Book

Bluffing as a Signaling Game takes Liar's Bar, the viral card game built on deception, suspicion, and a loaded revolver and turns it into a rigorous playground for game theory. Behind every declaration of "three Kings" lies a calculated bet: bluff too rarely and you leave value on the table; bluff too often and you get caught, and caught means consequences. This book builds a full Perfect Bayesian Equilibrium model of the game, treating each round as a signaling problem between a Sender who may or may not be telling the truth and a Receiver deciding whether to call the bluff. Unlike prior treatments that reduce the revolver mechanic to a simple coin flip, this analysis incorporates δ the probability the gun actually fires on a lost challenge as a continuous risk parameter that reshapes the entire equilibrium. As δ climbs toward certainty, bluffing collapses; as it falls, liars grow bold. The result is a closed-form threshold, q* = (1−ω)/δ, that pins down exactly how suspicious a rational Receiver should be. Written for readers who want the real mathematics Bayesian updating, indifference conditions, comparative statics without a wall of unexplained notation, this guide walks through the model from first principles, works numerical cases end to end, and shows precisely how deck composition, stakes, and danger level shift the optimal amount of lying. Whether you're a game theory student, a strategy-minded card shark, or just someone who's ever wondered if there's a "correct" amount of bluffing, this book gives you the framework and the formulas to find out.