Covariances between final scores in Yahtzee and UPPER SECTION BONUS = -11.24715 Three of a Kind and Yahtzee = -9.74259 Full House and Yahtzee = -8.07589 Three of a Kind and EXTRA YAHTZEE BONUS = -6.87950 Large Straight and Yahtzee = -5.08085 Four of a Kind and Yahtzee = -4.99448 Yahtzee and Chance = -3.76990 Small Straight and Yahtzee = -2.90217 Three of a Kind and UPPER SECTION BONUS = -1.73158 Chance and EXTRA YAHTZEE BONUS = -1.47196 Small Straight and UPPER SECTION BONUS = -1.09422 Threes and Yahtzee = -0.96138 Small Straight and EXTRA YAHTZEE BONUS = -0.94340 Small Straight and Large Straight = -0.94335 Twos and Yahtzee = -0.83625 Fours and Three of a Kind = -0.45592 Fours and Yahtzee = -0.45364 Threes and Three of a Kind = -0.43306 Twos and Three of a Kind = -0.28673 Aces and Yahtzee = -0.21110 Full House and EXTRA YAHTZEE BONUS = -0.20265 Fives and Yahtzee = -0.17103 Fives and Small Straight = -0.14057 Fours and Small Straight = -0.13453 Threes and Small Straight = -0.13095 Four of a Kind and Small Straight = -0.11793 Fives and Three of a Kind = -0.11677 Large Straight and UPPER SECTION BONUS = -0.11454 Twos and Four of a Kind = -0.11169 Twos and Fours = -0.10840 Twos and Small Straight = -0.09143 Aces and Three of a Kind = -0.08148 Sixes and Small Straight = -0.07926 Twos and Threes = -0.07152 Twos and Fives = -0.06821 Threes and Fives = -0.06412 Aces and Twos = -0.05928 Aces and Threes = -0.05514 Twos and Sixes = -0.05232 Aces and Chance = -0.05107 Threes and Fours = -0.04670 Aces and Fours = -0.04599 Threes and Sixes = -0.03936 Aces and Fives = -0.03218 Aces and Small Straight = -0.00285 Twos and Chance = -0.00116 Aces and Sixes = 0.01345 Aces and Full House = 0.02983 Full House and UPPER SECTION BONUS = 0.03193 Fours and Full House = 0.04984 Fours and Fives = 0.05445 Aces and Four of a Kind = 0.07012 Threes and Chance = 0.07465 Sixes and Yahtzee = 0.07575 Fives and Full House = 0.07892 Three of a Kind and Small Straight = 0.08472 Threes and Full House = 0.08959 Small Straight and Chance = 0.10940 Twos and Full House = 0.11754 Fours and Sixes = 0.18966 Full House and Small Straight = 0.19248 Threes and Four of a Kind = 0.19278 Fours and Chance = 0.21157 Sixes and Full House = 0.26508 Fives and Chance = 0.39681 Fives and Sixes = 0.40116 Fives and Large Straight = 0.47324 Twos and Large Straight = 0.50105 Fours and Large Straight = 0.50108 Four of a Kind and Full House = 0.50815 Aces and Large Straight = 0.55146 Threes and Large Straight = 0.56694 Three of a Kind and Large Straight = 0.59936 Sixes and Three of a Kind = 0.74999 Three of a Kind and Chance = 0.77368 Sixes and Chance = 0.77659 Fours and Four of a Kind = 0.81121 Full House and Chance = 0.84267 Sixes and Large Straight = 0.91144 Three of a Kind and Four of a Kind = 1.12851 Aces and EXTRA YAHTZEE BONUS = 1.31807 Three of a Kind and Full House = 1.36870 Aces and Aces = 1.47855 Fives and Four of a Kind = 1.88959 Four of a Kind and Chance = 1.89018 Aces and UPPER SECTION BONUS = 1.94219 Twos and EXTRA YAHTZEE BONUS = 2.28581 Large Straight and Chance = 2.58023 Chance and UPPER SECTION BONUS = 2.88226 Sixes and Four of a Kind = 3.55547 Threes and EXTRA YAHTZEE BONUS = 3.79352 Twos and Twos = 3.99162 Full House and Large Straight = 4.80684 Aces and GRAND TOTAL = 4.86457 Fours and EXTRA YAHTZEE BONUS = 5.56535 Twos and UPPER SECTION BONUS = 5.76126 Chance and Chance = 6.44774 Fives and EXTRA YAHTZEE BONUS = 7.28180 Threes and Threes = 7.36414 Four of a Kind and Large Straight = 9.52272 Small Straight and GRAND TOTAL = 9.67932 Sixes and EXTRA YAHTZEE BONUS = 10.10467 Fours and Fours = 10.80394 Twos and GRAND TOTAL = 10.97029 Chance and GRAND TOTAL = 11.69169 Threes and UPPER SECTION BONUS = 11.89186 Four of a Kind and UPPER SECTION BONUS = 12.46222 Fives and Fives = 14.83002 Four of a Kind and EXTRA YAHTZEE BONUS = 15.83324 Small Straight and Small Straight = 15.87338 Three of a Kind and GRAND TOTAL = 16.53267 Fours and UPPER SECTION BONUS = 18.76324 Sixes and Sixes = 21.55850 Threes and GRAND TOTAL = 22.17127 Fives and UPPER SECTION BONUS = 25.80139 Three of a Kind and Three of a Kind = 31.55534 UPPER SECTION BONUS and EXTRA YAHTZEE BONUS = 32.86433 Large Straight and EXTRA YAHTZEE BONUS = 32.96756 Fours and GRAND TOTAL = 35.70516 Sixes and UPPER SECTION BONUS = 36.77113 Fives and GRAND TOTAL = 50.61451 Full House and Full House = 54.40556 Full House and GRAND TOTAL = 54.50859 Sixes and GRAND TOTAL = 75.20197 Four of a Kind and Four of a Kind = 122.62884 Four of a Kind and GRAND TOTAL = 165.26893 Large Straight and Large Straight = 238.42226 UPPER SECTION BONUS and UPPER SECTION BONUS = 266.03750 Large Straight and GRAND TOTAL = 286.26546 Yahtzee and EXTRA YAHTZEE BONUS = 317.40543 UPPER SECTION BONUS and GRAND TOTAL = 401.02183 Yahtzee and Yahtzee = 558.87507 Yahtzee and GRAND TOTAL = 827.90984 EXTRA YAHTZEE BONUS and EXTRA YAHTZEE BONUS = 1161.19494 EXTRA YAHTZEE BONUS and GRAND TOTAL = 1581.11720 GRAND TOTAL and GRAND TOTAL = 3553.52329