1. from itertools import *
2.
3. faces = [1,2,3,4,5,6]
4.
5. def powerset(iterable):
6. """Standard recipe for computing a powerset (e.g. all options of dice to keep)"""
7. "powerset([1,2,3]) --> () (1,) (2,) (3,) (1,2) (1,3) (2,3) (1,2,3)"
8. s = list(iterable)
9. return chain.from_iterable(combinations(s, r) for r in range(len(s)+1))
10.
11. def score(dice):
12. """Calculate the score for a set of dice"""
13. total = 0
14. for i in [1,2,3]:
15. if dice.count(i) > 2:
16. total += (dice.count(i) + i - 3)
18.
19. def expectedScoreForChoice(rollsLeft, keepers, calculatedExpectedScores):
20. """Given that we keep a set of dice, and have a certain number of rolls left, what is our expected score?"""
21. numberToRoll = 6 - len(keepers)
22. sumOfScores = 0
23. for rolledDice in product(faces, repeat=numberToRoll):
24. dice = tuple(sorted(rolledDice+keepers))
25. sumOfScores += calculatedExpectedScores[rollsLeft-1][dice]
26. return 1.0*sumOfScores / (6**numberToRoll)
27.
28. def expectedScoreForBestChoice(rollsLeft, dice, calculatedExpectedScores):
29. """For a set of dice and certain numbers showing, what is our best move and expected score?"""
30. if rollsLeft == 0:
31. return dice, score(dice)
32. bestFoundScore = -1
33. bestKeepers = 'Unknown'
34. for keepers in powerset(dice):
35. expectedScore = expectedScoreForChoice(rollsLeft, keepers, calculatedExpectedScores)
36. if expectedScore > bestFoundScore:
37. bestKeepers = keepers
38. bestFoundScore = expectedScore
39. return bestKeepers, bestFoundScore
40.
41. # Store all calculations in this object, as we'll use the best move with n-1 rolls left to compute the best move with n rolls left.
42. calculatedExpectedScores = []
43. for rollsLeft in range(3):
44. calculatedExpectedScores.append({})
45. for dice in product(faces, repeat=6):
46. # We can ignore the ordering of our initial throw
47. if dice != tuple(sorted(dice)):
48. continue
49. bestKeepers, expectedScore = expectedScoreForBestChoice(rollsLeft, dice, calculatedExpectedScores)
50. calculatedExpectedScores[rollsLeft][dice] = expectedScore
51. print 'With %d rolls left and %s showing, we should keep %s (expected score %0.2f)'%(rollsLeft, dice, bestKeepers, calculatedExpectedScores[rollsLeft][dice])
52.
Time limit exceeded #stdin #stdout 5s 7908KB
stdin
Standard input is empty
stdout
With 0 rolls left and (1, 1, 1, 1, 1, 1) showing, we should keep (1, 1, 1, 1, 1, 1) (expected score 4.00)
With 0 rolls left and (1, 1, 1, 1, 1, 2) showing, we should keep (1, 1, 1, 1, 1, 2) (expected score 3.00)
With 0 rolls left and (1, 1, 1, 1, 1, 3) showing, we should keep (1, 1, 1, 1, 1, 3) (expected score 3.00)
With 0 rolls left and (1, 1, 1, 1, 1, 4) showing, we should keep (1, 1, 1, 1, 1, 4) (expected score 3.00)
With 0 rolls left and (1, 1, 1, 1, 1, 5) showing, we should keep (1, 1, 1, 1, 1, 5) (expected score 3.00)
With 0 rolls left and (1, 1, 1, 1, 1, 6) showing, we should keep (1, 1, 1, 1, 1, 6) (expected score 3.00)
With 0 rolls left and (1, 1, 1, 1, 2, 2) showing, we should keep (1, 1, 1, 1, 2, 2) (expected score 2.00)
With 0 rolls left and (1, 1, 1, 1, 2, 3) showing, we should keep (1, 1, 1, 1, 2, 3) (expected score 2.00)
With 0 rolls left and (1, 1, 1, 1, 2, 4) showing, we should keep (1, 1, 1, 1, 2, 4) (expected score 2.00)
With 0 rolls left and (1, 1, 1, 1, 2, 5) showing, we should keep (1, 1, 1, 1, 2, 5) (expected score 2.00)
With 0 rolls left and (1, 1, 1, 1, 2, 6) showing, we should keep (1, 1, 1, 1, 2, 6) (expected score 2.00)
With 0 rolls left and (1, 1, 1, 1, 3, 3) showing, we should keep (1, 1, 1, 1, 3, 3) (expected score 2.00)
With 0 rolls left and (1, 1, 1, 1, 3, 4) showing, we should keep (1, 1, 1, 1, 3, 4) (expected score 2.00)
With 0 rolls left and (1, 1, 1, 1, 3, 5) showing, we should keep (1, 1, 1, 1, 3, 5) (expected score 2.00)
With 0 rolls left and (1, 1, 1, 1, 3, 6) showing, we should keep (1, 1, 1, 1, 3, 6) (expected score 2.00)
With 0 rolls left and (1, 1, 1, 1, 4, 4) showing, we should keep (1, 1, 1, 1, 4, 4) (expected score 2.00)
With 0 rolls left and (1, 1, 1, 1, 4, 5) showing, we should keep (1, 1, 1, 1, 4, 5) (expected score 2.00)
With 0 rolls left and (1, 1, 1, 1, 4, 6) showing, we should keep (1, 1, 1, 1, 4, 6) (expected score 2.00)
With 0 rolls left and (1, 1, 1, 1, 5, 5) showing, we should keep (1, 1, 1, 1, 5, 5) (expected score 2.00)
With 0 rolls left and (1, 1, 1, 1, 5, 6) showing, we should keep (1, 1, 1, 1, 5, 6) (expected score 2.00)
With 0 rolls left and (1, 1, 1, 1, 6, 6) showing, we should keep (1, 1, 1, 1, 6, 6) (expected score 2.00)
