Liar's dice (Perudo): your hidden dice and the odds of every bid

How to use this liar's dice page

In the real game every player shakes five dice under a cup and peeks at their own without showing anyone. This page works the same way: press Roll or drag the dice and drop them in the tray, and you see only your own roll. If several of you are playing on phones, each player rolls on their own screen and puts it face down once they have looked.

1. Enter how many dice are left on the table, counting every player. At the start that is five each: 20 with four players, 30 with six.
2. Type the bid you want to assess, as a quantity and a face, for example ‘eight fours’.
3. Choose whether ones are wild. In standard Perudo they are; in the palifico round and in some variants they are not.
4. Read the probability that the bid is true and decide whether to raise, call dudo or call calza.

The count that matters is the dice you cannot see. If the bid is eight fours and under your cup you have two fours and a one, you already supply three, so five more are needed among the other players’ dice. That is why the same bid can be safe for one player and risky for another.

Where it comes from: Dudo, Cacho and Perudo

Liar's dice is a family of bluffing games in which each player knows their own dice and has to work out everyone else’s. The best known form is the South American one, called dudo after the Spanish word for ‘I doubt’, which is what you say to challenge a bid. In Chile, where it is very popular, it is also called cacho or cachito, which is also the local word for the dice cup.

You will often read that the game is Inca in origin and that Atahualpa taught it to Francisco Pizarro while he was held prisoner at Cajamarca in 1532 and 1533. That story does not appear in the chronicles of the conquest. People who have searched for written references to the game have found none earlier than the 19th century, and the Atahualpa and Pizarro tale only turns up in 20th century writing, so it is best treated as legend.

The name Perudo is a brand that joins Peru and dudo. Cosmo Fry and Alfredo Fernandini came up with it in the 1980s after discovering the game in Peru, and launched it with leather cups made by Peruvian craftsmen. It was first sold in London, spread across Europe from there and is now published by Asmodee. In English the whole family goes by liar's dice, and in Germany a version designed by Richard Borg, Bluff, won the 1993 Spiel des Jahres award.

Perudo rules step by step

These are the rules of Asmodee’s Perudo, the most widely used reference in Europe and the set followed by the online versions. Details change from country to country and from one group of friends to another; the most common variations are covered at the end.

Setting up

Each player takes five dice and a cup. The box holds six sets, so two to six people can play. Everyone rolls one die and the highest number starts.

Bidding

All players shake their dice at the same time, keep them covered and look at their own in secret. The first player makes a bid about the whole table: a quantity and a face. ‘Five threes’ means that across all the cups there are at least five dice that count as a three. Play passes to the left, and the next player must either raise the bid or call dudo. Raising means increasing the quantity, with any face you like, or keeping the quantity and choosing a higher face. After ‘seven fours’ you may bid ‘seven fives’ or ‘eight twos’, but not ‘six sixes’ or ‘seven twos’. You can raise by several dice at once.

Ones, or ‘pacos’, are wild

Ones count as whatever face is being bid. If the bid is five threes, the threes and the ones are added together when the cups are lifted. You can also bid on ones themselves, under three conditions:

• A round cannot open with ones, except in palifico.
• To switch to ones you only need half the previous quantity, rounded up. After ‘eleven threes’ you can bid ‘six ones’.
• To switch back from ones to another face you must bid double plus one. After ‘four ones’, the next bid on any other face must be at least nine.

Calling dudo

If you think the last bid is false, say ‘dudo’. Every cup is lifted and the dice showing the bid face are counted together with the ones. If there are fewer than the bid, the bidder loses a die. If there are as many or more, the challenger loses one. Whoever loses a die opens the next round; a player with no dice left is out, and the player to their left opens instead. The last player with any dice wins.

Calza

Calling calza means claiming that the last bid is exactly right. If the cups show precisely that quantity, the caller wins back a die, though nobody can hold more than five. If there are more or fewer, the caller loses one. Who may call calza depends on the edition: in Asmodee’s, any player except the one who made the bid. Calza is not used in palifico rounds or when only two players remain.

