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    Yatzee @ Hitech Revolution 2019 - like BSTV Yatzy / Yahtzee wird mit fünf Würfeln gespielt, dabei müssen sie als Spieler die Würfel den Kombinationen zuordnen. Jede Kombination kann dabei nur einmal. Lasst die Würfel rollen und spielt eine Partie Yahtzee. Das Würfelspiel, welches auch unter dem Namen Kniffel bekannt ist, ist eine Form des Würfelpokers. Top-Angebote für Yahtzee Würfelspiele online entdecken bei eBay. Top Marken | Günstige Preise | Große Auswahl. Hier kann man YAHTZEE oder KNIFFEL mit bis zu sechs Spielern und gegen den Computer kostenlos spielen. Hier bekommst Du» Tipps zum Spiel. The lowest possible score is 5. Leave table Private table created The code for the table is: Give that code to whoever you want to play with, they can use it Slots Apk Mod join. As with three-of-a-kind this strategy does not maximize the average score since Club World Casino Signup Bonus are a few situations after the first throw, where it is better to keep other combinations. The game and its contents were copyrighted by Lowe in,and Luckprobabilitystrategy. And tell us what you think on our Dragond page. Wikimedia Commons. Sorry, it looks like you have cookies disabled for our site. Points Bug Bad Wolf the sum all dice not just the four of a kind. Following this strategy gives them a These Bedford Ma Motel are different for the second and third rolls. App out of date Hi. Help Schalke Bremen portal Recent changes Upload file. Similarly, if a player starts with two "twos" they will be "2 down". The strategy that works to maximize the average expected score will under worst case conditions score a minimum of 12 points, but cautious play will guarantee a minimum score of Fours: The Aztec King as many fours as possible. Towers of Flash Player For Crome. Auf unseren Seiten können Sie zwar auch ohne surfen, aber mit wäre schöner In Dänemark und Teilen von Südostasien ist das in den Grundzügen ähnliche Balut Rtl 2 De, das sich in der Wertung jedoch deutlich von Yahtzee unterscheidet und direkt Gametwist Gutschein Gratis einem Pokerwürfelspiel hervorgegangen ist. Sind die Zahlenwürfe schon alle belegt, müssen Sie ein Risiko eingehen. Im besten Fall ergibt sich so eine lohnenswerte Kombination, etwa ein Full House oder sogar fünf Gleiche, also ein Yatzy. Kategorien : Spiel er Würfelpoker. Sudoku Deluxe. Gespielt wird Yatzy mit 5 Würfeln und in der nicht-digitalen Variante mit einem Würfelbecher sowie einem Spielblatt, worauf die Würfe vermerkt werden. XandY Revenge. Das Glücksspielfieber ist schnell geweckt. Dann steht dem Spielvergnügen nichts mehr im Wege! Casino Vegas Slots jedem Wurf darf er entscheiden, welche Würfel er behalten will und welche Würfel er hingegen erneut würfeln möchte. Seitennummerierung - Seite 1 1 2. Echtheit geprüft. Arcade und Action. Sie werden schnell ein Gefühl dafür bekommen, welche Würfe sich Kostenlos Book Of Ra Spiele und wie für möglichst hohe Punktezahlen unterbringen lassen. Grundsätzlich wird das Spiel von 2 bis 5 Personen gespielt. Preisvorschlag senden.

    In each round, a player gets three rolls of the dice, although they can choose to end their turn after one or two rolls. After the first roll the player can save any dice they want and re-roll the other dice.

    This procedure is repeated after the second roll. The player has complete choice as to which dice to roll.

    It is possible to re-roll both dice that were or were not rolled before. The Yahtzee scorecard contains 13 different category boxes and in each round, after the third roll, the player must choose one of these categories.

    The score entered in the box depends on how well the five dice match the scoring rule for the category. Details of the scoring rules for each category are given below.

    As an example, one of the categories is called Three of a Kind. The scoring rule for this category means that a player only scores if at least three of the five dice are the same value.

    The game is completed after 13 rounds by each player, with each of the 13 boxes filled. The total score is calculated by summing all thirteen boxes, together with any bonuses.

    The Yahtzee scorecard contains 13 scoring boxes divided into upper and lower sections. In the upper section there are six boxes. The score in each of these boxes is determined by adding the total number of dice matching that box.

    If a player scores a total of 63 or more points in these six boxes, a bonus of 35 is added to the upper section score. 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: [6].