With 0 rolls left and (1, 1, 1, 2, 2, 2) showing, we should keep (1, 1, 1, 2, 2, 2) (expected score 3.00)
With 0 rolls left and (1, 1, 1, 2, 2, 3) showing, we should keep (1, 1, 1, 2, 2, 3) (expected score 1.00)
With 0 rolls left and (1, 1, 1, 2, 2, 4) showing, we should keep (1, 1, 1, 2, 2, 4) (expected score 1.00)
With 0 rolls left and (1, 1, 1, 2, 2, 5) showing, we should keep (1, 1, 1, 2, 2, 5) (expected score 1.00)
With 0 rolls left and (1, 1, 1, 2, 2, 6) showing, we should keep (1, 1, 1, 2, 2, 6) (expected score 1.00)
With 0 rolls left and (1, 1, 1, 2, 3, 3) showing, we should keep (1, 1, 1, 2, 3, 3) (expected score 1.00)
With 0 rolls left and (1, 1, 1, 2, 3, 4) showing, we should keep (1, 1, 1, 2, 3, 4) (expected score 1.00)
With 0 rolls left and (1, 1, 1, 2, 3, 5) showing, we should keep (1, 1, 1, 2, 3, 5) (expected score 1.00)
With 0 rolls left and (1, 1, 1, 2, 3, 6) showing, we should keep (1, 1, 1, 2, 3, 6) (expected score 1.00)
With 0 rolls left and (1, 1, 1, 2, 4, 4) showing, we should keep (1, 1, 1, 2, 4, 4) (expected score 1.00)
With 0 rolls left and (1, 1, 1, 2, 4, 5) showing, we should keep (1, 1, 1, 2, 4, 5) (expected score 1.00)
With 0 rolls left and (1, 1, 1, 2, 4, 6) showing, we should keep (1, 1, 1, 2, 4, 6) (expected score 1.00)
With 0 rolls left and (1, 1, 1, 2, 5, 5) showing, we should keep (1, 1, 1, 2, 5, 5) (expected score 1.00)
With 0 rolls left and (1, 1, 1, 2, 5, 6) showing, we should keep (1, 1, 1, 2, 5, 6) (expected score 1.00)
With 0 rolls left and (1, 1, 1, 2, 6, 6) showing, we should keep (1, 1, 1, 2, 6, 6) (expected score 1.00)
With 0 rolls left and (1, 1, 1, 3, 3, 3) showing, we should keep (1, 1, 1, 3, 3, 3) (expected score 4.00)
With 0 rolls left and (1, 1, 1, 3, 3, 4) showing, we should keep (1, 1, 1, 3, 3, 4) (expected score 1.00)
With 0 rolls left and (1, 1, 1, 3, 3, 5) showing, we should keep (1, 1, 1, 3, 3, 5) (expected score 1.00)
With 0 rolls left and (1, 1, 1, 3, 3, 6) showing, we should keep (1, 1, 1, 3, 3, 6) (expected score 1.00)
With 0 rolls left and (1, 1, 1, 3, 4, 4) showing, we should keep (1, 1, 1, 3, 4, 4) (expected score 1.00)
With 0 rolls left and (1, 1, 1, 3, 4, 5) showing, we should keep (1, 1, 1, 3, 4, 5) (expected score 1.00)
With 0 rolls left and (1, 1, 1, 3, 4, 6) showing, we should keep (1, 1, 1, 3, 4, 6) (expected score 1.00)
With 0 rolls left and (1, 1, 1, 3, 5, 5) showing, we should keep (1, 1, 1, 3, 5, 5) (expected score 1.00)
With 0 rolls left and (1, 1, 1, 3, 5, 6) showing, we should keep (1, 1, 1, 3, 5, 6) (expected score 1.00)
With 0 rolls left and (1, 1, 1, 3, 6, 6) showing, we should keep (1, 1, 1, 3, 6, 6) (expected score 1.00)
With 0 rolls left and (1, 1, 1, 4, 4, 4) showing, we should keep (1, 1, 1, 4, 4, 4) (expected score 1.00)
With 0 rolls left and (1, 1, 1, 4, 4, 5) showing, we should keep (1, 1, 1, 4, 4, 5) (expected score 1.00)
With 0 rolls left and (1, 1, 1, 4, 4, 6) showing, we should keep (1, 1, 1, 4, 4, 6) (expected score 1.00)
With 0 rolls left and (1, 1, 1, 4, 5, 5) showing, we should keep (1, 1, 1, 4, 5, 5) (expected score 1.00)
With 0 rolls left and (1, 1, 1, 4, 5, 6) showing, we should keep (1, 1, 1, 4, 5, 6) (expected score 1.00)
With 0 rolls left and (1, 1, 1, 4, 6, 6) showing, we should keep (1, 1, 1, 4, 6, 6) (expected score 1.00)
With 0 rolls left and (1, 1, 1, 5, 5, 5) showing, we should keep (1, 1, 1, 5, 5, 5) (expected score 1.00)
With 0 rolls left and (1, 1, 1, 5, 5, 6) showing, we should keep (1, 1, 1, 5, 5, 6) (expected score 1.00)
With 0 rolls left and (1, 1, 1, 5, 6, 6) showing, we should keep (1, 1, 1, 5, 6, 6) (expected score 1.00)
With 0 rolls left and (1, 1, 1, 6, 6, 6) showing, we should keep (1, 1, 1, 6, 6, 6) (expected score 1.00)
With 0 rolls left and (1, 1, 2, 2, 2, 2) showing, we should keep (1, 1, 2, 2, 2, 2) (expected score 3.00)
With 0 rolls left and (1, 1, 2, 2, 2, 3) showing, we should keep (1, 1, 2, 2, 2, 3) (expected score 2.00)
With 0 rolls left and (1, 1, 2, 2, 2, 4) showing, we should keep (1, 1, 2, 2, 2, 4) (expected score 2.00)
With 0 rolls left and (1, 1, 2, 2, 2, 5) showing, we should keep (1, 1, 2, 2, 2, 5) (expected score 2.00)
With 0 rolls left and (1, 1, 2, 2, 2, 6) showing, we should keep (1, 1, 2, 2, 2, 6) (expected score 2.00)
With 0 rolls left and (1, 1, 2, 2, 3, 3) showing, we should keep (1, 1, 2, 2, 3, 3) (expected score 0.00)
With 0 rolls left and (1, 1, 2, 2, 3, 4) showing, we should keep (1, 1, 2, 2, 3, 4) (expected score 0.00)
With 0 rolls left and (1, 1, 2, 2, 3, 5) showing, we should keep (1, 1, 2, 2, 3, 5) (expected score 0.00)
