round is to throw a Yahtzee and put it in the Yahtzee box. This increases the final expected score from 254.59 to 320.84. Putting a Yahtzee of 6s in the 6s box results in an expected score of just 279.48. The second best outcome is to score 24 in the 6s box. This provides an expected score of 268.23. Putting 56666 in the 4-of-a-kind box has an expected score of 264.54. The worst first roll is 11236 which has an expected score of 249.83. After the second roll the worst position is 12356 which then has an expected score of 244.91. The worst third roll is 23446 which has an expected score of 238.96 when put in the Chance box. Extreme scores Maximum score The highest possible score is 1,575 and involves throwing 13 Yahtzees, scoring 12 Yahtzee bonuses of 100 points each, as well as 375 in the other categories. The 375 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 (30). The score of 1,575 requires using the "Joker" rules for the full house, small straight, and large straight categories. In order to score 1,575 the player must throw 13 successive Yahtzees. The probability of getting a Yahtzee is 4.60% and so the probability of a player rolling 13 Yahtzees in a row is 4.60% raised to the 13th power or . The probability of scoring 1,575 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. In about 18% of Yahtzees the player has some choice over the dice to keep. 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 1,575 is considerably less. Using the strategy that maximizes the average score, the probability of scoring 1,575 is . The highest