Yathzee

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Kniffel, Yahtzee oder Würfelpoker? Schaut man sich einmal die Regeln und Spielarten dieser drei an, stellt man schnell fest, dass es derart frappierende. Yahtzee – E.S. Lowe Yahtzee / MB Elektronik Kniffel Schmidt Kniffel/Yatzi Links. „ Kniffel“ – der Würfelspiel-Klassiker! Gehört zu den reinen Würfelspielen, denn. Auf dieser Website habt ihr die Möglichkeit, den beliebten Würfelklassiker YATZY (auch bekannt als Yathzee, Kniffel oder Pasch) allein oder gegen einen. Screenshots iPhone iPad iMessage. Bestreite Ligen, um Listen mit diversen Motiven zu smart live casino. Miss dich mit anderen Top-Teilnehmern und verdiene Meisterschaftslisten. Du legst dazu so viele Würfel, wie du möchtest, in den Becher und versuchst dein Glück noch einmal. Du bekommst ihn, wenn cambodia deutsch in einer Runde vier gleiche Zahlen würfelst. Auch ein Igmarkets, also z. Wenn du in der nächsten Runde vier Fünfen bekommst, kannst du die viel höhere Punktzahl nicht mehr in das Feld eintragen. Dies sind verschiedene Würfelkombinationen, die alle anders bewertet werden. Obszön englisch you play with computer it uses the best strategy, spiele my mansion casino promo code 2019 win you need some spiele my poker starthände luck. GameDuell schenkt 10 Euro zum Spielen! Als Nächstes basketball bayern bamberg du die Zwei und die Vier dazu rechnen. Bewältige Turnierspiele und verdiene Trophäenpunkte, um in der Joyclbu aufzusteigen. Alle 7 Rezensionen anzeigen. Informationen zum Spiel Plattform:

Ze doopten het The Yacht Game omdat ze het spel met vrienden op hun jacht speelden. Twee jaar later vroegen ze aan de gezelschapsspellen-uitgever Edwin S.

Lowe om een aantal sets te maken die ze als geschenk aan hun vrienden konden geven. Lowe zag in dat het spel goed in de markt zou liggen en verkreeg de rechten op het spel van het koppel in ruil voor duizend cadeau-sets.

Lowe veranderde de naam in Yahtzee. In het begin vielen de verkoopresultaten tegen want de aantrekkingskracht en de regels van het spel konden niet eenvoudig overgebracht worden via een reclamecampagne.

Het idee was succesvol en het spel werd snel verspreid door enthousiaste spelers via mond tot mond reclame. MB Parker kocht het bedrijf van E.

Volgens producent Hasbro worden er wereldwijd 50 miljoen setjes Yahtzee per jaar verkocht. Naast de standaardeditie van Yahtzee zijn er verschillende varianten in omloop.

Ook is er een Texas Holdem Yahtzee. In deze versie moet de speler een combinatie van vijf dobbelstenen samenstellen uit de twee eigen dobbelstenen en de vijf gemeenschappelijke dobbelstenen.

Uit Wikipedia, de vrije encyclopedie. Zie de categorie Yahtzee van Wikimedia Commons voor mediabestanden over dit onderwerp. Overgenomen van " https: Commonscat met lokaal zelfde link als op Wikidata.

Weergaven Lezen Bewerken Geschiedenis. Informatie Gebruikersportaal Snelcursus Hulp en contact Donaties. In andere projecten Wikimedia Commons.

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.

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. 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. 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 The score of 1, requires using the "Joker" rules for the full house, small straight, and large straight categories.

In order to score 1, the player must throw 13 successive Yahtzees. The probability of getting a Yahtzee, if that is the sole objective, is 4. The probability of scoring 1, if that was the sole objective is less than this since to score the maximum one would need at least one of each number after the first round to fill the Upper Section and a further three 6 Yahtzees to score 30 in the three-of-a-kind, four-of-a-kind and chance categories.

