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As with three-of-a-kind this strategy does not maximize the average score since there are a few situations after the first throw, where it is better to keep other combinations. According to Hasbro , the game was invented by an anonymous Canadian couple, who called it The Yacht Game because they played it on their yacht with their friends. In , the Milton Bradley Company purchased the E. The second best outcome is to score 24 in the 6s box. As with three-of-a-kind there are slightly different strategies depending on whether a player is simply trying to get a four-of-a-kind or he is trying to maximize his average score.

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Similarly, if a player starts with two "twos" they will be "2 down". Some players count a Yahtzee as being a valid Full House. However the official rule is that a Full House is "three of one number and two of another".

If a category is chosen but the dice do not match the requirements of the category the player scores 0 in that category. Some combinations offer the player a choice as to which category to score them under; e. The Chance category is often used for a turn that will not score well in any other category. A Yahtzee occurs when all five dice are the same.

If a player throws a Yahtzee but the Yahtzee category has already been used, special rules apply. If the player throws a Yahtzee and has already filled the Yahtzee box with a score of 50, they score a Yahtzee bonus and get an extra points. However, if they throw a Yahtzee and have filled the Yahtzee category with a score of 0, they do not get a Yahtzee bonus.

In either case they then select a category, as usual. Scoring is the same as normal except that, if the Upper Section box corresponding to the Yahtzee has been used, the Full House, Small Straight and Large Straight categories can be used to score 25, 30 or 40 respectively even though the dice do not meet the normal requirement for those categories.

In this case the Yahtzee is said to act as a "Joker". There are two alternative versions of the Joker rule used.

In the official rules [4] the player must act in the following way. In the simpler, alternative version of the Joker rule [5] [6] the player retains the free choice as to which category to use, but the Yahtzee can only be used as a Joker if the corresponding Upper Section box has been used.

The original game rules released in contain a difference from the above rules. The booklet stated that additional Yahtzees must be used as Jokers in the Lower Section and did not allow for their use in the Upper Section.

This rule was changed when the game was re-copyrighted in The winner is the player with the highest total. The rules do not specify what happens in the event of a tie. A detailed discussion of the optimal strategy is beyond the scope of this article but certain aspects can be considered here.

It is important to understand the probability of completing a Yahtzee. This depends on whether a particular Yahtzee is required or any Yahtzee. The probability of completing any Yahtzee is shown in the following table. The strategy is to keep any Yahtzee, four-of-a-kind, three-of-a-kind or pair that is thrown and re-roll the others.

With two pairs, either can be chosen. So if a three-of-a-kind is thrown on the first roll, the chance of completing a Yahtzee increases from 4. This section describes the last round strategy where there is no possibility of a Yahtzee bonus i.

These are the simplest situations to analyse, although even at this late stage the strategy may vary depending on the game situation. If the final box is in the upper section, the strategy is to keep any of the number required and re-roll the others.

The distribution is as follows:. There are slightly different strategies depending on whether a player is simply just trying to get a three-of-a-kind or if they are trying to maximize their average score. Different strategies will also be required should a specific target be needed to achieve. The strategy to maximize the chance of getting a three-of-a-kind involves keeping any three-of-a-kind that is rolled.

If a three-of-a-kind is rolled then after the first throw the player should keep any other 5s and 6s, while after the second throw the player should keep any other 4s, 5s, and 6s. An example is with the player keeps and throws the other 2. If a three-of-a-kind is not rolled the player should keep any pair that is rolled and re-roll the other dice, with two pairs the player should keep the higher pair, and with no pair the player should keep the highest die. Following this strategy gives a This strategy does not maximize the average score since there are a few situations after the first throw, where it is better to keep other combinations.

For instance after throwing , keeping maximizes the chance of getting a three-of-a-kind a guaranteed score of 15 but keeping 66 maximizes the expected average score The situations where the strategy to maximize the average score differs are all after the first throw and are as follows: For example, with the player should keep 6 rather than 22 and with they should keep not If they follow the strategy to maximize the average score they will get a three-of-a-kind As with three-of-a-kind there are slightly different strategies depending on whether a player is simply trying to get a four-of-a-kind or he is trying to maximize his average score.

