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Although 63 points corresponds to scoring exactly three-of-a-kind for each of the six boxes, a common way to get the bonus is by scoring four-of-a-kind for some numbers so that fewer of other numbers are needed.
A player can earn the bonus even if they score a "0" in an upper section box. In order to gauge how well a player is doing in the upper section, they often refer to being "up" or "down" compared to the average of three required for each box.
So that if a player scores four "sixes" they will be "6 up"; while if they then score just two "twos" they will then be only "4 up".
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 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 simpler, alternative version of the Joker rule 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.
The probability of completing a Yahtzee 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. On average 2. 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: keep 33, 44, 55, 66 rather than or , , keep 4, 5 or 6 rather than 11, keep 5 or 6 rather than 22, keep rather than 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 they are trying to maximize their average score.
Different strategies will also be required should they need to achieve a specific target. The strategy to maximize their chance of getting a four-of-a-kind involves keeping any four-of-a-kind that they have.
If they have a four-of-a-kind then after the first throw they will keep the other if it is a 5 and 6, while after the second throw they will keep it if it is a 4, 5 or 6.
So that with they keeps and will throw the 3. If they do not have a four-of-a-kind, the player should keep any three-of-a-kind or pair that they have and re-roll the other dice.
With two pairs they will keep the higher pair. With no pair they will keep the highest die. Following this strategy gives them 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.
The situations where the strategy to maximize the average score differs are all after the first throw and are as follows: keep 44, 55, 66 rather than , keep 4, 5 or 6 rather than 11, keep 6 rather than 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. 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 3. 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.
Source:  . 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 6 :.
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.
This has a value of The worst first roll is which has a value of The worst third roll is which has a value of The highest possible score is 1, and involves throwing 13 Yahtzees, scoring 12 Yahtzee bonuses of points each, as well as in the other categories.
The is achieved by scoring five aces 5 , five twos 10 , five threes 15 , five fours 20 , five fives 25 , five sixes 30 , the Upper Section bonus 35 , five sixes scored as Three-of-a-kind 30 , five sixes scored as a four-of-a-kind 30 , a full house 25 , a small straight 30 , a large straight 40 , a Yahtzee 50 , and five sixes scored as chance You can always put in 0 for a combination if you don't have it, even if you have some other combination.
Anyway, I hope you enjoy the game. If you have any questions or comments, send them to admin cardgames. My name is Einar Egilsson and over there on the left is my current Facebook profile picture!
In the last couple of years I've made a number of simple online card games, including Hearts and Spades. It's been a fun game to make, and I'm looking forward to seeing how well Bill will play against human opponents :.
Since I have no artistic talent whatsoever I used graphics that I found at OpenClipArt , a great site with free graphics.
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Happy Star Wars Day! May the 4th be with you! Gameplay In each turn a player may throw the dice up to three times.
Upper section combinations Ones: Get as many ones as possible. Twos: Get as many twos as possible. Threes: Get as many threes as possible.
Fours: Get as many fours as possible. Fives: Get as many fives as possible.There are 13 different scores and the game is finished when all are marked. Hauptseite Themenportale Zufälliger Artikel. Virtzee, the popular dice game Yahtzee in an online format Link. A stupid scratcher. For example if you throw throw 4 4 4 Zylom Gratis Spiele 6 you score Pocas Stars Online Gaming points if you select it as fours. Dann Beste Online Depots es jetzt herunter und finde es heraus! If you select TrainerGame the computer will get same dice as you. Beispiele hierfür:. The computer uses always the best strategy.