With 0 rolls left and (1, 1, 2, 2, 3, 6) showing, we should keep (1, 1, 2, 2, 3, 6) (expected score 0.00)
With 0 rolls left and (1, 1, 2, 2, 4, 4) showing, we should keep (1, 1, 2, 2, 4, 4) (expected score 0.00)
With 0 rolls left and (1, 1, 2, 2, 4, 5) showing, we should keep (1, 1, 2, 2, 4, 5) (expected score 0.00)
With 0 rolls left and (1, 1, 2, 2, 4, 6) showing, we should keep (1, 1, 2, 2, 4, 6) (expected score 0.00)
With 0 rolls left and (1, 1, 2, 2, 5, 5) showing, we should keep (1, 1, 2, 2, 5, 5) (expected score 0.00)
With 0 rolls left and (1, 1, 2, 2, 5, 6) showing, we should keep (1, 1, 2, 2, 5, 6) (expected score 0.00)
With 0 rolls left and (1, 1, 2, 2, 6, 6) showing, we should keep (1, 1, 2, 2, 6, 6) (expected score 0.00)
With 0 rolls left and (1, 1, 2, 3, 3, 3) showing, we should keep (1, 1, 2, 3, 3, 3) (expected score 3.00)
With 0 rolls left and (1, 1, 2, 3, 3, 4) showing, we should keep (1, 1, 2, 3, 3, 4) (expected score 0.00)
With 0 rolls left and (1, 1, 2, 3, 3, 5) showing, we should keep (1, 1, 2, 3, 3, 5) (expected score 0.00)
With 0 rolls left and (1, 1, 2, 3, 3, 6) showing, we should keep (1, 1, 2, 3, 3, 6) (expected score 0.00)
With 0 rolls left and (1, 1, 2, 3, 4, 4) showing, we should keep (1, 1, 2, 3, 4, 4) (expected score 0.00)
With 0 rolls left and (1, 1, 2, 3, 4, 5) showing, we should keep (1, 1, 2, 3, 4, 5) (expected score 0.00)
With 0 rolls left and (1, 1, 2, 3, 4, 6) showing, we should keep (1, 1, 2, 3, 4, 6) (expected score 0.00)
With 0 rolls left and (1, 1, 2, 3, 5, 5) showing, we should keep (1, 1, 2, 3, 5, 5) (expected score 0.00)
With 0 rolls left and (1, 1, 2, 3, 5, 6) showing, we should keep (1, 1, 2, 3, 5, 6) (expected score 0.00)
With 0 rolls left and (1, 1, 2, 3, 6, 6) showing, we should keep (1, 1, 2, 3, 6, 6) (expected score 0.00)
With 0 rolls left and (1, 1, 2, 4, 4, 4) showing, we should keep (1, 1, 2, 4, 4, 4) (expected score 0.00)
With 0 rolls left and (1, 1, 2, 4, 4, 5) showing, we should keep (1, 1, 2, 4, 4, 5) (expected score 0.00)
With 0 rolls left and (1, 1, 2, 4, 4, 6) showing, we should keep (1, 1, 2, 4, 4, 6) (expected score 0.00)
With 0 rolls left and (1, 1, 2, 4, 5, 5) showing, we should keep (1, 1, 2, 4, 5, 5) (expected score 0.00)
With 0 rolls left and (1, 1, 2, 4, 5, 6) showing, we should keep (1, 1, 2, 4, 5, 6) (expected score 0.00)
With 0 rolls left and (1, 1, 2, 4, 6, 6) showing, we should keep (1, 1, 2, 4, 6, 6) (expected score 0.00)
With 0 rolls left and (1, 1, 2, 5, 5, 5) showing, we should keep (1, 1, 2, 5, 5, 5) (expected score 0.00)
With 0 rolls left and (1, 1, 2, 5, 5, 6) showing, we should keep (1, 1, 2, 5, 5, 6) (expected score 0.00)
With 0 rolls left and (1, 1, 2, 5, 6, 6) showing, we should keep (1, 1, 2, 5, 6, 6) (expected score 0.00)
With 0 rolls left and (1, 1, 2, 6, 6, 6) showing, we should keep (1, 1, 2, 6, 6, 6) (expected score 0.00)
With 0 rolls left and (1, 1, 3, 3, 3, 3) showing, we should keep (1, 1, 3, 3, 3, 3) (expected score 4.00)
With 0 rolls left and (1, 1, 3, 3, 3, 4) showing, we should keep (1, 1, 3, 3, 3, 4) (expected score 3.00)
With 0 rolls left and (1, 1, 3, 3, 3, 5) showing, we should keep (1, 1, 3, 3, 3, 5) (expected score 3.00)
With 0 rolls left and (1, 1, 3, 3, 3, 6) showing, we should keep (1, 1, 3, 3, 3, 6) (expected score 3.00)
With 0 rolls left and (1, 1, 3, 3, 4, 4) showing, we should keep (1, 1, 3, 3, 4, 4) (expected score 0.00)
With 0 rolls left and (1, 1, 3, 3, 4, 5) showing, we should keep (1, 1, 3, 3, 4, 5) (expected score 0.00)
With 0 rolls left and (1, 1, 3, 3, 4, 6) showing, we should keep (1, 1, 3, 3, 4, 6) (expected score 0.00)
With 0 rolls left and (1, 1, 3, 3, 5, 5) showing, we should keep (1, 1, 3, 3, 5, 5) (expected score 0.00)
With 0 rolls left and (1, 1, 3, 3, 5, 6) showing, we should keep (1, 1, 3, 3, 5, 6) (expected score 0.00)
With 0 rolls left and (1, 1, 3, 3, 6, 6) showing, we should keep (1, 1, 3, 3, 6, 6) (expected score 0.00)
With 0 rolls left and (1, 1, 3, 4, 4, 4) showing, we should keep (1, 1, 3, 4, 4, 4) (expected score 0.00)
With 0 rolls left and (1, 1, 3, 4, 4, 5) showing, we should keep (1, 1, 3, 4, 4, 5) (expected score 0.00)
With 0 rolls left and (1, 1, 3, 4, 4, 6) showing, we should keep (1, 1, 3, 4, 4, 6) (expected score 0.00)
With 0 rolls left and (1, 1, 3, 4, 5, 5) showing, we should keep (1, 1, 3, 4, 5, 5) (expected score 0.00)
With 0 rolls left and (1, 1, 3, 4, 5, 6) showing, we should keep (1, 1, 3, 4, 5, 6) (expected score 0.00)
With 0 rolls left and (1, 1, 3, 4, 6, 6) showing, we should keep (1, 1, 3, 4, 6, 6) (expected score 0.00)