Different strategies will also be required should he need to achieve a specific target. The strategy to maximize his chance of getting a four-of-a-kind involves keeping any four-of-a-kind that he has.

If he has a four-of-a-kind then after the first throw he will keep the other if it is a 5 and 6, while after the second throw he will keep it if it is a 4, 5 or 6.

So that with he keeps and will throw the 3. If he does not have a four-of-a-kind, the player should keep any three-of-a-kind or pair that he has and re-roll the other dice. With two pairs he will keep the higher pair. With no pair he will keep the highest die.

Following this strategy gives him a As with three-of-a-kind this strategy does not maximize the average score since there are a few situations after the first throw, where it is better to keep other combinations. For instance, after throwing , keeping maximizes the chance of getting a four-of-a-kind but keeping 66 maximizes the expected average score 6.

Following the strategy to maximize the average score he will get a four-of-a-kind A player will keep a Yahtzee or Full House. A Yahtzee will score 25 under the Joker rule, even though it is not strictly a full house. He will keep any four-of-a-kind, three-of-a-kind or pairs that are thrown and re-roll the others. With two pairs he will keep both. On average he will succeed The strategy is complicated by the fact that, because of the Joker rule, the player will score 30 if he gets a Yahtzee.

Clearly he keeps any Small Straight or Yahtzee that he throws. After the first throw he will keep a run of 3 or 3 out of 4 e. Otherwise, he will keep a 3 or 4 or both and a 2 or 5 if he also has a 3 or 4 e. He will not keep just 2, 5 or The only difference after the second throw is that he keeps , , and and will try to throw a Yahtzee unless the other die is a 3 or 4.

Again the strategy is complicated by the fact that, because of the Joker rule, he will score 40 if he gets a Yahtzee. Clearly he will keep any Large Straight or Yahtzee that he throws.

The best strategy is also to keep a four-of-a-kind and try to throw a Yahtzee, even after the first throw. The player should not keep a three-of-a-kind. Keep a small straight or 4 out of 5 e. Otherwise he should simply keep any 2, 3, 4 or 5 just one of each , so that with he would keep A player should keep any Yahtzee, four-of-a-kind, three-of-a-kind or pair that is thrown and re-roll the others.

On average he will succeed 4. To get the maximum average score the strategy is straightforward. After the first throw the player will keep any 5s and 6s. After the second throw he will keep any 4s, 5s, and 6s. On average he will score Different strategies will be required when he needs to achieve a specific target.

The strategy for maximizing the expected score has been determined. It is important to note that the "Optimal" strategy simply maximises the average score. It does not maximise the chances of winning a game. There are two main reasons for this. Firstly, the Optimal strategy takes no account of any opponents. In normal gameplay a player will adjust their strategy depending on the scores of the other player or players.

Secondly, the Optimal strategy tends to give undue importance to Yahtzee bonuses. It is rare for a player without a Yahtzee bonus to beat a player with one. So, in normal gameplay, a players' strategy is not significantly influenced by the value given for a Yahtzee bonus. Consider the situation where the Yahtzee bonus was worth a million rather than a hundred. It would not influence normal gameplay where the objective is to score more than the opponent.

It would, however, affect the "Optimal" strategy since scoring a million would have a dramatic effect on the average score.

The "Optimal" strategy would be dominated by the prospect of a Yahtzee bonus. Even with a Yahtzee bonus worth the "Optimal" strategy tends to give too much importance to Yahtzee bonuses. Despite these limitations the "Optimal" strategy does provide a useful guide as to the best strategy, especially in the early rounds. The "Optimal" strategy for the first round is described in the next section.

After the first round, the number of different games rapidly makes detailed analysis difficult but, in the early rounds, players generally simply adapt the first round strategy based on the boxes used. For instance if a player throws in the first round they will keep 66 but if the 6s box was used in the first round and they throw in the second round they will naturally keep 55 instead.

