is used as a Joker and scored on Full House, Small Straight or Large Straight. In most of these cases the Yahtzee box has a score of 50 and so the Yahtzee also counts as a Yahtzee bonus. 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 254.59 the Median score is 248. The Mode is 266, which occurs 1.26% of the time. The 1st Percentile is 151 (i.e. 1% of scores are 151 or less) while the 99th Percentile is 473 (i.e. 99% of scores are 473 or less). First round 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.e., the one that follows the general rules. Although there are 7,776 different ways of throwing 5 dice, the order of the dice is not important due to the fact that roll order is irrelevant and that there are only 252 different combinations when you take order out of the equation. To use the strategy described therefore requires knowing 756 different situations. Second and third roll choices 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. Exceptions before the second roll: with a full house containing three 1s, keep all the dice and put in the Full House box. with 12344, keep the pair not the small straight. with a 3456 and a pair, keep the pair not the small straight. with a pair of 1s, keep, in order of preference, 345, 5, 4 or 6, not the pair of 1s. So, before the second roll one will never keep two pairs, one will never keep a pair of 1s and one will