With 0 rolls left and (1, 1, 3, 5, 5, 5) showing, we should keep (1, 1, 3, 5, 5, 5) (expected score 0.00)
With 0 rolls left and (1, 1, 3, 5, 5, 6) showing, we should keep (1, 1, 3, 5, 5, 6) (expected score 0.00)
With 0 rolls left and (1, 1, 3, 5, 6, 6) showing, we should keep (1, 1, 3, 5, 6, 6) (expected score 0.00)
With 0 rolls left and (1, 1, 3, 6, 6, 6) showing, we should keep (1, 1, 3, 6, 6, 6) (expected score 0.00)
With 0 rolls left and (1, 1, 4, 4, 4, 4) showing, we should keep (1, 1, 4, 4, 4, 4) (expected score 0.00)
With 0 rolls left and (1, 1, 4, 4, 4, 5) showing, we should keep (1, 1, 4, 4, 4, 5) (expected score 0.00)
With 0 rolls left and (1, 1, 4, 4, 4, 6) showing, we should keep (1, 1, 4, 4, 4, 6) (expected score 0.00)
With 0 rolls left and (1, 1, 4, 4, 5, 5) showing, we should keep (1, 1, 4, 4, 5, 5) (expected score 0.00)
With 0 rolls left and (1, 1, 4, 4, 5, 6) showing, we should keep (1, 1, 4, 4, 5, 6) (expected score 0.00)
With 0 rolls left and (1, 1, 4, 4, 6, 6) showing, we should keep (1, 1, 4, 4, 6, 6) (expected score 0.00)
With 0 rolls left and (1, 1, 4, 5, 5, 5) showing, we should keep (1, 1, 4, 5, 5, 5) (expected score 0.00)
With 0 rolls left and (1, 1, 4, 5, 5, 6) showing, we should keep (1, 1, 4, 5, 5, 6) (expected score 0.00)
With 0 rolls left and (1, 1, 4, 5, 6, 6) showing, we should keep (1, 1, 4, 5, 6, 6) (expected score 0.00)
With 0 rolls left and (1, 1, 4, 6, 6, 6) showing, we should keep (1, 1, 4, 6, 6, 6) (expected score 0.00)
With 0 rolls left and (1, 1, 5, 5, 5, 5) showing, we should keep (1, 1, 5, 5, 5, 5) (expected score 0.00)
With 0 rolls left and (1, 1, 5, 5, 5, 6) showing, we should keep (1, 1, 5, 5, 5, 6) (expected score 0.00)
With 0 rolls left and (1, 1, 5, 5, 6, 6) showing, we should keep (1, 1, 5, 5, 6, 6) (expected score 0.00)
With 0 rolls left and (1, 1, 5, 6, 6, 6) showing, we should keep (1, 1, 5, 6, 6, 6) (expected score 0.00)
With 0 rolls left and (1, 1, 6, 6, 6, 6) showing, we should keep (1, 1, 6, 6, 6, 6) (expected score 0.00)
With 0 rolls left and (1, 2, 2, 2, 2, 2) showing, we should keep (1, 2, 2, 2, 2, 2) (expected score 4.00)
With 0 rolls left and (1, 2, 2, 2, 2, 3) showing, we should keep (1, 2, 2, 2, 2, 3) (expected score 3.00)
With 0 rolls left and (1, 2, 2, 2, 2, 4) showing, we should keep (1, 2, 2, 2, 2, 4) (expected score 3.00)
With 0 rolls left and (1, 2, 2, 2, 2, 5) showing, we should keep (1, 2, 2, 2, 2, 5) (expected score 3.00)
With 0 rolls left and (1, 2, 2, 2, 2, 6) showing, we should keep (1, 2, 2, 2, 2, 6) (expected score 3.00)
With 0 rolls left and (1, 2, 2, 2, 3, 3) showing, we should keep (1, 2, 2, 2, 3, 3) (expected score 2.00)
With 0 rolls left and (1, 2, 2, 2, 3, 4) showing, we should keep (1, 2, 2, 2, 3, 4) (expected score 2.00)
With 0 rolls left and (1, 2, 2, 2, 3, 5) showing, we should keep (1, 2, 2, 2, 3, 5) (expected score 2.00)
With 0 rolls left and (1, 2, 2, 2, 3, 6) showing, we should keep (1, 2, 2, 2, 3, 6) (expected score 2.00)
With 0 rolls left and (1, 2, 2, 2, 4, 4) showing, we should keep (1, 2, 2, 2, 4, 4) (expected score 2.00)
With 0 rolls left and (1, 2, 2, 2, 4, 5) showing, we should keep (1, 2, 2, 2, 4, 5) (expected score 2.00)
With 0 rolls left and (1, 2, 2, 2, 4, 6) showing, we should keep (1, 2, 2, 2, 4, 6) (expected score 2.00)
With 0 rolls left and (1, 2, 2, 2, 5, 5) showing, we should keep (1, 2, 2, 2, 5, 5) (expected score 2.00)
With 0 rolls left and (1, 2, 2, 2, 5, 6) showing, we should keep (1, 2, 2, 2, 5, 6) (expected score 2.00)
With 0 rolls left and (1, 2, 2, 2, 6, 6) showing, we should keep (1, 2, 2, 2, 6, 6) (expected score 2.00)
With 0 rolls left and (1, 2, 2, 3, 3, 3) showing, we should keep (1, 2, 2, 3, 3, 3) (expected score 3.00)
With 0 rolls left and (1, 2, 2, 3, 3, 4) showing, we should keep (1, 2, 2, 3, 3, 4) (expected score 0.00)
With 0 rolls left and (1, 2, 2, 3, 3, 5) showing, we should keep (1, 2, 2, 3, 3, 5) (expected score 0.00)
With 0 rolls left and (1, 2, 2, 3, 3, 6) showing, we should keep (1, 2, 2, 3, 3, 6) (expected score 0.00)
With 0 rolls left and (1, 2, 2, 3, 4, 4) showing, we should keep (1, 2, 2, 3, 4, 4) (expected score 0.00)
With 0 rolls left and (1, 2, 2, 3, 4, 5) showing, we should keep (1, 2, 2, 3, 4, 5) (expected score 0.00)
With 0 rolls left and (1, 2, 2, 3, 4, 6) showing, we should keep (1, 2, 2, 3, 4, 6) (expected score 0.00)
With 0 rolls left and (1, 2, 2, 3, 5, 5) showing, we should keep (1, 2, 2, 3, 5, 5) (expected score 0.00)
With 0 rolls left and (1, 2, 2, 3, 5, 6) showing, we should keep (1, 2, 2, 3, 5, 6) (expected score 0.00)
