Yahtzee

Yahtzee

Present Yahtzee logo
Players	1 and up
Age range	8+
Playing time	30 minutes
Random chance	High
Skill(s) required	Luck, probability, strategy

Yahtzee is a dice game made by Milton Bradley (now owned by Hasbro), which was first marketed by game entrepreneur Edwin S. Lowe in 1956. The game is a development of earlier dice games such as Yacht and Generala. 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

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. 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. 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

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

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 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

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.

Gameplay

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 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

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

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

• 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 the 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 definitions in this variation as in Yahtzee's parent game, Yacht (see History above). 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.

Mathematics

Optimal strategy

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. The average score when using the optimal strategy is 254.59, with a standard deviation of 59.61 points.

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 (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 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. This requires employing the "Jokers" rule using the Yahtzees as wild cards in the small and large straight spots.

Minimum score

The lowest possible score is 5. The Chance box always scores the sum of the dice, 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.

Probabilities

The probability of a Yahtzee for any three-roll turn is about 0.04603 (or ), or roughly 1 in 22 attempts. 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 (). 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. 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).

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

Attaining 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 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 Yahtzees	Best Possible Score
0	301
1	351
2	457
3	562
4	666
5	769
6	871
7	972
8	1,073
9	1,174
10	1,275
11	1,375
12	1,475
13	1,575

Deluxe and collector editions

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

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.
• There are also miniature versions of the game, sold in sets contained either in cups that act as keychains (by the company Basic Fun) or in specially-shaped pens (by the company Stylus).

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. 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

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.

One online variation of Yahtzee, is Yahtzo ( www.yahtzo.com). Yahtzo contains the same basic rules and goals of Yahtzee, but the online gameplay allows the users to track statistics of their games and games of all Yahtzo players. Yahtzo.com also features logic to show the predicted final score and the highest possible score for the current game, which is updated each turn. The Yahtzo variation also shows a distribution chart and top scores of all games played.

Similar games

• Open Yahtzee is a popular cross-platform computer program version of Yahtzee.
• Kubus is another variant with variable bonus threshold and is also available for mobile devices.
• Balut is the name of a Danish dice game played by expatriates in many countries all over the world. The name of the game is taken from balut eggs. Games are organized monthly by IBF (International Balut Federation) members.
• Poker dice, with labels reminiscent of playing cards.
• 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 a pricing game on The Price Is Right played for a car, with one free roll. In the first part of the game, a contestant can win one or two more rolls of the five dice by pricing three grocery products by guessing whether each product is higher-priced or lower-priced than the last. In the second part of the game, the contestant rolls the dice, attempting to roll five "car" symbols (each die has three such symbols). The game ends, either after the car is won (in effect, a "Yahtzee in cars"); otherwise, after the rolls the contestant earned, he or she wins the total of all cash showing on the dice; each die has cash amounts of $500, $1,000, and $1,500 (for a maximum total of $2,500, $5,000, or $7,500 if cash were to be rolled on all dice). (As each die has three car symbols, the probability of rolling a "Yahtzee in cars" in two rolls is much higher than rolling one in the traditional game, assuming a three-roll turn.)
• To Court the King uses a similar roll and re-roll mechanic to Yahtzee with the added mechanic of using dice to claim character cards that give the player various abilities to manipulate their dice rolls. It was designed by Tom Lehmann and published by Amigo Spiele and Rio Grande Games in 2007.
• Richard Garfield deliberately created the game King of Tokyo because he wanted to create a game using the dice mechanics of Yahtzee; the "theme" of the game came later.
• YAMB or JAMB is a very popular Yahtzee-like game in Southeastern part of the Europe, especially ex-Yugoslavia. It features six dice (5 for playing and 1 as a joker) and more complex rules: it has 3 sections, upper, mid and lower section. Each of them can have up to 9 different columns that all have unique ways to play. For example, one column must be filled starting from the top section, one from the bottom, one is for announcing the result after the first throw, etc. Middle section has "maximum" and "minimum" rows and the goal is to get the highest/lowest number combination based on the 5 dice. To get the total for each column of the middle section, "maximum" result is subtracted from the "minimum" and that number is multiplied by the sum written in the box "one" from the upper section.
• Dice with Buddies follows the same rules as Yahtzee with the exception that additional Yahtzee rolls are scored as 50 points instead of 100. Dice with Buddies was added to the Apple App Store in 2011 and is currently available as an iPhone, iPad, Android, and Facebook app.