Liar’s Dice

Goal

Be the last player with dice left. Everyone starts with five dice hidden under their cup; every mistake costs you a die.

How a round works

• All players shake their cups and discreetly look at their dice.
• The first player makes a bid: a quantity and a value, for example “four 3s”, meaning there are at least four dice showing 3 under all the cups combined.
• Aces (1) are wild: they count as every value that is bid.
• On their turn, each player must either raise the bid, shout “Liar!”, or, if the rule is allowed, call “Spot on!”.

Raising the bid

• Increase the quantity (with any value), or keep the quantity with a higher value.
• Switching to aces: the quantity may be halved, rounded up (after “six 4s”, you can say “three aces”).
• Leaving aces: you need at least double plus one (after “three aces”, at least “seven” of another value).
• You cannot open a round with aces (except in palifico).

Liar! and Spot on!

• Liar!: all the cups are lifted. If there are at least as many as the bid, the player who challenged loses a die; otherwise, the player who made the bid loses a die.
• Spot on!: you claim the quantity is exact. If it is, you win a die back (five at most); otherwise, you lose one.
• The loser starts the next round.

Palifico

When a player drops to a single die for the first time (and more than two players remain), the next round is special: they open it with the value of their choice, aces are no longer wild and the value cannot change; only the quantity goes up.

Controls

• Choose the value, then the quantity, and tap Bid.
• Keyboard: keys 1 to 6 for the value, arrows or + and − for the quantity, Enter to bid, M for Liar, P for Spot on.
• With friends, pass the device around: everyone looks at their dice when their turn comes.

About the AI

The AI never sees your dice. It calculates the probability of each bid from its own dice and binomial distributions, then refines its beliefs about the opposing hands by interpreting past bids (a player who bids 5s often holds some). It also estimates the risk that the next player will challenge. The Master level goes further: before each decision, it draws hundreds of plausible opposing hands according to its beliefs and simulates the end of the round for every possible action, then picks the one that minimizes its risk of losing a die. The bluffing is calibrated to the level.