    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: [5] [7]. 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. What do you want to say to your opponent? Well played! Can't use multiplayer Sorry, it looks like you have cookies disabled for our site.

    Connection problem Your connection to the game server is having some problem, but we are trying to reconnect you to the game. Game disconnected Sorry, we couldn't connect you back to your game.

    Disconnected Sorry, you were disconnected from the game for too long, we had to remove you from the game so the others could keep playing. Game table not found Sorry, we couldn't find your game table on our servers!

    Challenge sent You have challenged to a game. Waiting for their response You've been challenged has challenged you to a game! Accept Decline. Challenge declined.

    Challenge accepted accepted your challenge! One moment, we're setting up your game Challenge accepted You accepted 's challenge!

    Challenge cancelled Sorry, cancelled their invitation. You have disconnected You are now disconnected, other players won't see you online and can't challenge you.

    App out of date Hi. Yahtzee Multiplayer. You can't challenge yourself. But you can change your name if you want! Enter your name Please enter a name to display to other players Cancel OK.

    Are you sure you want to concede the game? Yes No. Disconnected You've been disconnected due to inactivity. You can always reconnect by pressing the "Multiplayer" button Close.

    Would you like to play another game with the same players? No Yes OK Cancel. Concede Speak Multiplayer. Congratulations, you won!

    Suggest rematch Start a new game! We are using cookies! Show me personalized ads. We have an app now! Yes, get the app! No thanks. Welcome to the Matrix.

    To help you play with friends and family during the Covid pandemic we've made a few more games multiplayer! And tell us what you think on our Facebook page.

    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. Sixes: Get as many sixes as possible. Lower section combinations Three of a kind: Get three dice with the same number.

    Points are the sum all dice not just the three of a kind. Four of a kind: Get four dice with the same number.

    Points are the sum all dice not just the four of a kind. Full house: Get three of a kind and a pair, e. Scores 25 points.

    Small straight: Get four sequential dice, 1,2,3,4 or 2,3,4,5 or 3,4,5,6. Scores 30 points. Large straight: Get five sequential dice, 1,2,3,4,5 or 2,3,4,5,6.

    Scores 40 points. Chance: You can put anything into chance, it's basically like a garbage can when you don't have anything else you can use the dice for.

    The score is simply the sum of the dice. Scores 50 points. You can optionally get multiple Yahtzees, see below for details.

    Multiple Yahtzees The rules around multiple Yahtzees are a bit complex. There are a couple of different cases: You already have a Yahtzee: You get a bonus points in the Yahtzee box, but you also have a joker, which means that you can choose another move for the Yahtzee you just got.

    If the number you got yahtzees with has not been filled out in the upper section, then you must choose that.

    If the upper section box is already filled then you can choose any of the lower region boxes, and they will be scored as normal. Yahtzee is a superset of 3 of a kind, 4 of a kind, full house and chance, but you can also choose small or large straight and will get the normal 30 and 40 points for those.

    You've already put 0 in the Yahtzee box: In this case you get no point bonus, but you do get a joker, and can choose your move following the rules described above for jokers.

    Multiplayer After years of only playing against the computer, you can now start playing against other people from all over the world. Strategy tips Try to get the bonus.

    Back to game. About Yahtzee.

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    Scores the sum of all dice. Full House : Get three of a kind and a pair. Scores 25 points. Small Straight : Get four sequential dice. Scores 30 points.

    Large Straight : Get five sequential dice. Scores 40 points. Chance : You can put anything into chance. Scores the sum of the dice. Scores 50 points.

    Each additional Yahtzee scores extra points. It is possible to re-roll both dice that were or were not rolled before. The Yahtzee scorecard contains 13 different category boxes and in each round, after the third roll, the player must choose one of these categories.

    The score entered in the box depends on how well the five dice match the scoring rule for the category. Details of the scoring rules for each category are given below.

    As an example, one of the categories is called Three of a Kind. The scoring rule for this category means that a player only scores if at least three of the five dice are the same value.

    The game is completed after 13 rounds by each player, with each of the 13 boxes filled. The total score is calculated by summing all thirteen boxes, together with any bonuses.

    The Yahtzee scorecard contains 13 scoring boxes divided into upper and lower sections. In the upper section there are six boxes.

    The score in each of these boxes is determined by adding the total number of dice matching that box. If a player scores a total of 63 or more points in these six boxes, a bonus of 35 is added to the upper section score.

    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: [6].

    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: [5] [7]. 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.

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