Palifico

When a player drops to a single die, the next round is palifico. That player opens it and may open on ones, ones stop being wild, and the face of the bid cannot change, only the quantity. Each player triggers this special round once per game, and it no longer applies when only two players are left.

Dudo and Cacho variants

In South American dudo the ones are called ases (aces) and the equivalent of palifico is called obligar: a player who drops to one die can force a round in which aces are not wild. That round can be open, with everyone seeing the other players’ dice, or closed, with only the one-die player seeing their own. Calzar, the local name for calza, is usually allowed only while at least half the dice remain on the table or when the caller has a single die, and depending on house rules a wrong call costs one or two dice. Some tables play without wild ones from the start, and others drop them at the end, when only two players remain.

Odds: how many dice of a face are on the table

Each hidden die has a 1 in 6 chance of showing a given face. If ones are wild, the chance that a die counts towards your bid rises to 2 in 6, or 1 in 3, because either the face itself or a one will do. The number of matching dice follows a binomial distribution, and that is what gives the probability of there being at least a certain quantity.

The table shows 20 hidden dice, which is what you face at the start of a five-player game: 25 dice in total, minus your own five.

With wild ones, betting on seven of a face among 20 hidden dice is close to a coin toss (52.1%), and eight is already more likely false than true (33.9%). Without wild ones the same step falls between three (67.1%) and four (43.3%).

The average for the dice still in play

The average number of hidden dice showing a face is the number of hidden dice divided by 6, or by 3 with wild ones. The second table gives that average and the highest quantity that still has at least a 50% chance of being on the table.

A worked example with your own dice

Five players, all dice still in play (25). Under your cup you have two fours, a one, a three and a six, so you already hold three towards fours. ‘Eight fours’ needs five more among the 20 you cannot see: 84.8%. ‘Nine fours’ needs six: 70.3%. ‘Ten fours’ needs seven: 52.1%. ‘Eleven fours’ needs eight: 33.9%. If an opponent bids eleven fours and you have nothing else to go on, calling dudo is the more likely winner.

Why calza so rarely works

Hitting the exact number is hard even on the most likely outcome. With 20 hidden dice and wild ones, there is an 18.2% chance of exactly six and another 18.2% of exactly seven. Without wild ones the most likely exact result is three, at 23.8%. Calza makes most sense once you have already lost dice, because it is the only way to win them back.

Strategy: bidding from the average

Common hand and poker dice: the other liar's game

Besides Perudo, where bids are about every die on the table, there is a common-hand form usually played with poker dice, whose faces show nine, ten, jack, queen, king and ace.

One player rolls all five dice under the cup, looks at the result and announces a poker hand, which may or may not be true. The cup then passes to the next player, who decides whether to believe it. If not, they lift the cup: if the dice match or beat the announced hand, the doubter loses, and if they fall short, the announcer loses. If they accept the claim, they may re-roll some or all of the dice without showing them and must announce a higher hand when passing the cup on. Rules vary a lot between tables, especially the ranking of hands and how many re-rolls are allowed.

Liar's dice trivia

• In Pirates of the Caribbean: Dead Man's Chest (2006) the crew of the Flying Dutchman gamble years of service at liar's dice. Will Turner challenges Davy Jones, offering an eternity of service for the key to the chest. His father, Bootstrap Bill, joins the game and makes an absurdly high bid so that he loses instead and his son goes free.
• The video game Red Dead Redemption (Rockstar, 2010) includes liar's dice as one of its gambling minigames.
• Richard Borg’s version first appeared in 1987 from Milton Bradley as Liar's Dice, with a wild star in place of the six. Renamed Bluff and published by F.X. Schmid, it won the 1993 Spiel des Jahres, the German game of the year award. It was later reissued in the United States as Call My Bluff.
• Mathematicians are interested in the game because it mixes chance with hidden information. Game theory papers have worked out optimal two-player strategies, and one of their findings matches the tables above: bidding the average rounded down has better than a 50% chance of being true.
• The brand name Perudo was made by blending the country, Peru, with the word shouted to make a challenge, dudo.