With 0 rolls left and (1, 2, 2, 3, 6, 6) showing, we should keep (1, 2, 2, 3, 6, 6) (expected score 0.00)
With 0 rolls left and (1, 2, 2, 4, 4, 4) showing, we should keep (1, 2, 2, 4, 4, 4) (expected score 0.00)
With 0 rolls left and (1, 2, 2, 4, 4, 5) showing, we should keep (1, 2, 2, 4, 4, 5) (expected score 0.00)
With 0 rolls left and (1, 2, 2, 4, 4, 6) showing, we should keep (1, 2, 2, 4, 4, 6) (expected score 0.00)
With 0 rolls left and (1, 2, 2, 4, 5, 5) showing, we should keep (1, 2, 2, 4, 5, 5) (expected score 0.00)
With 0 rolls left and (1, 2, 2, 4, 5, 6) showing, we should keep (1, 2, 2, 4, 5, 6) (expected score 0.00)
With 0 rolls left and (1, 2, 2, 4, 6, 6) showing, we should keep (1, 2, 2, 4, 6, 6) (expected score 0.00)
With 0 rolls left and (1, 2, 2, 5, 5, 5) showing, we should keep (1, 2, 2, 5, 5, 5) (expected score 0.00)
With 0 rolls left and (1, 2, 2, 5, 5, 6) showing, we should keep (1, 2, 2, 5, 5, 6) (expected score 0.00)
With 0 rolls left and (1, 2, 2, 5, 6, 6) showing, we should keep (1, 2, 2, 5, 6, 6) (expected score 0.00)
With 0 rolls left and (1, 2, 2, 6, 6, 6) showing, we should keep (1, 2, 2, 6, 6, 6) (expected score 0.00)
With 0 rolls left and (1, 2, 3, 3, 3, 3) showing, we should keep (1, 2, 3, 3, 3, 3) (expected score 4.00)
With 0 rolls left and (1, 2, 3, 3, 3, 4) showing, we should keep (1, 2, 3, 3, 3, 4) (expected score 3.00)
With 0 rolls left and (1, 2, 3, 3, 3, 5) showing, we should keep (1, 2, 3, 3, 3, 5) (expected score 3.00)
With 0 rolls left and (1, 2, 3, 3, 3, 6) showing, we should keep (1, 2, 3, 3, 3, 6) (expected score 3.00)
With 0 rolls left and (1, 2, 3, 3, 4, 4) showing, we should keep (1, 2, 3, 3, 4, 4) (expected score 0.00)
With 0 rolls left and (1, 2, 3, 3, 4, 5) showing, we should keep (1, 2, 3, 3, 4, 5) (expected score 0.00)
With 0 rolls left and (1, 2, 3, 3, 4, 6) showing, we should keep (1, 2, 3, 3, 4, 6) (expected score 0.00)
With 0 rolls left and (1, 2, 3, 3, 5, 5) showing, we should keep (1, 2, 3, 3, 5, 5) (expected score 0.00)
With 0 rolls left and (1, 2, 3, 3, 5, 6) showing, we should keep (1, 2, 3, 3, 5, 6) (expected score 0.00)
With 0 rolls left and (1, 2, 3, 3, 6, 6) showing, we should keep (1, 2, 3, 3, 6, 6) (expected score 0.00)
With 0 rolls left and (1, 2, 3, 4, 4, 4) showing, we should keep (1, 2, 3, 4, 4, 4) (expected score 0.00)
With 0 rolls left and (1, 2, 3, 4, 4, 5) showing, we should keep (1, 2, 3, 4, 4, 5) (expected score 0.00)
With 0 rolls left and (1, 2, 3, 4, 4, 6) showing, we should keep (1, 2, 3, 4, 4, 6) (expected score 0.00)
With 0 rolls left and (1, 2, 3, 4, 5, 5) showing, we should keep (1, 2, 3, 4, 5, 5) (expected score 0.00)
With 0 rolls left and (1, 2, 3, 4, 5, 6) showing, we should keep (1, 2, 3, 4, 5, 6) (expected score 0.00)
With 0 rolls left and (1, 2, 3, 4, 6, 6) showing, we should keep (1, 2, 3, 4, 6, 6) (expected score 0.00)
With 0 rolls left and (1, 2, 3, 5, 5, 5) showing, we should keep (1, 2, 3, 5, 5, 5) (expected score 0.00)
With 0 rolls left and (1, 2, 3, 5, 5, 6) showing, we should keep (1, 2, 3, 5, 5, 6) (expected score 0.00)
With 0 rolls left and (1, 2, 3, 5, 6, 6) showing, we should keep (1, 2, 3, 5, 6, 6) (expected score 0.00)
With 0 rolls left and (1, 2, 3, 6, 6, 6) showing, we should keep (1, 2, 3, 6, 6, 6) (expected score 0.00)
With 0 rolls left and (1, 2, 4, 4, 4, 4) showing, we should keep (1, 2, 4, 4, 4, 4) (expected score 0.00)
With 0 rolls left and (1, 2, 4, 4, 4, 5) showing, we should keep (1, 2, 4, 4, 4, 5) (expected score 0.00)
With 0 rolls left and (1, 2, 4, 4, 4, 6) showing, we should keep (1, 2, 4, 4, 4, 6) (expected score 0.00)
With 0 rolls left and (1, 2, 4, 4, 5, 5) showing, we should keep (1, 2, 4, 4, 5, 5) (expected score 0.00)
With 0 rolls left and (1, 2, 4, 4, 5, 6) showing, we should keep (1, 2, 4, 4, 5, 6) (expected score 0.00)
With 0 rolls left and (1, 2, 4, 4, 6, 6) showing, we should keep (1, 2, 4, 4, 6, 6) (expected score 0.00)
With 0 rolls left and (1, 2, 4, 5, 5, 5) showing, we should keep (1, 2, 4, 5, 5, 5) (expected score 0.00)
With 0 rolls left and (1, 2, 4, 5, 5, 6) showing, we should keep (1, 2, 4, 5, 5, 6) (expected score 0.00)
With 0 rolls left and (1, 2, 4, 5, 6, 6) showing, we should keep (1, 2, 4, 5, 6, 6) (expected score 0.00)
With 0 rolls left and (1, 2, 4, 6, 6, 6) showing, we should keep (1, 2, 4, 6, 6, 6) (expected score 0.00)
With 0 rolls left and (1, 2, 5, 5, 5, 5) showing, we should keep (1, 2, 5, 5, 5, 5) (expected score 0.00)
With 0 rolls left and (1, 2, 5, 5, 5, 6) showing, we should keep (1, 2, 5, 5, 5, 6) (expected score 0.00)
