Yahtzee

Players Present Yahtzee logo 1+ (1 means solitaire) 8+ 30 minutes high Luck, Probability, and Strategy

Yahtzee is a popular dice game made by Milton Bradley (now owned by Hasbro). The object of the game is to score the most points by rolling five dice to make certain combinations. The dice can be rolled up to three times in a turn to try to make one of the thirteen possible scoring combinations. A game of Yahtzee consists of thirteen rounds during which the player chooses which scoring combination is to be used in that round. Once a combination has been used in the game, it cannot be used again.

The scoring combinations have varying point values, some of which are fixed values and others of which have the cumulative value of the dice. A Yahtzee is five-of-a-kind and holds the game's highest point value of 50 (not counting multiple "Yahtzees" in the same game).

Rules overview

The Yahtzee scorecard contains thirteen boxes divided between two sections: the upper section, and the lower section.

Logo of the game as originally published in 1954. It includes a caricature of E. S. Lowe, the person responsible for the game's production.

Upper section

In the upper section, each box is scored by summing the total number of dice faces matching that box. For example, if a player were to roll three "twos," the score would be recorded as 6 in the twos box. If a player scores a total of at least 63 points in these boxes, a bonus of 35 points is added to the upper section score. Though 63 points corresponds to three-of-a-kind for each of the six die faces, a common way to get the bonus is rolling four (or five, often using a "Yahtzee as a joker") of a larger number so that fewer of the smaller numbers are needed (a player can earn the bonus even if a he or she scores a "0" in an upper section box).

Lower section

The lower section contains a number of poker-themed combinations with specific point values:

Category Description Score Example
Three-Of-A-Kind At least three dice showing the same face Sum of all dice
Four-Of-A-Kind At least four dice showing the same face Sum of all dice
Full House A three-of-a-kind and a pair 25
Small Straight Four sequential dice
(1-2-3-4, 2-3-4-5, or 3-4-5-6)
30
Large Straight Five sequential dice
(1-2-3-4-5 or 2-3-4-5-6)
40
Yahtzee All five dice showing the same face 50
First Yahtzee only
Chance Any combination
often acts as discard box for a turn that will not fit in another category (thus the name), although during a lucky game it can be used to record a high score
Sum of all dice

A certain combination can be scored in more than one appropriate category; e.g., a full house can be scored in the Full House, Three-Of-A-Kind, or Chance categories.

Game play

Although Yahtzee is a commercial game with its own components, the game can also be played with just five dice (such as the dice in this image), some pencils or pens and sheets of paper, and the knowledge of the rules and scoring categories.

On each turn, a player gets up to three rolls of the dice. He or she can save any dice that are wanted to complete a combination and then re-roll the other dice. After the third roll, the player must find a place to put the score (though he or she can choose to end the turn and score after one or two rolls, if desired). If the resulting combination of dice will not fit in any unused scoring category, the player must place a "zero" in one of the unused boxes. Each player's total score is calculated by summing all thirteen score boxes.

Yahtzees and bonus chips

A Yahtzee occurs when all five dice have the same value during a player's turn. Yahtzee is the most difficult combination to throw in a game and has the high score of 50 points. If a player scores one or more additional Yahtzees during the same game, that player is awarded bonus points and is given bonus chips that correspond to each additional Yahtzee that a player rolls. Bonus Yahtzees are worth 100 points each. Bonus chips are only awarded for subsequent Yahtzees if the first Yahtzee was placed in the 50-point Yahtzee score box.

Additional Yahtzees may be used as wild cards in the Lower Section provided that the corresponding Upper Section box has been filled. For example, if a player rolled five threes (a Yahtzee in threes), the player could only use it as a wild card in the Lower Section if he or she already had a score in the Threes box in the Upper Section. If the Threes box was still open, the player must score 15 in the threes (sum of five threes).

In case a Yahtzee occurs after its corresponding box is scored zero, the Bonus Yahtzee score is not awarded; but the wild card rule stated above still applies.

The original game rules released in 1956 contain a discrepancy in the rule above. The booklet stated that additional Yahtzees must be used as Jokers in the Lower Section and does not allow for their use in the Upper Section. However, the booklet also declares the highest possible score as 375, which would require the placement of Yahtzees in the Upper Section. This problem was corrected when the game was re-copyrighted in 1961.

Game played solitaire

Yahtzee may also be played solitaire with the player attempting to reach the maximum possible score of 375.

