External Sampling MCCFR

Texas Hold'em GTO

MCCFR external sampling on Heads-Up No-Limit Hold'em. 169-bucket preflop abstraction with suit isomorphism, using the same bucket numbering as the C++ engine.

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External Sampling MCCFR

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Pre-flop Range Chart

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Hand Details

Select a hand class in the matrix.

GTO Concepts

Polarised Range

A balanced betting range mixes very strong hands (for value) with weak hands (bluffs), making the opponent indifferent to calling.

Bluff-to-Value Ratio

At Nash, the bluff frequency is calibrated so opponent's fold equity exactly offsets their calling EV. Pot odds determine the ratio.

Suit Isomorphism

AKs has the same strategy regardless of specific suits. This abstraction reduces 1326 starting hands to 169 canonical classes.

MCCFR External Sampling

Per iteration: sample one deal, traverse ALL actions for the traversing player, sample ONE action for the opponent. O(|A|^d/2) vs O(|A|^d).

Note: With only 1,000 MCCFR iterations, the strategy is still converging. Full HUNL requires millions of iterations with more sophisticated abstractions (e.g., the Libratus / Pluribus approach). This demonstrates the architecture and GTO concepts, not a production solver.