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A set of Poker dice as used in Liar dice (individual hand). Liar's dice, or Liar dice, with roots originating in South America and popularized in early Spanish History, was brought to Spain by the Spanish conqueror Francisco Pizarro during the 16th century.[1] Liar's Dice is known for being a game in pirate history, and a name for 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. Versions of the game are known as Dudo or Cachito in South America. 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 the game is known in Germany. There are at least three different versions of Liar's Dice; it's uncertain which version is the original. In all of them, dice are rolled in a concealed fashion and bids made about the result of the roll. Players must then either raise the bid or challenge the previous bid in turn. For the purposes of this article, the three versions discussed are referred to as "individual hand", "common hand", and "Mexican". In "common hand", each player has a set of dice, all players roll one 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.
[edit] Rules (common hand)Five six-sided dice with traditional dot faces are generally used per player, with dice cups used for concealment. Poker dice can also be used, but some systems for bidding become difficult or impossible to use. Each round, the players roll their dice while keeping them concealed from the other players. One player begins bidding, picking a quantity of a face 2 through 6. The quantity states the player's opinion on how many of the chosen face have been rolled in total on the table. A 1 ("ace") is often wild and counts as the stated face of the current bid, however the game can also be played without wilds (see variants). In a five-dice, three-player game with wilds, the lowest bid is "one 2" and the highest bid "fifteen 6s". Each player has two choices during his turn: make a higher bid, or challenge the previous bid as being wrong. Raising the bid means either increasing the quantity, or the face value, or both, according to the specific bidding rules used. Different bidding rule sets are described below. If the current player thinks the previous player's bid is wrong, he challenges it, and then all dice are revealed to determine whether the bid was valid. If the number of the relevant face revealed is at least as high as the bid, then the bid is valid, in which case the bidder wins. Otherwise, the challenger wins. A challenge is generally indicated by simply revealing one's dice, though it is customary to verbally make the challenge, by saying "I call you up", "I call", "You're a liar", or simply "Liar".
[edit] Bidding RulesThe most common systems for bidding are listed below, in order of the amount of restriction they place on bidders. All variants are described in relation to the face value and quantity of the previous bid.
Raises must be at least the minimum, however the current player may raise the bid to any legal bid. Given "four fours", a player may (in any of these systems) call "seven sixes". Such "bid jumping" has strategic value, but a large increase such as in this example has a high probability of being incorrect, and so is likely to trigger a challenge. It is also considered bad form, as bid jumping reduces the amount of information that can normally be gained by more conservative raises, and makes for shorter games. [edit] Variants
[edit] GamblingThere are a number of different ways to gamble with Liar's Dice. The simplest and probably most popular scheme is for all players to agree on a wager for the game before the first round, and for the game to be played winner-take-all using the multi-round "lose a round, lose a die" variant. Another popular method is played round-by-round with no dice lost, and the loser pays the winner their wager after each round, with other players breaking even. [edit] Drinking GameAlso known as Mexacali,[2] a popular way of playing Liar's Dice as a drinking game is to play in rounds, and the losing player or players for each round take a drink of alcohol. If played with the variants where players lose dice when they lose a round, they may be required to take a drink for each die lost and an additional pre-arranged number of drinks upon being eliminated from the game, or a drink for every round played thereafter until the game is over. Care must be taken with this last variant; the player eliminated first from a game with 4 or 5 players may have to drink 15 or 20 drinks in a relatively short time if this rule is in effect using shots or full beers as "drinks". Sometimes the drinking is based upon the difference between the quantities bid and revealed. For a failed out-of-sequence challenge, the out-of-sequence challenger drinks a greater quantity (eg double). If played with "Spot On" calls, a successful "Spot On" call means everyone else drinks, while a failed call means the caller drinks double. [edit] Elements of Common Hand StrategyPlaying 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, for instance "three threes" when the player making the bid has no threes under his cup, is likely to be correct by simple probability (depending on the number of players), however, 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, however the "expected quantity" has a greater than 50% chance of being correct, and the highest probability of being exactly correct ("Spot On"). Bids higher than the expected quantity become exponentially unlikely; the chances of 60% of the dice in play having any one value are less than 1 in 10,000. 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. [edit] Basic Dice OddsFor 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 combinations (irrespective of sequence) of n dice taken q at a time. 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, entered into a spreadsheet program like Microsoft Excel, 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:
[edit] Rules (individual hand)A closely related game, known as Liar Dice, is played with one set of 5 poker dice. Each die is marked with Ace (A), King (K), Queen (Q), Jack (J), ten (T) and nine (9); the faces, as listed here, are in order of value with Ace being the best. [edit] SummaryA player is slid the dice cup with dice concealed under it, along with a claim as to what poker hand is shown on the dice. The player must either challenge the claim or roll the dice and make his or her own claim, which must always be higher than the previous claim. If a claim is challenged, the dice are revealed. If the dice show a poker hand at least as high as the claim, the challenger loses a "life" (a point). If the dice show a lower poker hand than claimed, the claimant loses a life. When a player has lost a number of lives (often 3), that player is out of the game. The last player remaining wins. [3] [edit] PlayAny number of players sit round a convenient table so that a set of poker dice can be passed clockwise from player to player without disturbing the rolls. The game is best with 5-8 players. The starting player is determined by highest die roll. Matching highest players re-roll to tie-break. In turn, each player rolls all / some / none of the dice at his