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 lookchips / hand
Best-found achievable value passing this detector
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