With 0 rolls left and (1, 2, 5, 5, 6, 6) showing, we should keep (1, 2, 5, 5, 6, 6) (expected score 0.00)
With 0 rolls left and (1, 2, 5, 6, 6, 6) showing, we should keep (1, 2, 5, 6, 6, 6) (expected score 0.00)
With 0 rolls left and (1, 2, 6, 6, 6, 6) showing, we should keep (1, 2, 6, 6, 6, 6) (expected score 0.00)
With 0 rolls left and (1, 3, 3, 3, 3, 3) showing, we should keep (1, 3, 3, 3, 3, 3) (expected score 5.00)
With 0 rolls left and (1, 3, 3, 3, 3, 4) showing, we should keep (1, 3, 3, 3, 3, 4) (expected score 4.00)
With 0 rolls left and (1, 3, 3, 3, 3, 5) showing, we should keep (1, 3, 3, 3, 3, 5) (expected score 4.00)
With 0 rolls left and (1, 3, 3, 3, 3, 6) showing, we should keep (1, 3, 3, 3, 3, 6) (expected score 4.00)
With 0 rolls left and (1, 3, 3, 3, 4, 4) showing, we should keep (1, 3, 3, 3, 4, 4) (expected score 3.00)
With 0 rolls left and (1, 3, 3, 3, 4, 5) showing, we should keep (1, 3, 3, 3, 4, 5) (expected score 3.00)
With 0 rolls left and (1, 3, 3, 3, 4, 6) showing, we should keep (1, 3, 3, 3, 4, 6) (expected score 3.00)
With 0 rolls left and (1, 3, 3, 3, 5, 5) showing, we should keep (1, 3, 3, 3, 5, 5) (expected score 3.00)
With 0 rolls left and (1, 3, 3, 3, 5, 6) showing, we should keep (1, 3, 3, 3, 5, 6) (expected score 3.00)
With 0 rolls left and (1, 3, 3, 3, 6, 6) showing, we should keep (1, 3, 3, 3, 6, 6) (expected score 3.00)
With 0 rolls left and (1, 3, 3, 4, 4, 4) showing, we should keep (1, 3, 3, 4, 4, 4) (expected score 0.00)
With 0 rolls left and (1, 3, 3, 4, 4, 5) showing, we should keep (1, 3, 3, 4, 4, 5) (expected score 0.00)
With 0 rolls left and (1, 3, 3, 4, 4, 6) showing, we should keep (1, 3, 3, 4, 4, 6) (expected score 0.00)
With 0 rolls left and (1, 3, 3, 4, 5, 5) showing, we should keep (1, 3, 3, 4, 5, 5) (expected score 0.00)
With 0 rolls left and (1, 3, 3, 4, 5, 6) showing, we should keep (1, 3, 3, 4, 5, 6) (expected score 0.00)
With 0 rolls left and (1, 3, 3, 4, 6, 6) showing, we should keep (1, 3, 3, 4, 6, 6) (expected score 0.00)
With 0 rolls left and (1, 3, 3, 5, 5, 5) showing, we should keep (1, 3, 3, 5, 5, 5) (expected score 0.00)
With 0 rolls left and (1, 3, 3, 5, 5, 6) showing, we should keep (1, 3, 3, 5, 5, 6) (expected score 0.00)
With 0 rolls left and (1, 3, 3, 5, 6, 6) showing, we should keep (1, 3, 3, 5, 6, 6) (expected score 0.00)
With 0 rolls left and (1, 3, 3, 6, 6, 6) showing, we should keep (1, 3, 3, 6, 6, 6) (expected score 0.00)
With 0 rolls left and (1, 3, 4, 4, 4, 4) showing, we should keep (1, 3, 4, 4, 4, 4) (expected score 0.00)
With 0 rolls left and (1, 3, 4, 4, 4, 5) showing, we should keep (1, 3, 4, 4, 4, 5) (expected score 0.00)
With 0 rolls left and (1, 3, 4, 4, 4, 6) showing, we should keep (1, 3, 4, 4, 4, 6) (expected score 0.00)
With 0 rolls left and (1, 3, 4, 4, 5, 5) showing, we should keep (1, 3, 4, 4, 5, 5) (expected score 0.00)
With 0 rolls left and (1, 3, 4, 4, 5, 6) showing, we should keep (1, 3, 4, 4, 5, 6) (expected score 0.00)
With 0 rolls left and (1, 3, 4, 4, 6, 6) showing, we should keep (1, 3, 4, 4, 6, 6) (expected score 0.00)
With 0 rolls left and (1, 3, 4, 5, 5, 5) showing, we should keep (1, 3, 4, 5, 5, 5) (expected score 0.00)
With 0 rolls left and (1, 3, 4, 5, 5, 6) showing, we should keep (1, 3, 4, 5, 5, 6) (expected score 0.00)
With 0 rolls left and (1, 3, 4, 5, 6, 6) showing, we should keep (1, 3, 4, 5, 6, 6) (expected score 0.00)
With 0 rolls left and (1, 3, 4, 6, 6, 6) showing, we should keep (1, 3, 4, 6, 6, 6) (expected score 0.00)
With 0 rolls left and (1, 3, 5, 5, 5, 5) showing, we should keep (1, 3, 5, 5, 5, 5) (expected score 0.00)
With 0 rolls left and (1, 3, 5, 5, 5, 6) showing, we should keep (1, 3, 5, 5, 5, 6) (expected score 0.00)
With 0 rolls left and (1, 3, 5, 5, 6, 6) showing, we should keep (1, 3, 5, 5, 6, 6) (expected score 0.00)
With 0 rolls left and (1, 3, 5, 6, 6, 6) showing, we should keep (1, 3, 5, 6, 6, 6) (expected score 0.00)
With 0 rolls left and (1, 3, 6, 6, 6, 6) showing, we should keep (1, 3, 6, 6, 6, 6) (expected score 0.00)
With 0 rolls left and (1, 4, 4, 4, 4, 4) showing, we should keep (1, 4, 4, 4, 4, 4) (expected score 0.00)
With 0 rolls left and (1, 4, 4, 4, 4, 5) showing, we should keep (1, 4, 4, 4, 4, 5) (expected score 0.00)
With 0 rolls left and (1, 4, 4, 4, 4, 6) showing, we should keep (1, 4, 4, 4, 4, 6) (expected score 0.00)
With 0 rolls left and (1, 4, 4, 4, 5, 5) showing, we should keep (1, 4, 4, 4, 5, 5) (expected score 0.00)
With 0 rolls left and (1, 4, 4, 4, 5, 6) showing, we should keep (1, 4, 4, 4, 5, 6) (expected score 0.00)
