## Kniffel Yahtzee Kniffel Spielanleitung: Das sind die Regeln

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### Kniffel Yahtzee - Inhaltsverzeichnis

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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 or 6, while after the second throw they will keep the die if it is a 4, 5 or 6.

So that with they keep 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 keep the higher pair. With no pair keep the highest die. Following this strategy provides 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 one 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. Keep any four-of-a-kind, three-of-a-kind, or pairs that are thrown and re-roll the others.

With two pairs keep both. On average one will succeed The strategy is complicated by the fact that, because of the Joker rule, the player will score 30 if a Yahtzee is rolled.

Clearly one keeps any Small Straight or Yahtzee that is thrown. After the first throw keep a run of 3 or 3 out of 4 e.

Otherwise, keep a 3 or 4 or both and a 2 or 5 if one also has a 3 or 4 e. Do not keep just 2, 5, or The only difference after the second throw is that one 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, one will score 40 if one gets a Yahtzee.

Clearly one will keep any Large Straight or Yahtzee that is thrown. 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 one should simply keep any 2, 3, 4 or 5 just one of each , so that with one 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 one 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 one will keep any 4s, 5s, and 6s. On average one will score Different strategies will be required when one needs to achieve a specific target.

The strategy for maximising the expected score has been determined. The "Optimal" strategy simply maximises the average score, not 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 player's 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, 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 one will never keep two pairs, one will never keep a pair of 1s and one will never throw all the dice again.

So there are specific differences compared to the second roll. Now one 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.

Keep all large and small straights. One will normally keep a pair of 1s although is still better and keep rather than 5 when all the dice are different.

If one has any of the following 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 put it in the appropriate Upper Section box.

The only exception is that when one has a 3-of-a-kind where the sum of the dice is 25 or more one 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. The rule depends on whether the 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 provides an expected score of The worst first roll is which has an expected score of The worst third roll is which has an expected score 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. Using the strategy that maximizes the average score, the probability of scoring 1, is 1.

The highest possible score without a Yahtzee bonus is , which is achieved with scoring a five-of-a-kind as a Yahtzee, 84 in the Upper Section four-of-a-kind in each category , and 29 in each of 3 of a kind, 4 of a kind, and Chance.

The highest possible score without rolling a five-of-a-kind is 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, In normal gameplay the probability of scoring this number of Yahtzees is considerably less.

The following table shows the probability of getting certain scores using the "Optimal" strategy. The lowest possible score is 5.

The Chance box always scores the sum of the dice, so that a minimum of 5 must be scored in that category. 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 A score of 18 will be achieved if is thrown each round and then, whatever is re-thrown, getting again after the second and third throws, scoring 2 in the 1s box, 4 in the 2s box, 3 in the 3s box and 9 for the Chance category.

Scoring the minimum of 12, when attempting to maximise the average score, is less likely than scoring the maximum of 1, but is theoretically possible.

Suppose that in the first two rounds after each roll. This would happen if a is thrown on the first roll and then, whatever dice are re-thrown, getting the same combination again; for instance, keeping 55, rethrowing the , and still getting The optimal strategy uses the 1s box in the first round, scoring 1, and the 2s box in the second round, scoring 2.

Now suppose that for the next 3 rounds results after each roll. Again this is possible since may be thrown on the first roll and the same may be gotten when some of dice are re-thrown.

The optimal strategy uses the four-of-a-kind and Yahtzees boxes in the third and fourth rounds and then the 3s box in the fifth round, scoring 0 each time.

For the last 8 rounds suppose is rolled each time. Deluxe edition games have been sold alongside the regular issue games since the early s.

They all contain components that are more luxurious than standard game parts. In recent years, a number of collector issue Yahtzees have been sold as well.

Some of these collector issues have dice that replace the pips with certain symbols connected to a theme, but still correspond to the numbers one to six.

Since the s, Travel Yahtzee has been sold in various forms as part of Milton Bradley's line of travel games. Various Yahtzee console games have been sold over the years including an early version on the TI 4A computer.

In , the game was first released to PC and Mac users by Atari. Later, GameHouse also released an authorized special version of the game for Windows users.

There are also several electronic versions of the game such as a handheld LCD version, and a cell phone version called Yahtzee Deluxe , which feature the original rules along with Duplicate and Rainbow modes, as well as independently produced versions for the Palm OS and Pocket PC and several cellphone models.

It was sold in a three pack that included Life , Payday , and Yahtzee. The game has also been released for the iPod , iPod touch and the iPhone , to be purchased through the iTunes Store , [12] [13] as well as Google Play.

A number of related games under the Yahtzee brand have been produced. They all commonly use dice as the primary tool for gameplay, but all differ generally.

The first was Triple Yahtzee, developed in There are a large number of versions of Yahtzee which can be played online or are available to download.

There are a large number of related games. Yatzy is one of the most popular. You can browse this list selecting Scores.

You can select an individual game from the window to see the exact points in each combination. Network Scores Best results are saved on the game server.

You can browse the list selecting Network Scores You can select an individual game from the window to see the exact results in each combination If a result from your computers Score list is better than it will be also sent to server.

You can wait until someone invites you into a game or you can send an invitation to a player selected from the list "Select Opponent".

Preferences In preferences you can set the user name you want to use in Network Game. If you select "Receive invitations from other players" you may receive invitations to network Game.

You can play Yahtzee Club alone, with another player online or against the computer AI. No Flash, no Java needed or no install needed.

No registration necessary. You can play it in any Browser your PC or mobile. If you play with the computer robot artificial intelligence, it uses the best strategy, so to win you need some skill and luck.

You can also ask for advice from the computer, so it can teach you how to win. High Score list is maintained on a Game Server.

More information related to Yahtzee can be found Wikipedia. Server application of the game is Java application running in the Google App Engine.

Please wait Rules The aim of the game is to collect maximum amount of points by throwing five dice. You can ask for advice or hints from the computer AI, so the robot can teach you how to win Scoring You can score in any of the scoring buttons that are not already selected.

You can select an individual game from the window to see the exact points in each combination Network Scores Best results are saved on the game server.

You can browse the list selecting Network Scores You can select an individual game from the window to see the exact results in each combination If a result from your computers Score list is better than it will be also sent to server Multiplayer NetworkGame If you want to play in network Login first, then choose "Network".

You can wait until someone invites you into a game or you can send an invitation to a player selected from the list "Select Opponent" Preferences In preferences you can set the user name you want to use in Network Game.

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