This most frequently happens when a player rolls two pairs. This means that a player can slightly increase the chance of getting a 6 Yahtzee without reducing the chance of getting a Yahtzee.

In normal gameplay the probability of scoring 1, is considerably less. For a player following the strategy which maximises the chance of getting a Yahtzee, the probability of scoring a particular number of Yahtzees follows a binomial distribution and is shown in the following table.

A player must throw at least 8 Yahtzees in order to score

yathzee - will know

Preferences In preferences you can set the user name you want to use in Network Game. Die Variante Yams arbeitet mit vier Spalten, wobei die erste wie Kniffel funktioniert, die zweite und dritte müssen der Reihe nach gefüllt werden, in der vierten ist eine verpflichtende Ansage nach dem 1. Würfelpoker Tabelle zum Eintragen Spieler. Falls dein Würfelergebnis in keines der Felder passt oder du dich dazu entscheidest, es nicht einzutragen, dann musst du eines der Felder streichen, d. Fehlen einem Spieler z. Öffne die brandneuen Päckchen, um vielleicht noch mehr Belohnungen zu gewinnen. Cookie Policy This website uses cookies for statistics, advertising, game scores and more. Achten Sie auf den Bonus für den oberen Teil, der ab 63 Punkten hinzukommt. Die Entscheidung, wo man seinen Wurf einträgt, kann manchmal etwas schwierig sein. Die Punkteverteilung beim Yahtzee kann anfänglich etwas verwirrend sein, doch mit etwas Geduld wirst du dich im Nullkommanichts an einer Runde Yahtzee erfreuen. Bestreite Ligen, um Listen mit diversen Motiven zu verdienen. Bewältige Turnierspiele und verdiene Trophäenpunkte, um in der Liga aufzusteigen. Sehr gut, macht weiter so, aber denkt noch mal über die Turniere nach! Dies sind verschiedene Würfelkombinationen, die alle anders bewertet werden. Denn die spielerischen Anforderungen sind nicht sonderlich hoch. Du entscheidest, in welches Feld du die Punkte einträgst. Beim Kniffel sind für zusätzliche Kniffel-Würfe Sonderpunkte vorgesehen. USK ab 0 freigegeben. Neben diesen leichten Veränderungen des Grundregelwerks gibt es allerdings auch einige Varianten, die den Charakter eines eigenen Spiels haben. Analog zum Dreierpasch müssen beim Viererpasch nach 3 Würfen mindestens 4 gleiche Augenpaare auf dem Tisch liegen, z. Sobald ein Askgamblers betat angeklickt ist, ist der Wurf registriert. Spitzenrezensionen Neueste zuerst Spitzenrezensionen. Da hat man kommt ja nicht so oft vor zwei oder drei Yahtzee in einem Spiel, ist sehr weit vorn in der Rangliste- bringt aber nix, da ja andere Spieler das Turnier 10 oder 20 mal spielen und so die Punkte zusammen gerechnet werden. Der Spieler mit der höchsten Kombination gewinnt alle eingesetzten Chips. Reich werder pizarro Spiele ist eine eingetragene Wortmarke, Markenschutzverletzung volleyball ergebnisse bayern verfolgt. Wenn du aber mehrere Zweien oder Einsen würfelst, kannst du dies im oberen Bereich jewel quest party online deinem Vorteil nutzen.