discretion, usually hiding them from the other players' view. The starting player must roll all 5 dice. A player must state accurately how many dice he is rolling. He then offers the (usually hidden) dice to the player on his left stating that they are some poker bid (excluding runs). This bid must be better than the offer made when he accepted the dice. (The starting player may name any bid). The next player may either accept the dice and have his turn, or he may challenge. If challenging, the dice are exposed. If the hand equals or betters the stated bid, the recipient loses a life and the dice pass to the player on the recipient's left who starts again. If the hand is worse than the bid then the offerer loses a life and the recipient becomes the starting player. The above procedure is often done in a confusing manner in order to make other players play harder. Each bid need not be fully specified, in which case it is deemed to be the weakest possible bid meeting constraints stated. Better is a valid bid, as is Way better meaning Better than better, etc. Should a player make an undercall, it is treated as Better. The undercall can be pointed out by any player at any point in the future of this hand, up to and including the exposure of a challenged set of dice. When the bid reaches five aces (AAAAA), the player who needs to improve the bid must roll all and then may roll all / some / none of the dice twice more to achieve another five aces. If he achieves this then no-one loses a life and the next player starts a new hand, otherwise he loses a life. Each player has three lives and is out of the game when he has lost them all. The winner is the final player with a life. As a concession to the first player to lose all three lives, he may get an extra life by standing and "barking like a dog" (a decent howl, not just saying 'woof'). Should a player decline the dog's life, it remains available for a subsequent player to claim on losing his last life. If a player is absent when his turn comes, perhaps buying a round of drinks, he is deemed to have accepted the bid and to be passing the dice, unrolled, on as "Better". This is the Königswinter rule. [edit] BidsThere are no runs in Liar Dice. Getting progressively stronger, the types of bids are:
Here follows an example, stating what was said and the least it can mean:
A bid is often just "better". You have to pay attention since after 3 or 4 "betters" in a row, it is easy to lose track of what level the bid has reached. There is no obligation for a player to repeat his bid to clarify a situation for any player once the dice have been accepted by the recipient. You must be truthful about the number of dice that you roll. You do not have to be truthful about which dice you are rolling. For example, if you accept a bid of "four of a kind" (implying 9999T) and it happens to be JJJJQ, then you can roll 1 die - stating "rolling one die - a singleton Queen" and actually roll one of the Jacks to trash the hand for the next player. [edit] TechniquesYou do not have to look at the dice on your turn, though it is wise to do so. Certain confusions are in standard usage, for example "three pairs of Jacks" actually means "three jacks" as the 3 pairs are J1+J2, J2+J3 and J3+J1! Similarly six pairs means four of a kind. It is necessary to remember what the most recent bid is - even if this is determined by analysing "betters". It is advisable to remember exactly what dice you passed on to your left and how many dice each player has thrown since you saw them. Cooperation with the players to your left and right is a good strategy, ganging up on the players on the far side of the table. Mistakenly claiming a lower hand than is required can be beneficial. For example, if the previous player called "three jacks" and your roll included four kings, you may mistakenly state that you have "three tens". Players will quickly remind you that you need to roll better than the "three jacks", to which you respond, "Okay, then, four kings". The next player will almost certainly call you on this "mistake". You can only lose lives by calling the person to your right a liar, or by the person to your left calling you one. You have a better chance of staying in the game by accepting most of what is passed to you, and looking after the person to your left, so that when there are tough calls they will take what you offer. Sometimes looking after lefty means giving them a fighting chance so that a good throw will save them, for example passing three aces on as four nines gives three players a chance to throw two dice and make the fourth ace. If you have a killer hand, like five queens, be careful not to pass on a call so low that it comes back to bite you, call high enough to nail someone on the opposite side of the table. It all changes when down to just two players, always call the highest that you can, there is no point in giving a "better" call to an opponent you want to beat! Now winning depends on luck and how devious you can get, for example, if given three kings, call rolling two dice, but roll two of the kings, hand back rubbish and don't take it back again. [edit] An example handIn a four player ( [a], [b], [c] and [d] ) game.
The above may not be good quality play, but it is a valid hand. [edit] Stanford Variation of Individual HandThe Stanford variation is played with one set of six standard dice. Play is still the same, although the points are often eliminated. Players can reveal dice or remove them from view, as well as roll them inside or outside of the box. [edit] BidsHands are evaluated in this manner
Here are some examples
When making the claim, the bidder does not describe every die in the hand. Instead, the hand is assumed to be the minimum hand to fit the claim. For example, the call "Three 6s" is shorthand for the minimum hand that has three 6s, 666321. The call "Four of a kind and a pair" is shorthand for 111122, the minimum hand to fit the description. The term "Minimum Raise" means "the next greatest hand." You may roll die inside the box or outside the box. You cannot lie about how many die you roll, though you can conceal which die you are rolling. [edit] Rules (Mexican)The game starts by one person rolling 3 dice under a cup to keep the results hidden from the next player. (Some variations play with 2 dice). The roller then places the cup over his dice tells the next player what he rolled (but he may bluff). The next player may do one of two things:
Play continues as the roll results (or the claims of those results) get higher and higher until someone finally rolls a "Mexican" or a bluff is called.
After a Mexican, a new round commences. Adding to the fun, the value of the dice is read through code, like this: [edit] Modern variants[edit] Commercial versions
[edit] See also
[edit] In popular cultureIn the film Pirates of the Caribbean: Dead Man's Chest, Liar's Dice plays an important role as a plot element, in that Will Turner plays a game of Liar's Dice with his father and Davy Jones; the end result is that Bootstrap Bill is forced to serve an eternity aboard the Flying Dutchman. [edit] Notes and references
[edit] External links
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