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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.
To determine who goes first, each player places all five dice in the dice cup and rolls out all the dice; the player with the highest total starts the game.
The play then continues clockwise. If you get the exact combo you want, mark your score card right away. Otherwise, continue with your 2nd roll. If you get the exact combo you need, mark your score card.
Otherwise, continue with your 3rd roll. If your roll doesn't suit any of your empty boxes, you have to enter a zero somewhere.
BUT scoring even a single die value is better than a zero. There are 13 scoring boxes. This is the greatest scoring for any category.
At the end of all the rounds, the winner of the activity is the gamer who scores the most points.
If you roll a second Yahtzee in a game, and you scored your first yahtzee in the Yahtzee box, you would score a further bonus points in the yahtzee box.
You must also put this roll into another category, as follows; -If the corresponding Upper section category is not filled then you must score there.
In 3 of a Kind, 4 of a Kind, and Chance categories you would score the total of the die faces. Chance You can roll anything and be able to put it in the Chance category.
You score the total of the die faces. Scratch or Dump scores. You can score any roll in any category at any time, even if the resulting score is zero.
Eg, you can take in the 5's category. A low straight is any sequence that runs through four numbers and is worth 30 points.
If you do not have a sequence that includes four consecutive numbers, then score 0. A high straight is any sequence that runs through five numbers and is worth 40 points.
If you do not have a sequence that includes five consecutive numbers, then score 0. A yahtzee is where all five dice are the same and is worth 50 points!
If you do not have five numbers the same, then score 0. If you have already scored 50 points in your yahtzee box, and then you roll another yahtzee and manage to score more than 0 with it, in another box, then you receive a bonus of points automatically.
That includes using the yahtzee joker see below. On your turn you must fill in a box, even if you score yourself zero. The score card is separated into 2 sections: Upper Section and Lower Section.
The objective of the Upper Section is to score, by any combination, 63 points in order to earn a 35 point bonus.
Score only in this section if you roll 3 or more of the same number dice. Alternative Scoring: You can score each number individually in the upper section or score the total in the chance section.
Score only in this section if you roll 4 or more of the same number dice. Alternative Scoring: You can also score the total in the 3 of a kind box or the chance box.
You may also divide the numbers up and score them in the upper section individually. One scores a Full House when three of one number and two dice of another.