    table: HashMap<InfoSetKey, [f64; NUM_ACTIONS]>,
}

struct StrategyTable {
    table: HashMap<InfoSetKey, [f64; NUM_ACTIONS]>,
}

    InfoSetKey: A unique identifier for an information set.
    NUM_ACTIONS: The number of possible actions in your abstracted action space.

6. Main Training Loop

Run the CFR algorithm over many iterations to converge towards a Nash equilibrium.

fn train(iterations: u32) {
    let mut regrets = RegretTable::new();
    let mut strategies = StrategyTable::new();

    for i in 0..iterations {
        let mut game_state = GameState::new();

        // Initialize game state (deal cards, set blinds, etc.)

        // Run CFR for both players
        cfr(
            &game_state,
            0,
            &vec![],
            [1.0, 1.0],
            &mut regrets,
            &mut strategies,
        );
    }

    // After training, extract average strategies
}

Additional Considerations
Abstractions to Manage Complexity

    Limit Game Phases: Focus on a subset of the game (e.g., pre-flop and flop only).
    Hand Bucketing: Group similar hands together to reduce the number of unique hand strengths.
    Action Abstraction: Limit the number of betting options to reduce branching in the game tree.

Parallelization

    Multi-threading: Utilize Rust's concurrency features to parallelize parts of the computation.
    Asynchronous Programming: Use async features if appropriate.

External Crates

    Hand Evaluation: rust-poker
    Data Structures: hashbrown for efficient hash maps.
    Logging: Use crates like log for debugging.

Testing and Validation

    Unit Tests: Write tests for individual components (e.g., hand evaluator, game state transitions).
    Simulation: Run simulations against known strategies to validate the performance.