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