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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, 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.
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Report inappropriate content. Thanks for helping keep SourceForge clean. X You seem to have CSS turned off. The aim of the game is to get as many points as possible by smart dicing.
Each player has to dice once per turn. Each turn contains up to three throws of the dice. The first throw takes place with all five dice.
Then each player can put aside the dice he wants to keep. Bottom rows score if your throw belongs to one of these special cases: Three of a Kind 3 dice of the same kind sum of all the dice Four of a Kind 4 dice of the same kind sum of all the dice FullHouse 2 dice of one kind, 3 of another 25 points Small Straight 4 consecutive numbers 30 points Large Straight 5 consecutive numbers 40 points Kniffel 5 dice of the same kind 50 points Chance any combination sum of all the dice In the top section first six rows you get a bonus 35 points in any of the four columns if your subtotal for that column is greater than or equal to When selecting scores you have to proceed scoring in the first column from top to bottom.
Second column is filled from bottom to top and forth can be filled in any order. Third column can be filled in any order but it will score only after the first throw.
If you can't select any score which will give you points you have to mark zero to that scoring row of the first or second column which is next in turn or to any row of the third or fourth column.
Scores List of ten best scoring games is saved on the game server. You can browse this list selecting Scores. When your result is to be added to the list computer asks your name.
Neu e Spiele. Kniffel Rating: 3. Bubble Shooter. Mensch Ärgere Dich Nicht. Schlangen und Leitern. Bricks Breaking. Klassisches Mahjong.