Liar's dice

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A set of Poker dice as used in Liar dice (individual hand).

Liar's dice or Liar dice is a class of dice games for two or more players. They are easy to learn, require little equipment, and can be played as gambling or drinking games. Playing them well requires the ability to deceive and detect an opponent's deception.

It has roots in South America and was popularized in early Spanish History, was brought to Spain by the Spanish conqueror Francisco Pizarro during the 16th century. It became extremely popular in Hong Kong and consequentially China. It is a popular game in China, where most bars and clubs will have dice and cups stationed at tables. ^[1]

Versions

Versions of the game are known as Deception Dice, Diception, Dudo, or Cachito. The equivalent drinking game is sometimes called Mexicali or Mexican in the United States; the latter term may be a corruption of Mäxchen ("Little Max"), the name by which a similar game, Mia, is known in Germany, while Liar's dice is known in Germany as Bluff.

There are at least three different versions of liar's dice; it's uncertain which version is the original. In each of them, dice are rolled in a concealed fashion and bids made about the result of the roll. Players must either raise the bid or challenge the previous bid in turn.

In "common hand", each player has a set of dice, all players roll once, and the bids relate to the dice each player can see (their hand) plus all the concealed dice (the other players' hands).

In "individual hand", there is one set of dice which is passed from player to player. The bids relate to the dice as they are in front of the bidder after selected dice have been re-rolled.

Common hand

Five six-sided dice are used per player, with dice cups used for concealment.

Each round, each player rolls their dice under their cups and looks at their new hand while keeping it concealed from the other players. The first player begins bidding, picking a face and a quantity. The quantity is the claim of how many of the chosen face have been rolled in total on the table. The 1s are often wild and count as the face of the current bid.

Each player has two choices during his turn: make a higher bid, or challenge the previous bid. Raising the bid means either increasing the quantity, or the face value, or both, according to the specific bidding rules used.

If the current player challenges the current bid, all dice are revealed. If the bid is valid, the bidder wins. Otherwise, the challenger wins.

Variants

• Instead of the current player being the only one who can challenge (or "call up") the previously-made bid, any player may challenge a bid at any time.
• With some bidding systems, a player may elect to choose one or more dice of matching value from under his cup, place them outside the cup in view of the other players, re-roll the remaining dice, and make a new bid.
• When a player has no two dice with the same face, he may choose to pass once in a game round. If he does so, the bid won't be raised. The next player can raise the bid using standard rules, or call the bluff. By doing so, he challenges the claim of the passing player having no two dice with the same face. This is commonly used in multi-round games where dice are removed from the game, as it helps players with few dice left to gain more information about the other dice without risk.
• Instead of raising or challenging, the player can claim that the current bid is exactly correct. If the number is higher or lower, the player loses to the previous bidder, but if they are correct, they win.

Elements of strategy

Playing Liar's dice involves many subtleties and interpersonal skills similar to other bluffing games such as Poker. However, there are some universal elements of strategy.

Perhaps foremost, a bid gives others at the table information. Players, through subsequent bids, reveal the players' confidence in the quantity of each face value rolled. A player with two or three of a certain face value under his or her own cup may make a bid favoring that face value. Players can thus use these bids to build a mental picture of the unknown values, which either strengthens or weakens their confidence in a bid they are considering. Others may consider a bid as evidence it is true, and if their own dice support the same conclusion, may increase the bid on that face value, or if their dice refute it may bid on a different face, or challenge the previous bid.

Conversely, bids can also be bluffs. Bluffs in liar's dice can be split into two main categories: early bluffs and late bluffs. An early bluff is likely to be correct by simple probability (depending on the number of players), but other players may believe the bidder made that bid because his or her dice supported it. Thus, the bluff is false information that can lead to incorrect bids being made on that face value. Players will thus attempt to trick other players into overbidding by use of early bluffs to inflate a particular face value. A late bluff, on the other hand, is usually less voluntary; the player is often unwilling to challenge a bid, but as a higher bid is even more likely to be incorrect it is even less appealing. A late bluff is thus a critical part of the game; convincing bluffs, as well as reliable detection of bluffs, allow the player to avoid being challenged on an incorrect bid.

