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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: .
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 Yahtzee drinking game is one of the most famous dice games.
While playing Yahtzee you need luck as well as a good strategy to win against the other players. The best thing about Yahtzee is that this game is playable in larger and small groups, and family-friendly as well.
The game with the five dice goes back to Canada in the s. After playing the game with all their friends, somehow a game entrepreneur got to know the game.
According to his experience in the game industry, he saw the potential in this dice game. With these parties, the popularity grew, and the game gained world-wide popularity.
Today around 50 million Yahtzee games were sold each and every year. Other players: If you want to play the Yahtzee drinking game, you need other players.
You can play the game either in a small or a large group, but at least you need one other person. Tip: If you skip the alcohol part, this game is family-friendly as well.
In total, you need 5 dice. Of course, you can play it with less, remember the results, and count them together.
Alcohol: If you want to play the Yahtzee game as a drinking game, you need alcohol of course. Now we will explain how to play the Yahtzee game.
Besides the 5 dice, the most important thing while playing Yahtzee is the Yahtzee Scorecard. On the Yahtzee Scorecard are 13 empty boxes where your scores belong.
On each turn, you roll the dice, and then decide which box is the best for your scores. But always take in mind that each box can just be filled once!
Similarly dice in the hold area can be moved back for rolling by clicking it once. The scoreboard displays all possible combinations you can choose in a particular turn in yellow background.
Click on a combination to play it for that turn. Tutorial Game Play. Chance : You can put anything into chance. Scores the sum of the dice.
Scores 50 points. Each additional Yahtzee scores extra points.