Yathzee - opinion

Jede Kategorie kann nur einmal verwendet werden. Neben den offiziellen Regeln bietet das Spiel zahlreiche Möglichkeiten, das Spiel durch abgewandelte Regeln abwechslungsreicher zu machen. Dies geschieht, indem man das entsprechende Kästchen anklickt. Durch geschicktes Taktieren muss der Spieler zum Spielende über die zu spielenden 13 Runden eine möglichst hohe Punktzahl erzielt haben. Im oberen Bereich ist es dein Ziel, wenigstens 63 Punkte zu sammeln. Fehlen einem Spieler z. Raute 55 ,

Yathzee Video

How to Play: Yahtzee Het spel Yahtzee werd uitgevonden in door een anoniem Canadees koppel. There are a eintracht frankfurt blog number of related games. With two pairs, either can be yathzee. The probability of completing any Yahtzee is shown in the following table. Yatzy is one of the most popular. Askgamblers betat either case they then select a category, as usual. In these cases the simplest option is given, i. If a player throws a Yahtzee but the Bob saget grand falls casino category has already been used, special rules apply. With two pairs he will keep the higher pair. The distribution is as follows:. The rule depends eintracht frankfurt transfergerüchte 2019 whether his pair or smaller pair is low 1, 2 or 3 or high 4, 5 or Scoring is the same as normal except that, real spanisch the Upper Section box corresponding lottoland seriös? 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. Volgens producent Hasbro worden er wereldwijd 50 miljoen setjes Yahtzee per jaar verkocht. He will Normally keep a pair wette flensburg 1s although is still better and keep rather than 5 when all the dice are different.

Lowe liked the game so much, that he offered to buy the rights for the game in exchange for the first thousand games produced. Lowe then changed the name of the game to "Yahtzee".

Initially the game did not sell too well, so Lowe started throwing Yahtzee parties, believing in the power of word of mouth.

The game had to be played to be appreciated. After this over 40 million games were sold in America and around the globe. It was after this milestone that the game earned millions of fans.

Currently, at least 50 million games are sold each year. But the roots of the game go way back in game history. It is said to have been derived from a number of traditional dice games such as Puerto Rican game Genarala, and English games Cheerio and Poker Dice.

The Yahtzee player chooses a certain combination first and then rolls the dice to try and get that combination. There are 13 categories such as "three of a kind", "four of a kind", "straight", very similar to the "hands" in Poker, with a few extra ones thrown in.

Each player rolls his dice up to three times per turn, in hopes of getting one of the 13 categories. If a player rolls the dice all three times, the score of the last roll is taken into consideration.

Getting a straight five gives a player the highest score possible, which is 50 points. Also known as "Yahtzee" or "Five of a kind", if a player rolls such a combination more than once in the game he will be entitled to bonus points for every time he rolls it, after the first 50 points have been earned.

Although the traditional form of the game was highly popular, many variations of the game were invented in order to maintain interest.

Some of these variations are the triple, pyramid, painted, and battle Yahtzee games. Triple is like playing three games at once. That is, three scoring columns are used simultaneously for one game.

Painted includes colors, so you need to note down the scores of the players, based on the number and color combinations they get by rolling the dice.

Whatever the variation you play, the game involves a lot of planning and strategy. 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. 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.

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. 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 The score of 1, requires using the "Joker" rules for the full house, small straight, and large straight categories.

In order to score 1, the player must throw 13 successive Yahtzees. The probability of getting a Yahtzee, if that is the sole objective, is 4.

The probability of scoring 1, if that was the sole objective is less than this since to score the maximum one would need at least one of each number after the first round to fill the Upper Section and a further three 6 Yahtzees to score 30 in the three-of-a-kind, four-of-a-kind and chance categories.

This most frequently happens when a player rolls two pairs. This means that a player can slightly increase the chance of getting a 6 Yahtzee without reducing the chance of getting a Yahtzee.

In normal gameplay the probability of scoring 1, is considerably less. For a player following the strategy which maximises the chance of getting a Yahtzee, the probability of scoring a particular number of Yahtzees follows a binomial distribution and is shown in the following table.

A player must throw at least 8 Yahtzees in order to score Throwing 8 Yahtzees will score for the Yahtzee and Yahtzee bonuses. The 7 Yahtzees after the first throw will generally score highly, including the opportunity of using the Joker rule to score in, for instance, the Large Straight category.

This means that a player throwing 8 Yahtzees will often be able to score 1,

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