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.

How To Win At Yahtzee

You've played the game and you badly want to know how to win most matches. (Well, yeah, otherwise you wouldn't be here.) Congratulations, you've just stumbled upon someone who has played a lot of Yahtzee, both in traditional form and electronic form. Playing the single-player version has given me both experience and a good mind for tactics that can be utilised in the multi-player games.

On with the show.

General Tactics: Upper Half

You need a total of 63 to score the 35 bonus points, which means you can get any score in the ranges 0-62 and 98-140. 140 is nigh on impossible - you'd need to get 5 of each of the numbers. Aim for 3 of each number - if this is achieved then your score is exactly 63. Generally, however, people don't get 3 of each number - most times they will be forced to put a 4 in twos, or even (the horror!) 10 in fives.

The idea is to stick your first four-of-a-kind into the appropriate section in the lower half, then the next one into the upper half if possible. (Do not put it in 3 of a kind! There's a special strategy for that.) With that, you should make the 63 even if you had to score low in one category.

Detailed Tactics: Upper Half

  • Ones: The lowest-scoring field on practically every Yahtzee game, this can score between 0 and 5. It is always OK to score 1 or 2 in this section if you can't help it, just try to get four of another section. (This is likely and possible!) Note that you should never put four ones in 4 of a kind, this will result in a low score and potentially the difference between 290 and 300. We all love 300.

  • Twos: Four of these should also not be stuck in 4 of a kind. Tow of these can also be scored without much pain, but be cautious about scoring 2 in this section. Normally, if you score less than 3 of any given number in the upper section you will need four of a higher number to make up for it, or in extreme circumstances, five of a higher number.

  • Threes: You can get away with putting four of these and higher numbers into 4 of a kind. Sixes are incredibly sought-after, but rarely scored, so threes, fours and fives will do fine. Put 2 threes into this section with caution: this restricts your make-up options badly. All in all, not a good idea, unless you're desperate.

  • Fours: Same as threes.

  • Fives: Never, under any circumstances, accept less than three of these numbers. You'd need to get either 4 sixes or a heap of lower numbers. Bad. If you're really in a hole, score a small number in ones or twos, or take a Chance.

  • Sixes: Basically, the same strategy as fives. If you roll 4 sixes, however, have a look at the odd number out. If it's 1 or 2, think twice about sticking it in 4 of a kind. If it's a 3, 4 or 5, put it in 4 of a kind without delay.

General Tactics: Lower Half

This is where all of the points are scored, but the combinations are tricky to obtain deliberately, especially Large/Long Straight (for simplicity I'm going to use Large Straight here), and even more expecially if trying to fill an inside straight. Also in this section is what I call the escape route: Chance. More on that later.

Whenever I play Yahtzee, I always try to fill out what I call the Big Five: Yahtzee, Small Straight, Large Straight, Full House and the upper half's bonus. Together, these score 180 points, and together with an average of 20 points each for 3 of a kind, 4 of a kind and Chance and at least 63 points for the upper half, 300 looks very, very realistic. Of course, when that's not possible, a good, winning score with yahtzee is 275; without is 235. Don't ask me how I got different figures.

Detailed Tactics: Lower Half

  • 3 Of A Kind: I usually don't score this until I have 3 numbers that I haven't already put into the upper half. This is a good place to use for backup when going for a yahtzee, and it can be used for ones and twos without much of a problem. If you get everything else, you'll still score 270-odd. At least.

  • 4 Of A Kind: As mentioned above, don't try putting 4 ones or twos in unless you're really in a pinch. The best score is 30 but a good score is about half that. I tend to score 20+, or 0 in this section, and when I don't it's usually because I'm having a bad game. (Remember, folks, although there's tactics involved, it's mostly a game of chance!)

  • Full House: Never leave the game without one of these! Also, never try to fill a gap if you only have two pairs. Sure, the odds are in your favour, but in my experience, it's a million-to-one chance... and these crop up nine times out of ten. In any case, Full Houses are very easy to get by accident. If you get one, score it immediately unless you already have one. It's a good way to score 25 free points.

  • Straights: When you get a small straight on the first roll and you have neither small or large straights, keep the small but go for the large. It's either 40 points and a potentially good game, or 30 points and still a good game. It's best if you get the Large Straight first and get it out of the way, because the odds are very good for getting a small straight. The trick, as mentioned above, is to never try to fill an inside straight. Never. If you really need a Large Stright that badly, wait until you roll a 2-3-4-5 and therefore increase the odds slightly. Large straight should be the first thing you score 0 for if you're in dire straits, followed by Yahtzee. The reason? Getting these two in a game is difficult, but you still need to stay optimistic enough to want to score 50 points.

  • Chance: This should never be touched until after about turn 6, when you're about halfway through and have filled in a few sections. If you're lucky and have filled out all of the categories except for Chance, then try and go for another Yahtzee. If you're successful, you'll score 100 plus the score of the Yahtzee; if you're not, you still score points regardless.

  • Yahtzee: The most self-explanatory and least explainable of all the categories. Score 5 of a kind and get 50 points, and that's it. Easy. (Well, the odds of getting one are apparently about 5%, so it is likely that you will not get a Yahtzee in the game. Try anyway! It feels good when you get one!)

And finally, a quick word on scores. Since the maximum score possible is 675 (375 without Yahtzee Bonus, which some people do still play), I'd say a good score, given the odds of scoring a Yahtzee, is around 250, but aim for 300 if possible. A score that will practically ensure you a win is 275, however don't take that as a guarantee. For the single player game, I tend to get 225+ around 80% of the time, 250+ around 50% of the time, and 300+ around 15% of the time. Get 230 and you're cruising.

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