Yahtzee

2008/9 Schools Wikipedia Selection. Related subjects: Games

Yahtzee is the trademarked name of 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.

Each of the scoring combinations has a different point value, some of which are fixed values and others of which have the cumulative value of the dice. A Yahtzee is a five-of-a-kind and holds the game's highest point value of 50.

Overview of the Rules

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 obtains or exceeds 63 points, 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) of a larger number so that fewer of the lower ones are needed.

Lower Section

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

• Three-of-a-Kind (sum all dice)
• Four-of-a-Kind (sum all dice)
• Full House 25pts
• Small straight 30pts
• Large straight 40pts
• Five-of-a-Kind (Yahtzee) 50pts
• Chance (sum all dice)

Chance 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.

Game Play

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 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 out five threes (a Yahtzee in the 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).

The original game rules released in 1956 contain a discrepancy in the rule above. The booklet states 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.

Mathematics of Yahtzee

Maximum Score

The maximum score of 375 is achieved by scoring five aces (5 points), five deuces (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 1575 points. These nine bonuses are awarded for each of the top row Yahtzees and the Yahtzees in Three-of-a-kind, Four-of-a-kind, and Chance boxes. In this case, one would fill in the Yahtzee score first, the fills in the upper scores and then use the remaining Yahtzees as wild cards for the rest of the boxes.

Minimum Score

The lowest possible score is 0, as it is always valid to strike out a box. However, striking out the Chance box, for example, is absurd, so with a minimal throw of five 1s (having struck out the boxes Ones and Yatzhee previously), at least 5 points would be scored in the Chance box. 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..

Probabilities

The probability of a Yahtzee at any point in the game when rolling for it is about .04603 (). This is about 4.6% or about 1 in 22 attempts. The probability of a specific Yahtzee (e.g. all aces) when rolling for it is about .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 since it is partly a function of game tactics. 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).

Getting the minimum score

The minimum score is achieved by one specific Yahtzee (that of all aces) and careful scoring of zero in all the other boxes. A specific Yahtzee has a probability of about .013272 () or about 1.3% or 1 in 75 rolls. In order to avoid over-complicating the probability calculations, it is necessary to keep rolling dice without starting a game until one gets a Yahtzee made up of aces, then carefully using the remaining twelve rolls to ensure that zero is scored in the other boxes.

Getting the maximum score

Using bonus chips, a 1575-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 obatined 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 be specific on the threes or twos. Therefore, this is a very difficult calculation.

History

E.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 toy and game entrepreneur Edwin S. 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 E.S. 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" where 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.

However, 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 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 (must attain 23456 and 12345), full house is scored by summing all dice, there is no three-of-a-kind category, and the highest possible score is 302. Wood classifies Yacht and a similar three dice game called Crag as sequence dice games.

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 E.S. 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, fifty 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 E.S. Lowe company. After 1973, the logo changed various times. This logo is found on the scorecards and the game boxes. (See image of the logos in the "Rules" section above)

Deluxe and Collector Edition Games

Deluxe edition games have been sold alongside the regular issue games since the early 1960’s. 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.

Other Versions of Standard Yahtzee

Since the 1970s, Travel Yahtzee has been sold in various forms as part of Milton Bradley's line of travel games. Currently, a zip-up cloth deluxe folio edition is sold instead of the old travel game edition. 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 customers. This "Ultimate Yahtzee" CD-ROM game contained standard Yahtzee as well as other varieties. There are also several electronic versions of the game such as a handheld LCD version, and a cell phone version called Yahtzee Deluxe, which features the original rules along with several other modes.

Related Games

A number of related games under the Yahtzee brand have been produced. These include: Triple Yahtzee (1972), Word Yahtzee (1978), Casino Yahtzee (1986), Jackpot Yahtzee (1980), Showdown Yahtzee (1991), Yahtzee Texas Hold'em (2005), and Yahtzee Deluxe Poker (2005). An additional variant, Power Yahtzee (which features a sixth "Power" multiplier die and an expanded score sheet) was produced by Winning Moves Games in 2007.

The 1970s TV game show Spin-Off was based on the game. 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 is ItsYourTurn.com's spinoff of the game. The only real difference would appear to be the name.
• Poker Dice
• 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.