Swedish/Norwegian/Finnish scoring variation

Swedish rules for the game follow a slightly different set of scoring categories and rules in scoring. This Swedish variation is used mainly in Scandinavian and Finnish versions of the game.[1]

• The bonus for reaching 63 or more points in the Upper Section is 50 points.
• There are "One Pair" and "Two Pair" categories, which score the total of the pair(s) involved. In case of Two Pair, the pairs must be distinct; a four-of-a-kind counts only as One Pair for two of the four dice having the same face.
• In a similar vein, the Three-of-a-Kind and Four-of-a-Kind categories are scored by the total of the needed number of same-faced dice. (For instance, 5-5-5-5-6 will score 20 points in Four-of-a-Kind and 15 points in Three-of-a-Kind; under standard rules, the same combination would give the player 26 points in either category.)
• Small Straight and Large Straight have the same definition in this variation as they are in Yahtzee's parent game, Yacht (see History below). Here, a Small Straight is 1-2-3-4-5 and scores 15 points (the total of the dice faces); the Large Straight is 2-3-4-5-6 and awards 20 points (again the combined value of the dice).
• Full House scores the total of all dice (same as in Yacht).
• Succeeding Yahtzees can be scored to the other categories except Two Pair, Full House, and Small Straight/Large Straight under the same scoring restrictions (for example, a Yahtzee of sixes can only score 12 under One Pair, 18 under Three-of-a-Kind, 24 under Four-of-a-Kind, and 30 under either Sixes or Chance.) There are no Yahtzee bonuses.

The maximum score to be obtained under this variation is 374 points, close to the 375-point cap under standard rules, minus Yahtzee bonuses.

Mathematics of Yahtzee

Maximum score

The maximum score of 375 is achieved by scoring five aces (5 points), five twos (10 points), five threes (15 points), five fours (20 points), five fives (25 points), five sixes (30 points), the Bonus for Upper Box row score equaling or exceeding 63 points (35 points), five sixes played as Three-of-a-kind as (30 points), five sixes played as a Four-of-a-kind (30 points), a Full House (25 points), a Small Straight (30 points), a Large Straight (40 points), a Yahtzee (50 points), and five sixes played as Chance (30 points).

If one includes the Yahtzee bonuses, this score can be elevated to 1,575 points. These 12 bonuses of 100 points are awarded for each of the 12 non-Yahtzee boxes. In this case, one would fill in the Yahtzee box first, then each box in the Upper Section, and then use the remaining Yahtzees as wild cards for the Lower Section boxes.

Minimum score

Theoretically, the lowest possible score is 5. The Chance box always scores the sum of the dice,[2] so with a minimal throw of five 1s, at least 5 points would be scored in the Chance box. All other boxes can be scored as 0 points. However, this would require that the player assign a 0 score to every box other than Chance. It is possible to guarantee a minimum score of 18, and the strategy which works to maximize the average expected score will under worst case conditions score a minimum of 12 points.[3]

Probabilities

The probability of a Yahtzee for any three-roll turn is about .04603 (or $\tfrac{347897}{7558272}$). or roughly 1 in 22 attempts.[4] The odds of rolling a Yahtzee in the first roll of any turn is 1 in 1296. The probability of a specific Yahtzee (e.g., all aces) is about .013272 ($\tfrac{6240321451}{470184984576}$). [5] This is about 1.3% or about 1 in 75 attempts. The pure probability of beating a given score in a single game is virtually incalculable since it is partly a function of game tactics. However, this can be assessed by playing many games and observing scores achieved.[6] A program has been written for choosing the correct dice at any point in a game, which maximizes the expected score (i.e., for an infinite number of games from that point).[7]

The probability of a player rolling 13 Yahtzees in a game is about 1 in 283 quadrillion (15 zeros).

Getting the maximum score

Using bonus chips, a 1,575-point overall score would require thirteen Yahtzee rolls, nine of which would have to be of a specific face (aces to sixes in the Upper Section and 30, which is five sixes, as Three-of-a-kind, Four-of-a-kind, and Chance).

That does not mean, however, that a person would have to be rolling for a Yahtzee of a specific side to get that Yahtzee. For instance, during the first two turns of the game, whichever Yahtzee is obtained would be with a probability of about .046 (for example, rolling for whichever dice turns up most the first roll). That would give a Yahtzee then a score of five-of-a-kind in some boxes in the upper section (such as 25 in Fives box). During subsequent turns, the probability of a Yahtzee is diminished, but there are still several possibilities (e.g., aces to fours or sixes in the Upper Section on turn 3).

