The classic shake and score dice game!

Definition
Yahtzee is a dice game currently (2005) produced by Hasbro. It is a game almost entirely governed by chance. Common sense helps determine which dice to keep and which to re-roll, but assuming all players use common sense and the dice are fair, the outcome of the game is random. In the game, a yahtzee is statistically the most difficult roll to obtain as it is comprised of five dice all showing the same face. The probability of obtaining a yahtzee in a single roll is 0.1%, and the probability of obtaining a yahtzee in three rolls is 4.6%. "Yahtzee!" is also an English-language colloquialism synonymous with "Bingo!." It may be heard at baseball games when a home run is hit and at bingo parlors when one completes a bingo.

History
Yahtzee was invented by a Canadian couple. This couple wanted an easy, fun game that could be played aboard their yacht. Thus, Yahtzee was born under its original name, Yacht. Yacht was a success among the couple's friends, and they all wanted a copy. The couple saw a great earning potential in Yacht.

The couple pitched Yacht to Edwin S. Lowe in 1956. Lowe had had success selling Bingo games in the past so he was a logical choice to make professional-looking Yacht games. Lowe, just like the couple's friends, fell in love with the game. He offered to buy the rights, and the couple was to be paid the profit made on the first 1000 games. At this point, Yacht officially became known as Yahtzee.

Unfortunately, Yahtzee didn't sell well. Advertisements didn't do the game justice. Yahtzee was easy to understand, but it needed to be played to be appreciated. Lowe didn't give up; he started throwing Yahtzee parties of his own (just like the original couple), and Yahtzee took off through the oldest form of advertising, word of mouth.

Yahtzee was made by the E.S. Lowe Company until 1973, when the company was purchased by Milton Bradley. Milton Bradley, in turn, was acquired by Hasbro in 1984. At the time or writing, Hasbro produces and owns Yahtzee.

Rules
Object: Roll the dice resulting in the highest scoring combination possible.

Summary: The player may roll any or all of the dice up to three times each turn. The player stops when satisfied or three rolls have been taken. The player decides which of the 13 roll categories to score depending on which criteria are met and which result in the most points. The game is over when all players have completed all 13 roll categories. The player with the highest score is the winner.

Instructions: Yahtzee is a game suitable for any number of players (even one). Each player takes a score sheet (or a sheet of adequately prepared notebook paper) and rolls all five dice. The player with the highest total begins the game and play continues in a clockwise fashion.

At the start of his/her turn, the player rolls all five dice. If the player wants to keep any of the dice, s/he may do so and re-roll the others. If the player keeps all of the dice, the turn is over and scored. On each successive roll, any or all dice may be rolled. For example, dice kept from the first roll may be re-rolled on the third roll. After three rolls or all dice are kept by the player, the turn is over and scored.

Scoring
The scoring categores are:

  • Aces (Ones): Record the sum of all ones rolled.
    Valid Roll: (1, *, *, *, *)
    Minimum Score: 1, Maximum Score: 5
     
  • Twos: Record the sum of all twos rolled.
    Valid Roll: (2, *, *, *, *)
    Minimum Score: 2, Maximum Score: 10
     
  • Threes: Record the sum of all threes rolled.
    Valid Roll: (3, *, *, *, *)
    Minimum Score: 3, Maximum Score: 15
     
  • Fours: Record the sum of all fours rolled.
    Valid Roll: (4, *, *, *, *)
    Minimum Score: 4, Maximum Score: 20
     
  • Fives: Record the sum of all fives rolled.
    Valid Roll: (5, *, *, *, *)
    Minimum Score: 5, Maximum Score: 25
     
  • Sixes: Record the sum of all sixes rolled.
    Valid Roll: (6, *, *, *, *)
    Minimum Score: 6, Maximum Score: 30
     
  • 3 of a Kind: At least three dice must show the same face. Record the sum of all dice.
    Valid Roll: (1, 1, 1, 2, 3); (5, 5, 5, 5, 5); etc.
    Minimum Score: 5, Maximum Score: 30
     
  • 4 of a Kind: At least four dice must show the same face. Record the sum of all dice.
    Valid Roll: (1, 1, 1, 1, 2); (5, 5, 5, 5, 5); etc.
    Minimum Score: 5, Maximum Score: 30
     
  • Full House: Three dice must show the same face, and the other two dice must show the same face. Any Full House is worth 25 points.
    Valid Roll: (1, 1, 1, 2, 2); etc.
    Score: 25
     
  • Small Straight: Four dice must be numbered in sequence. Any Small Straight is worth 30 points.
    Valid Roll: (1, 2, 3, 4, *); (2, 3, 4, 5, *); (3, 4, 5, 6, *)
    Score: 30
     
  • Large Straight: All five dice must be numbered in sequence. Any Large Straight is worth 40 points.
    Valid Roll: (1, 2, 3, 4, 5); (2, 3, 4, 5, 6)
    Score: 40
     
  • YAHTZEE: All five dice must show the same face. The first YAHTZEE is woth 50 points; all subsequent YAHTZEEs are scored according the the YAHTZEE BONUS rules.
    Valid Roll: (6, 6, 6, 6, 6); etc.
    Score: 50
     
  • YAHTZEE BONUS: On every YAHTZEE rolled after the initial YAHTZEE, the player takes a 100 point bonus chip and places a checkmark in the YAHTZEE BONUS space on the score sheet. The roll is then scored according the the JOKER RULES.
    Valid Roll: see YAHTZEE
    Score: 100 + JOKER RULES score
     
  • JOKER RULES: Score the roll in any of the following categories that are appropriate (Group 1): Aces, Twos, Threes, Fours, Fives, or Sixes. If all the appropriate categories have already been scored, score the roll in any of the other categories (Group 2) regardless of qualification. If all the appropriate categories have already been scored, a zero is entered in one of the Group 1 boxes.
    Example: (5, 5, 5, 5, 5). Take a bonus chip, and check the YAHTZEE BONUS space. If Fives has not been scored, record 25 in the Fives space. If Fives has been scored, score any Group 2 space (e.g. Small Straight for 30 points).
    Score: Varies
     
  • Chance: Record the sum of all dice rolled. The Chance roll is usually filled in when the roll doesn't meet the requirements of any other rolls.

Game Over
The game ends when all players have completed their score sheets. Add up the points from Group A. If the total is greater than 62, add a 35 point bonus. Add the points from Group B to the total. Add 100 points for each bonus chip. The player with the highest score wins.

Single Player Game
The single player version of Yahtzee works just like the normal version. The only difference is that the player competes against his/her prior best score instead of actual opponents. All other rules apply as in normal play.

SOURCES:
http://mathforum.org/library/drmath/view/52174.html
http://www.hasbro.com/pl/page.corporate_history_yahtzee/dn/default.cfm
http://www.hasbro.com/common/instruct/Yahtzee.pdf
http://www.tutorgig.com/ed/Timeline_of_video_games

Thanks to xq for correcting my very flawed odds (I've changed them to probabilities) and for catching a typographical error.