Yahtzee

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Yahtzee
Yahtzee logo.svg
Present Yahtzee logo
Players1 and up
Age range8+
Playing time30 minutes
Random chanceHigh
Skill(s) requiredLuck, probability, strategy
 
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This article is about the game. For the game developer and journalist, see Ben "Yahtzee" Croshaw.
Yahtzee
Yahtzee logo.svg
Present Yahtzee logo
Players1 and up
Age range8+
Playing time30 minutes
Random chanceHigh
Skill(s) requiredLuck, probability, strategy

Yahtzee is a dice game made by Milton Bradley (now owned by Hasbro), which was first marketed as "Yatzie" by National Association Service of Toledo, Ohio, in the early 1940s. Yatzie was included in a game set called "LUCK - 15 Grand Dice Games". It was marketed under the name of Yahtzee by game entrepreneur Edwin S. Lowe in 1956. The game is a development of earlier dice games such as Yacht, Generala, and Yogi. A public domain version of Yahtzee, which is popular especially in Scandinavia, is Yatzy. Yahtzee is also similar to the English game of Poker Dice and the Cheerio dice game.

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 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).

Yahtzee was marketed by the E.S. Lowe company from 1956 till 1973. In 1973, the Milton Bradley Company 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.

History[edit]

The Original 1956 Yahtzee Board 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. Another game, Yap, shows close similarities to Yahtzee; this game was copyrighted by Robert Cissne in 1952.

The most notable is the dice game named "Yacht", which is an English cousin of Generala.[1] 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:

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.[2] 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 by Marvin Kaye.

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 of 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.

In 1988, Yahtzee became a television game show, hosted by Peter Marshall. The show was taped in Atlantic City, New Jersey. The first set of episodes took place at Trump Castle, then the show moved to the Showboat Hotel & Casino.

Rules overview[edit]

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[edit]

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 dice 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 he or she scores a "0" in an upper section box).

Lower section[edit]

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

CategoryDescriptionScoreExample
Three-Of-A-KindAt least three dice showing the same faceSum of all diceDice-2.svgDice-3.svgDice-4.svgDice-4.svgDice-4.svg
Four-Of-A-KindAt least four dice showing the same faceSum of all diceDice-4.svgDice-5.svgDice-5.svgDice-5.svgDice-5.svg
Full HouseA three-of-a-kind and a pair25Dice-2.svgDice-2.svgDice-5.svgDice-5.svgDice-5.svg
Small StraightFour sequential dice
(1-2-3-4, 2-3-4-5, or 3-4-5-6)
30Dice-1.svgDice-3.svgDice-4.svgDice-5.svgDice-6.svg
Large StraightFive sequential dice
(1-2-3-4-5 or 2-3-4-5-6)
40Dice-1.svgDice-2.svgDice-3.svgDice-4.svgDice-5.svg
YahtzeeAll five dice showing the same face50
First Yahtzee only
Dice-1.svgDice-1.svgDice-1.svgDice-1.svgDice-1.svg
ChanceAny 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 diceDice-1.svgDice-1.svgDice-3.svgDice-3.svgDice-5.svg

Some combinations offer the player a choice as to which category to score them under; e.g., a full house could be scored in the Full House, the Three-Of-A-Kind, or the Chance category.

Gameplay[edit]

Yahtzee components.jpg
Five ivory dice.jpg
Although Yahtzee is a commercial game with its own components (game set in upper image), the game can also be played with just five dice (such as the dice in the lower 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[edit]

A Yahtzee occurs when all five dice have the same value during one 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. A player must still score in an empty box as per normal in addition to receiving the 100-point bonus.

Additional Yahtzees may be used as wild cards in the Lower Section (scoring full points in a lower section box, such as a long straight, despite not having the normally required dice) 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 the Yahtzee box contains 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.

Solitaire[edit]

Yahtzee may also be played solitaire with the player attempting to reach the maximum possible score of 375 (1575 if bonuses are included).

Scoring variations[edit]

Rules and scoring categories are slightly different for the Swedish, Norwegian, Danish and Finnish versions.[3]

Mathematics[edit]

Optimal strategy[edit]

Discussion of the optimal strategy is beyond the scope of this article, but the strategy for maximizing the expected score has been determined. The strategy will sometimes involve zeroing out rows.[4] The average score when using the optimal strategy is 245.87, without bonus and jokers and 254.59, with bonus 100 for extra yahtzee.[5]

Maximum score[edit]

The maximum score of 375 is achieved by scoring five aces (five 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 (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 the Yahtzee bonuses are included, this score can be elevated to 1,575 points. This would mean twelve bonuses of 100 points are awarded for each of the twelve 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. This requires employing the "Jokers" rule using the Yahtzees as wild cards in the small and large straight spots.

Minimum score[edit]

The lowest possible score is 5. The Chance box always scores the sum of the dice, [6] so a score of five can only be achieved by rolling 5 aces. Although this roll is technically a Yahtzee, a player may choose not to score it as one, or cannot if a zero was previously placed in the Yahtzee score box. It is possible for all other boxes to be scored as 0 points. The strategy that works to maximize the average expected score will under worst case conditions score a minimum of 12 points, but cautious play will guarantee a minimum score of 18.[7]

Probabilities[edit]

The probability of a Yahtzee for any three-roll turn is about 0.04603 (or \tfrac{347897}{7558272}), or roughly 1 in 22 attempts.[8] The probability 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 0.013272 (\tfrac{6240321451}{470184984576}).[9] 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. However, this can be assessed by playing many games and observing scores achieved.[10] 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).[11]

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

Attaining the maximum score[edit]

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 thirty points for five sixes in 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 a score of five-of-a-kind in some boxes in the upper section (such as 25 in Fives box). During subsequent turns, 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. For instance, suppose nine 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.

With this thought process in mind, we can calculate the best possible scores based on the number of Yahtzees rolled. This would require obtaining Yahtzees in a specific order to maximize scoring. That is, the second Yahtzee would be in Sixes, adding six points to the Upper Section score; then Fives, Fours, Threes, and Twos. Then, in no particular order, since there would only be one additional point for counting die faces: Aces, Three-of-a-kind, Four-of-a-kind, and Chance. The Full House, Small Straight and Large Straight are saved for last because there is no additional score for counting the die faces.

# of YahtzeesBest Possible Score
0301
1351
2457
3562
4666
5769
6871
7972
81,073
91,174
101,275
111,375
121,475
131,575

Deluxe and collector editions[edit]

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[edit]

1986 Travel Yahtzee

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

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 Game Boy 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.[15][16] Yahtzee is available on the Xbox 360 in the Family Game Night game by Hasbro. Pogo.com released a version in 2009, and the game is also available on the Pogo Facebook site as well.

Related games[edit]

A number of related games under the Yahtzee brand have been produced. They all commonly use dice as the primary tool for gameplay, 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.

Similar games[edit]

Cultural references[edit]

References[edit]

External links[edit]