At least four Yahtzees with sixes must be obtained in this game, but that does not necessarily mean rolling two sixes instead of three threes if the threes are open as well—though it could at some point (e.g., if Three-of-a-kind, Four-of-a-kind, Chance, and Threes are the only remaining categories, the one which is best for the player). The only turn for which the probability of a Yahtzee for a specific face would apply is for the last roll of the game if a score is needed in any category but Full House or the Straights. For instance, suppose eleven Yahtzees were obtained and only Threes and Twos are left. The probability of a Yahtzee in Turn 12 would still be slightly better than that for a specific die face (about 1 in 77) because there are two sides to choose from - i.e., rolls don't necessarily need to be specific on the threes or twos. Therefore, this is a very difficult calculation.

History

Original 1956 Yahtzee Game

The overall concept of Yahtzee traces its roots to a number of traditional dice games. Among these are the Puerto Rican game Generala, and the English games of Poker Dice and Cheerio. Most notable is the dice game named Yacht[1][2] which is an English cousin of Generala. This game is fully explained in The Complete Book of Games by Clement Wood and Gloria Goddard (1940). This predecessor is extremely similar to Yahtzee in both name and content. The game's rules differ from those of Yahtzee in the following ways:

• It does not have an upper section bonus.
• Both straights are a sequence of five ("Large Straight" is 2-3-4-5-6, "Small Straight" is 1-2-3-4-5).
• Full House is scored by summing all dice faces.
• There is no three-of-a-kind category.
• The highest possible score is 302.

Wood classifies Yacht, and a similar three-dice game called Crag, as sequence dice games.

The present-day commercial Yahtzee began when toy and game entrepreneur Edwin S. Lowe filed Yahtzee as a trademark with the U.S. Patent Office on April 19, 1956. The first commercial usage of the name Yahtzee was a few weeks earlier on April 3. Lowe classified his product as a "Poker Dice Game."

According to Hasbro, the game was invented in 1954 by an anonymous Canadian couple, who called it "The Yacht Game" because they played it on their yacht with their friends.[8] Two years later they asked Lowe if he would make up some sets to be given as gifts to their friends who enjoyed the game. Lowe perceived the possibility of marketing the game, and acquired the rights to the game from the couple in exchange for 1,000 gift sets. This story is expanded by Lowe in the 1973 book, A Toy is Born. According to Lowe, the game did not initially do well commercially, since the rules and appeal were not easily conveyed in an advertisement. Eventually, he had the idea of organizing Yahtzee parties at which people could play the game and thereby gain a firsthand appreciation for it. The idea was successful, and enthusiasts quickly popularized the game through word of mouth.

The E.S. Lowe company sold Yahtzee from 1956 to 1973. During Lowe's ownership, a number of changes were made to the game's packaging, contents, and appearance. Between 1956 and 1961, the game's advertising slogan was changed from "The Game That Makes You Think While Having Fun" to "The Fun Game That Makes Thinking Fun!"

The game and its contents were copyrighted by Lowe in 1956, 1961, 1967, and 1972. In 1973, Milton Bradley purchased the E.S. Lowe Company and assumed the rights to produce and sell Yahtzee. During Lowe's ownership over 40 million Yahtzee games were sold in America and around the globe. The game has maintained its popularity. According to current owner Hasbro, 50 million Yahtzee games are sold each year.

Over time, the Yahtzee logo has taken several forms. The original version of the logo was used throughout the entire period that the game was produced solely by the Lowe company. After 1973, the logo changed various times. This logo is found on the scorecards and the game boxes.

Deluxe and collector edition games

Deluxe edition games have been sold alongside the regular issue games since the early 1960s. They all contain components that are more luxurious than standard game parts. In recent years, a number of collector issue Yahtzees have been sold as well. Some of these collector issues have dice that replace the pips with certain symbols connected to a theme, but still correspond to the numbers one to six.

Other versions of standard Yahtzee

1986 Travel Yahtzee

Since the 1970s, Travel Yahtzee has been sold in various forms as part of Milton Bradley's line of travel games.

