possible score without a Yahtzee bonus is 351, 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 301. (In some sources, the technical high score when not taking a Yahtzee bonus is still the base 375 maximum, as described above. In that case, you would score your 50 point Yahtzee score as your last roll having scored all of your other 5-of-a-kind in various Upper and Lower boxes along the way. This is theoretical, however, as it's unlikely that anyone would score five sixes in the Chance box when the Yahtzee score was still open, e.g.) Other high scores 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. A player must throw at least 8 Yahtzees in order to score 1000. Throwing 8 Yahtzees will score 750 for the Yahtzee and Yahtzee bonuses. The 7 Yahtzees after the first throw will generally score highly, including the opportunity of using the Joker rule to score in, for instance, the Large Straight category. This means that a player throwing 8 Yahtzees will often be able to score 1,000. In normal gameplay the probability of scoring this number of Yahtzees is considerably less. The following table shows the probability of getting certain scores using the "Optimal" strategy. Minimum score The lowest possible score is 5. The Chance box always scores the sum of the dice, so that a minimum of 5 must be scored in that category. The strategy that works to maximize the average expected score will under worst case conditions score a minimum of 12 points, but cautious play will guarantee a minimum score of 18. A score of 18 will be achieved if 11223 is thrown each round and then, whatever is re-thrown, getting 11223 again after the second and third throws, scoring 2 in the 1s box, 4 in the 2s box, 3 in the 3s box and 9 for the Chance category. Scoring the minimum of 12, when attempting to maximise the average score, is less likely than scoring the maximum of 1,575 but is theoretically possible. Suppose that