As with any game of chance, probability is highly important. The key element is the "expected quantity"; the quantity of any face value that has the highest probability of being present. For six-sided dice, the expected quantity is one-sixth the number of dice in play, rounded down. When wilds are used, the expected quantity is doubled as players can expect as many aces, on average, as any other value. Because each rolled die is independent of all others, any combination of values is possible, but the "expected quantity" has a greater than 50% chance of being correct, and the highest probability of being exactly correct. For example, when 15 dice are in play and wilds are used, the expected quantity is 5. The chances of a bid of 5 being correct are about 59.5%; in contrast, the chances of a bid of 8 being correct are only about 8.8%.

However, a high bid is not necessarily incorrect, because bids incorporate information the player knows. A player who holds a preponderance of a single value (for instance, four out of the five dice in his hand are threes) may make a bid, with fifteen dice on the table, of "six threes". To an outside observer who sees none of the dice, this has an extremely low probability of being correct (even with wilds), however since the player knows the value of five of those dice, the player is actually betting that there are two additional threes among the ten unknown dice. This is far more likely to be true.

Basic dice odds

For a given number of unknown dice n, the probability that exactly a certain quantity q of any face value are showing, P(q), is

Where C(n,q) is the number of unique subsets of q dice out of the set of n unknown dice. In other words, the number of dice with any particular face value follows the binomial distribution .

For the same n, the probability P'(q) that at least q dice are showing a given face is the sum of P(x) for all x such that q ≤ x ≤ n, or

These equations can be used to calculate and chart the probability of exactly q and at least q for any or multiple n. For most purposes, it is sufficient to know the following facts of dice probability:

• The expected quantity of any face value among a number of unknown dice is one-sixth the total unknown dice.
• A bid of the expected quantity (or twice the expected value when playing with wilds), rounded down, has a greater than 50% chance of being correct and the highest chance of being exactly correct.

Individual hand

The "individual hand" version is for two players. Each player rolls a die to determine the first caller. Both players then roll their dice at the same time, and examine their hands. Hands are called in style similar to poker:

• Five of a kind: e.g., 44444
• Four of a kind: e.g., 22225
• Full house: e.g., 66111
• High straight: 23456
• Low straight: 12345
• Three of a kind: e.g., 44432
• Two pair: e.g., 22551
• Pair: e.g., 66532
• Runt: e.g., 13456

After the each announcement, the other place may call a higher-ranking hand, call the bluff, or re-roll some or all of their dice.

When a bluff is called, the accused bluffer reveals their dice and the winner is determined.^[2]

Stanford variation

The Stanford variation is played with one set of dice. Players can reveal dice or remove them from view, as well as roll them inside or outside of the box.

Mexican

The first player rolls two dice under a cup and claims a roll. Most claims are scored by reading the higher die as the 10s place and the lower as the 1s, e.g., a roll of 1 and 4 is read as "41". Doubles are higher than "65", and what would be the lowest roll 2-1, is a "Mexican" and higher than 6-6.

Special rolls:

• 3-1 Social (everyone drinks, cancel all previous rolls, roll again to open)
• 3-2 Reverse (change direction, cancel all previous rolls, roll again to open)

The next player may do one of two things:

• If he believes the roller, he simply takes the dice (without looking at the result), rolls, and claims a higher scoring roll.
• If he does not believe the roller, the cup is lifted, revealing the roller's hand. Either the bluffer or incorrect challenger must drink.

Commercial versions

• 1974 Liars Dice, published by E.S. Lowe
• 1984 Liars Dice, Milton Bradley, designed by Richard Borg.
• 1993 Call My Bluff, by FX Schmid, designer Richard Borg, won the 1993 Spiel des Jahres and Deutscher Spiele Preis awards.^[3]
• 1994 Perudo, published by University Games, designed by Cosmo Fry.
• 2001 Bluff, from Ravensburger (after acquiring FX Schmid), reissue of Call My Bluff, won the 2006 Årets Spel adult game of the year award.
• 2002 Liars Dice, by Endless Games
• 2011 Diception by Four Clowns Game and Toy Co
• 2011 Liar's Dice Live by FrontDev

See also

• Bullshit (card game), a card game with a similar emphasis on bluffing and detecting bluffs
• Liar's poker, a structurally similar game using the digits of the serial numbers on dollar bills

References

External links

• Liar's Dice at BoardGameGeek
• Information on and publishing history of Liar's Dice on boardgamegeek.com