# Liar's Dice > A browser reimplementation of the traditional bluffing dice game (Dudo / Perudo / Cacho / Bluff / > Call My Bluff). Five six-sided dice a player under cups, aces wild, bids of a quantity and a rank, > and a call of "dudo" to end the round. Runs entirely in the page: no accounts, no network calls, > no analytics, no model. Site: https://liars-dice.skillsafe.ai/ ## What is unusual about this implementation - **The dice are simulated, not sampled.** Every die, including the ones under the bots' cups, is thrown by a hand-written rigid-body simulator: a 19.05 mm cube, impulse contacts with restitution 0.36 and Coulomb friction 0.34, integrated at 1/2000 s. A throw makes about 11.4 table contacts and settles in about 0.57 s. Over 2,000,000 throws the face distribution gives chi-square 5.64 on 5 degrees of freedom (p = 0.34). - **Fairness is not purely geometric, and this app measured that.** A geometrically perfect cube thrown from a FIXED release orientation lands on one face 100% of the time, and is still detectably biased (chi-square 96.8 over 40,000 throws) when the velocity is wobbled by as much as the whole throw speed. Symmetry of the solid gives equivariance; uniformity additionally requires the distribution over release ORIENTATIONS to be invariant under the cube's 24 rotations, which is what a shaken cup provides. The app's own throw draws the orientation uniformly on SO(3) and also draws the slot-to-pip labelling from the 24 rotations, which forces exactly 1/6 per pip value for any throw whatsoever by a counting argument rather than a statistic. - **Unpredictability is dynamical, and it was measured per bounce.** Holding the die, the mass, the gravity and the throw distribution fixed and changing only restitution, the decorrelation scale on vertical velocity falls from 5.8e-2 m/s (restitution 0, 4.6 contacts) to 8.1e-6 m/s (restitution 0.55, 19.4 contacts) - about a factor of 1.8 per table contact. Sensitivity is strongly non-uniform across the throw: horizontal release position has EXACTLY zero influence (0 flips in 45,000 throws at a one-metre shift), while release height decorrelates at 1.6e-4 m. - **A die can be fair and useless.** A no-bounce drop from a uniformly random orientation is exactly fair (chi-square 2.06 over 20,000) and 100.00% predictable from the release. - **The odds are exact and checked two independent ways.** Binomial tails are compared against a brute-force enumeration of all 4,031,076 hands of up to eight dice (wild and non-wild) and against exact BigInt rational arithmetic. - **The published rules contradict each other and the page says so.** Compendia, Wikipedia's Dudo article and Neller & Hnath (from Knizia) disagree about whether a quantity raise may change the rank, what it costs to bid aces and to leave them, how many dice a lost round costs, when palifico starts and what a wrong calza costs. All three rulesets ship (LD-1, LD-W, LD-2) and the disagreements are tabulated on the page with sources. ## Rulesets - **LD-1** (default) - the Compendia rules sheet that Wikipedia's Dudo article cites. One die lost per round; aces at half rounded up, out at double plus one; palifico at one die; calza. - **LD-W** - Wikipedia's Dudo article read literally: a quantity raise may change the rank, palifico at two dice, a wrong calza costs two dice. - **LD-2** - Neller & Hnath (ACG 2011), from Knizia (1999): a single total claim order in which n x 1 immediately precedes 2n x 2, and challenges cost the DIFFERENCE between claim and count. Games are much shorter: 10.9 rounds against 19.1 over 300 games each. ## Files - `/` - the game and all of the above as static prose - `/CREDITS.txt` - every source, every figure tagged DOCUMENTED / qualified / MEASURED / DERIVED / CALIBRATED / RECONSTRUCTED, and the six sources that could not be opened - `/LICENSE.txt` - MIT, for this implementation only ## Not affiliated Liar's Dice is a traditional public-domain game. Milton Bradley published a version in 1987 and Richard Borg's Call My Bluff / Bluff (F.X. Schmid, 1993) won the Spiel des Jahres. Neither is reimplemented here and no artwork, text, component design or trademark from any commercial edition is used. This app is not affiliated with, endorsed by or connected to any publisher.