The following table shows the average score obtained using the Optimal strategy and the proportion of the time that zero is scored in a particular category: It is possible to calculate the maximum average score with different rules.

When the rules are changed so that there is no Upper Section bonus the average score drops from This compares with an average bonus score of The average number of Yahtzees thrown in a game is 0.

In about a quarter of these cases the Yahtzee box has a score 0 and so there is no Yahtzee bonus. Although the average score is The 1st Percentile is i.

The strategy for the first round described here is based on that used by the "Optimal" strategy. Sometimes there are two possible plays which are almost equally good. In these cases the simplest option is given, i. Although there are different ways of throwing 5 dice, because the order of the dice is not important there are only different combinations.

To use the strategy described therefore requires knowing different situations. The general principle after the first and second throws is to keep the largest number of similar dice and rethrow the rest. When a player has a full house he will keep the three-of-a-kind. With two pairs, keep the higher pair and rethrow the other three dice. If a large straight is rolled, keep it.

If a small straight is rolled, keep it and re-roll the fifth die. If all the dice are different and there is no straight, keep only the 5. There are a number of exceptions to these rules. These exceptions are different for the second and third rolls.

So, before the second roll he will never keep two pairs, he will never keep a pair of 1s and he will never throw all the dice again. So there are specific differences compared to the second roll. Now he will keep the Full House if the three-of-a-kind is 2 or 3 and keep two pairs when they are 1 and 2 or 1 and 3. He will Keep all large and small straights. He will Normally keep a pair of 1s although is still better and keep rather than 5 when all the dice are different.

If he has any of the following he will put it in the appropriate Lower Section box: Yahtzee, full house, large straight, small straight. With a 4-of-a-kind or 3-of-a-kind he will put it in the appropriate Upper Section box. The only exception is that when he has a 3-of-a-kind where the sum of the dice is 25 or more he should use the 3-of-a-kind box.

The 4-of-a-kind box is never used in the first round. In these situations there is no appealing option, the choice being between using an Upper Section box and using Chance. With two pairs follow the rule for the lower of the two pairs he has.

The rule depends on whether his pair or smaller pair is low 1, 2 or 3 or high 4, 5 or The best outcome in the first round is to throw a Yahtzee and put it in the Yahtzee box. This increases the final expected score from The second best outcome is to score 24 in the 6s box. Lorem ipsum dolor sit amet, consectetur adipisicing elit.

Eum maiores asperiores nihil vel dolorum esse, velit adipisci tempora omnis laudantium illum facilis ad hic, iste recusandae fugiat voluptatum dolore odit. The player who is the first to have no cards left wins the game. Deal 5 cards one at a time, face down, beginning with the player to the left. The balance of the pack is placed face down in the center of the table and forms the stock. Each card played other than an eight must match the card showing on the starter pile, either in suit or in denomination.

If unable to play, cards are drawn from the top of the stock until a play is possible, or until the stock is exhausted. If unable to play when the stock is exhausted, the player must pass. All eights are wild! That is, an eight may be played at any time in turn, and the player need only specify a suit for it but never a number. The next player must play either a card of the specified suit or an eight. Does 1 player have to keep picking up from the stock until he gets the right suit or just pick up 1 card and then the other persons turn?

Hello Lynne, Rules for the game Crazy Eights and others can be found on our website at; http: You are free to make the rules for those and assign which card does what. The Eights stay constant though. Played according to many different house rules, Presidents is a fun, social game often accompanied by many drinks. Four means war in the Quadruple War playing card game, a two player game where all cards are up for the taking.

Club Login Log in to Club Rewards using the email and password you provided when you signed up. Signup Lorem ipsum dolor sit amet, consectetur adipisicing elit. The classic game where eights are wild. The Pack The standard card pack is used. Object of the Game The goal is to be the first player to get rid of all the cards in his hand.