With 0 rolls left and (1, 4, 4, 4, 6, 6) showing, we should keep (1, 4, 4, 4, 6, 6) (expected score 0.00)
With 0 rolls left and (1, 4, 4, 5, 5, 5) showing, we should keep (1, 4, 4, 5, 5, 5) (expected score 0.00)
With 0 rolls left and (1, 4, 4, 5, 5, 6) showing, we should keep (1, 4, 4, 5, 5, 6) (expected score 0.00)
With 0 rolls left and (1, 4, 4, 5, 6, 6) showing, we should keep (1, 4, 4, 5, 6, 6) (expected score 0.00)
With 0 rolls left and (1, 4, 4, 6, 6, 6) showing, we should keep (1, 4, 4, 6, 6, 6) (expected score 0.00)
With 0 rolls left and (1, 4, 5, 5, 5, 5) showing, we should keep (1, 4, 5, 5, 5, 5) (expected score 0.00)
With 0 rolls left and (1, 4, 5, 5, 5, 6) showing, we should keep (1, 4, 5, 5, 5, 6) (expected score 0.00)
With 0 rolls left and (1, 4, 5, 5, 6, 6) showing, we should keep (1, 4, 5, 5, 6, 6) (expected score 0.00)
With 0 rolls left and (1, 4, 5, 6, 6, 6) showing, we should keep (1, 4, 5, 6, 6, 6) (expected score 0.00)
With 0 rolls left and (1, 4, 6, 6, 6, 6) showing, we should keep (1, 4, 6, 6, 6, 6) (expected score 0.00)
With 0 rolls left and (1, 5, 5, 5, 5, 5) showing, we should keep (1, 5, 5, 5, 5, 5) (expected score 0.00)
With 0 rolls left and (1, 5, 5, 5, 5, 6) showing, we should keep (1, 5, 5, 5, 5, 6) (expected score 0.00)
With 0 rolls left and (1, 5, 5, 5, 6, 6) showing, we should keep (1, 5, 5, 5, 6, 6) (expected score 0.00)
With 0 rolls left and (1, 5, 5, 6, 6, 6) showing, we should keep (1, 5, 5, 6, 6, 6) (expected score 0.00)
With 0 rolls left and (1, 5, 6, 6, 6, 6) showing, we should keep (1, 5, 6, 6, 6, 6) (expected score 0.00)
With 0 rolls left and (1, 6, 6, 6, 6, 6) showing, we should keep (1, 6, 6, 6, 6, 6) (expected score 0.00)
With 0 rolls left and (2, 2, 2, 2, 2, 2) showing, we should keep (2, 2, 2, 2, 2, 2) (expected score 5.00)
With 0 rolls left and (2, 2, 2, 2, 2, 3) showing, we should keep (2, 2, 2, 2, 2, 3) (expected score 4.00)
With 0 rolls left and (2, 2, 2, 2, 2, 4) showing, we should keep (2, 2, 2, 2, 2, 4) (expected score 4.00)
With 0 rolls left and (2, 2, 2, 2, 2, 5) showing, we should keep (2, 2, 2, 2, 2, 5) (expected score 4.00)
With 0 rolls left and (2, 2, 2, 2, 2, 6) showing, we should keep (2, 2, 2, 2, 2, 6) (expected score 4.00)
With 0 rolls left and (2, 2, 2, 2, 3, 3) showing, we should keep (2, 2, 2, 2, 3, 3) (expected score 3.00)
With 0 rolls left and (2, 2, 2, 2, 3, 4) showing, we should keep (2, 2, 2, 2, 3, 4) (expected score 3.00)
With 0 rolls left and (2, 2, 2, 2, 3, 5) showing, we should keep (2, 2, 2, 2, 3, 5) (expected score 3.00)
With 0 rolls left and (2, 2, 2, 2, 3, 6) showing, we should keep (2, 2, 2, 2, 3, 6) (expected score 3.00)
With 0 rolls left and (2, 2, 2, 2, 4, 4) showing, we should keep (2, 2, 2, 2, 4, 4) (expected score 3.00)
With 0 rolls left and (2, 2, 2, 2, 4, 5) showing, we should keep (2, 2, 2, 2, 4, 5) (expected score 3.00)
With 0 rolls left and (2, 2, 2, 2, 4, 6) showing, we should keep (2, 2, 2, 2, 4, 6) (expected score 3.00)
With 0 rolls left and (2, 2, 2, 2, 5, 5) showing, we should keep (2, 2, 2, 2, 5, 5) (expected score 3.00)
With 0 rolls left and (2, 2, 2, 2, 5, 6) showing, we should keep (2, 2, 2, 2, 5, 6) (expected score 3.00)
With 0 rolls left and (2, 2, 2, 2, 6, 6) showing, we should keep (2, 2, 2, 2, 6, 6) (expected score 3.00)
With 0 rolls left and (2, 2, 2, 3, 3, 3) showing, we should keep (2, 2, 2, 3, 3, 3) (expected score 5.00)
With 0 rolls left and (2, 2, 2, 3, 3, 4) showing, we should keep (2, 2, 2, 3, 3, 4) (expected score 2.00)
With 0 rolls left and (2, 2, 2, 3, 3, 5) showing, we should keep (2, 2, 2, 3, 3, 5) (expected score 2.00)
With 0 rolls left and (2, 2, 2, 3, 3, 6) showing, we should keep (2, 2, 2, 3, 3, 6) (expected score 2.00)
With 0 rolls left and (2, 2, 2, 3, 4, 4) showing, we should keep (2, 2, 2, 3, 4, 4) (expected score 2.00)
With 0 rolls left and (2, 2, 2, 3, 4, 5) showing, we should keep (2, 2, 2, 3, 4, 5) (expected score 2.00)
With 0 rolls left and (2, 2, 2, 3, 4, 6) showing, we should keep (2, 2, 2, 3, 4, 6) (expected score 2.00)
With 0 rolls left and (2, 2, 2, 3, 5, 5) showing, we should keep (2, 2, 2, 3, 5, 5) (expected score 2.00)
With 0 rolls left and (2, 2, 2, 3, 5, 6) showing, we should keep (2, 2, 2, 3, 5, 6) (expected score 2.00)
With 0 rolls left and (2, 2, 2, 3, 6, 6) showing, we should keep (2, 2, 2, 3, 6, 6) (expected score 2.00)
With 0 rolls left and (2, 2, 2, 4, 4, 4) showing, we should keep (2, 2, 2, 4, 4, 4) (expected score 2.00)
With 0 rolls left and (2, 2, 2, 4, 4, 5) showing, we should keep (2, 2, 2, 4, 4, 5) (expected score 2.00)
