All work06 / 2026

Independent research · game theory

Poker & detectability

The price of a poker face.

Studying what colluding players can gain—and how much they keep when they have to pass a detector.

Take a closer look
PythonCFRLinear programmingExact evaluation

Same game. Different definition of honest.

Who sets the table?

≥ +1.95

chips / hand
Best-found achievable value passing this detector

Detector
Passing this detector1.947
Unconstrained best found3.692

Exactly evaluated strategies in three-player Leduc hold’em, against a fixed opponent. All values are best-found lower bounds, not certified global optima. The controls select recorded results.

01 / The question

Who gets to define honest play?

02 / What I built

I studied a colluding pair against a fixed opponent in three-player Leduc hold’em, using CFR, constrained per-seat linear programming, and explicit strategy constructions.

The same detector family was calibrated against different populations of honest agents. Every reported value evaluates a concrete strategy exactly.

03 / What happened

The best-found unconstrained value is at least +3.69 chips per hand. Against the three-feature detector box, feasible constructions retain about +1.95 for the mixed honest reference population and +0.51 for the narrower selfish-CFR reference.

04 / Where it stops

These are best-found achievable values, not certified global optima. Leduc is a small game, and the findings are conditional on the fixed opponent, reference populations, and detectors. Exactly evaluating a strategy does not certify the full value–detectability frontier.

One more? / 01

VODLens CS2