# Poker Strategy

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## SECRETS OF THE WORLD CHAMPIONS

They can re-roll a die for the third roll that was not rolled on the second roll. 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 between two 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 a player throws a Yahtzee but the Yahtzee category has already been used, special rules apply. 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 official rules [4] the player must act in the following way.

In the simpler, alternative version of the Joker rule [5] [6] 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. A detailed discussion of the optimal strategy is beyond the scope of this article but certain aspects can be considered here. It is important to understand the probability of completing a Yahtzee.

This 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. 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: 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 he is trying to maximize his average score.

Different strategies will also be required should he need to achieve a specific target. The strategy to maximize his chance of getting a four-of-a-kind involves keeping any four-of-a-kind that he has. If he has a four-of-a-kind then after the first throw he will keep the other if it is a 5 and 6, while after the second throw he will keep it if it is a 4, 5 or 6. So that with he keeps and will throw the 3. If he does not have a four-of-a-kind, the player should keep any three-of-a-kind or pair that he has and re-roll the other dice.

With two pairs he will keep the higher pair. With no pair he will keep the highest die. Following this strategy gives him 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. 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.

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