• In the past, the travel form of Yahtzee was composed of the five dice contained in a special apparatus (see image at the right). "Rolling" the dice is initiated by turning the apparatus over, running it on one hand and turning the apparatus upright to see the faces of the dice. Dice to be saved for the next roll are locked by snapping the reverse of the apparatus.
• Currently, a zip-up cloth deluxe folio edition is sold. It consists of the set of dice, the cup, the scoresheets, and a tray for the dice to roll on, which includes a holder for the dice to be saved for the next roll. The cup has an oblong lip for easy storage.
• There also exists a red circular travel edition, which includes the dice and scoresheets, as well as a collapsible cup and detachable dice holder. The bottom half of the case acts as a dice tray. It should be noted that this one uses a different logo from the standard one (the name of the game in uppercase with an exclamation point in front of a green oval) and it is sold outside of the United States.[9]
• There are also miniature versions of the game, sold in sets contained either in cups that act as keychains (by the company Basic Fun)[10] or in specially-shaped pens (by the company Stylus)[11].

Various Yahtzee console games have been sold over the years including an early version on the TI-99 4A computer. In 1996, the game was first released to PC and Mac users by Atari. The Ultimate Yahtzee CD-ROM game contained standard Yahtzee as well as other varieties. Later, GameHouse also released an authorized special version of the game for Windows users. Independently-produced versions, downloadable and online ones, also exist.

There are also several electronic versions of the game such as a handheld LCD version, and a cell phone version called Yahtzee Deluxe, which feature the original rules along with Duplicate and Rainbow modes, as well as independently-produced versions for the Palm OS and Pocket PC and several cellphone models. The version for the Nintendo GameBoy was licensed from Hasbro and was produced by DSI Games and Black Lantern Studios Inc. It was sold in a three pack that included Life, Payday, and Yahtzee. The game has also been released for the iPod, iPod touch and the iPhone, to be purchased through the iTunes Store.[12][13]

Related games

A number of related games under the Yahtzee brand have been produced. They all commonly use dice as the primary tool for game play, but all differ generally. As Yahtzee itself has been sold since 1954, the variants released over the years are more recent in comparison, with the oldest one, Triple Yahtzee, developed in 1972, eighteen years after the introduction of the parent game.

In addition, the 1970s television game show Spin-Off was based on Yahtzee. Another, similarly short-lived, TV game show adaptation, Yahtzee, was syndicated to local stations during the 1987 season.

Other games similar to Yahtzee

• Open Yahtzee is a popular cross-platform implementation of Yahtzee.
• 5dice is a Cocoa variant for the iPhone/iPod Touch.
• Balut is the name of a Danish Dice game played by expatriates in many countries all over the world. The name of the game has been taken from Balut eggs. Games are organized monthly by IBF (International Balut Federation) members.
• Boatzee[3] is a spinoff of the game. The only real difference would appear to be the name (a pun, since "Boat" is a much cheaper kind of "Yacht".)
• Poker dice, with labels reminiscent of playing cards.
• Greased Lightning Yahtzee is a fast paced version of the game
• Kismet has rules almost identical to those of Yahtzee but have dice with multiple colors. Numbers and colors are taken into account when scoring in these games.
• Let 'em Roll is the pricing game from The Price Is Right played for a car, with one free roll. In the grocery part, a player must win two more rolls to roll five dice. The player then rolls five dice and attempts to roll "Car" symbols, or otherwise rolls a cash prize. The game ends after all rolls are taken, with the player winning a car if they successfully roll five Car symbols in their rolls, or the total of whatever cash prizes they rolled.
• Let it Roll is a simplified variant for the iPhone and iPod Touch by Kudit.com.
• Phase 10 Dice, also produced by Fundex Games, was inspired by the card game Phase 10 but is similar to Yahtzee in that specific "hands" of dice (called Phases) must be completed in order to score points.
• Red Hot Yott, a game produced by Fundex Games, has rules almost identical to Yahtzee, but with aces being wild. For effect, Japanese dice, which have oversized, red-colored aces, are used in this game.
• To Court the King uses a similar roll and re-roll mechanic to Yahtzee with the added machanic of using dice to claim character cards that give the player various abilities to manipuluate their dice rolls. It was designed by Tom Lehmann and published by Amigo Spiele and Rio Grande Games in 2007.
• YAMB is a more complex variant of Yahtzee, played with 6 dice, has at least 4 vertical columns (6 is common) that all require different strategies in order to win. There are some other changes as well. Its origin is not known, but it's extensively being played in several former Yugoslavian republics.