With 0 rolls left and (2, 2, 2, 4, 4, 6) showing, we should keep (2, 2, 2, 4, 4, 6) (expected score 2.00)
With 0 rolls left and (2, 2, 2, 4, 5, 5) showing, we should keep (2, 2, 2, 4, 5, 5) (expected score 2.00)
With 0 rolls left and (2, 2, 2, 4, 5, 6) showing, we should keep (2, 2, 2, 4, 5, 6) (expected score 2.00)
With 0 rolls left and (2, 2, 2, 4, 6, 6) showing, we should keep (2, 2, 2, 4, 6, 6) (expected score 2.00)
With 0 rolls left and (2, 2, 2, 5, 5, 5) showing, we should keep (2, 2, 2, 5, 5, 5) (expected score 2.00)
With 0 rolls left and (2, 2, 2, 5, 5, 6) showing, we should keep (2, 2, 2, 5, 5, 6) (expected score 2.00)
With 0 rolls left and (2, 2, 2, 5, 6, 6) showing, we should keep (2, 2, 2, 5, 6, 6) (expected score 2.00)
With 0 rolls left and (2, 2, 2, 6, 6, 6) showing, we should keep (2, 2, 2, 6, 6, 6) (expected score 2.00)
With 0 rolls left and (2, 2, 3, 3, 3, 3) showing, we should keep (2, 2, 3, 3, 3, 3) (expected score 4.00)
With 0 rolls left and (2, 2, 3, 3, 3, 4) showing, we should keep (2, 2, 3, 3, 3, 4) (expected score 3.00)
With 0 rolls left and (2, 2, 3, 3, 3, 5) showing, we should keep (2, 2, 3, 3, 3, 5) (expected score 3.00)
With 0 rolls left and (2, 2, 3, 3, 3, 6) showing, we should keep (2, 2, 3, 3, 3, 6) (expected score 3.00)
With 0 rolls left and (2, 2, 3, 3, 4, 4) showing, we should keep (2, 2, 3, 3, 4, 4) (expected score 0.00)
With 0 rolls left and (2, 2, 3, 3, 4, 5) showing, we should keep (2, 2, 3, 3, 4, 5) (expected score 0.00)
With 0 rolls left and (2, 2, 3, 3, 4, 6) showing, we should keep (2, 2, 3, 3, 4, 6) (expected score 0.00)
With 0 rolls left and (2, 2, 3, 3, 5, 5) showing, we should keep (2, 2, 3, 3, 5, 5) (expected score 0.00)
With 0 rolls left and (2, 2, 3, 3, 5, 6) showing, we should keep (2, 2, 3, 3, 5, 6) (expected score 0.00)
With 0 rolls left and (2, 2, 3, 3, 6, 6) showing, we should keep (2, 2, 3, 3, 6, 6) (expected score 0.00)
With 0 rolls left and (2, 2, 3, 4, 4, 4) showing, we should keep (2, 2, 3, 4, 4, 4) (expected score 0.00)
With 0 rolls left and (2, 2, 3, 4, 4, 5) showing, we should keep (2, 2, 3, 4, 4, 5) (expected score 0.00)
With 0 rolls left and (2, 2, 3, 4, 4, 6) showing, we should keep (2, 2, 3, 4, 4, 6) (expected score 0.00)
With 0 rolls left and (2, 2, 3, 4, 5, 5) showing, we should keep (2, 2, 3, 4, 5, 5) (expected score 0.00)
With 0 rolls left and (2, 2, 3, 4, 5, 6) showing, we should keep (2, 2, 3, 4, 5, 6) (expected score 0.00)
With 0 rolls left and (2, 2, 3, 4, 6, 6) showing, we should keep (2, 2, 3, 4, 6, 6) (expected score 0.00)
With 0 rolls left and (2, 2, 3, 5, 5, 5) showing, we should keep (2, 2, 3, 5, 5, 5) (expected score 0.00)
With 0 rolls left and (2, 2, 3, 5, 5, 6) showing, we should keep (2, 2, 3, 5, 5, 6) (expected score 0.00)
With 0 rolls left and (2, 2, 3, 5, 6, 6) showing, we should keep (2, 2, 3, 5, 6, 6) (expected score 0.00)
With 0 rolls left and (2, 2, 3, 6, 6, 6) showing, we should keep (2, 2, 3, 6, 6, 6) (expected score 0.00)
With 0 rolls left and (2, 2, 4, 4, 4, 4) showing, we should keep (2, 2, 4, 4, 4, 4) (expected score 0.00)
With 0 rolls left and (2, 2, 4, 4, 4, 5) showing, we should keep (2, 2, 4, 4, 4, 5) (expected score 0.00)
With 0 rolls left and (2, 2, 4, 4, 4, 6) showing, we should keep (2, 2, 4, 4, 4, 6) (expected score 0.00)
With 0 rolls left and (2, 2, 4, 4, 5, 5) showing, we should keep (2, 2, 4, 4, 5, 5) (expected score 0.00)
With 0 rolls left and (2, 2, 4, 4, 5, 6) showing, we should keep (2, 2, 4, 4, 5, 6) (expected score 0.00)
With 0 rolls left and (2, 2, 4, 4, 6, 6) showing, we should keep (2, 2, 4, 4, 6, 6) (expected score 0.00)
With 0 rolls left and (2, 2, 4, 5, 5, 5) showing, we should keep (2, 2, 4, 5, 5, 5) (expected score 0.00)
With 0 rolls left and (2, 2, 4, 5, 5, 6) showing, we should keep (2, 2, 4, 5, 5, 6) (expected score 0.00)
With 0 rolls left and (2, 2, 4, 5, 6, 6) showing, we should keep (2, 2, 4, 5, 6, 6) (expected score 0.00)
With 0 rolls left and (2, 2, 4, 6, 6, 6) showing, we should keep (2, 2, 4, 6, 6, 6) (expected score 0.00)
With 0 rolls left and (2, 2, 5, 5, 5, 5) showing, we should keep (2, 2, 5, 5, 5, 5) (expected score 0.00)
With 0 rolls left and (2, 2, 5, 5, 5, 6) showing, we should keep (2, 2, 5, 5, 5, 6) (expected score 0.00)
With 0 rolls left and (2, 2, 5, 5, 6, 6) showing, we should keep (2, 2, 5, 5, 6, 6) (expected score 0.00)
With 0 rolls left and (2, 2, 5, 6, 6, 6) showing, we should keep (2, 2, 5, 6, 6, 6) (expected score 0.00)
With 0 rolls left and (2, 2, 6, 6, 6, 6) showing, we should keep (2, 2, 6, 6, 6, 6) (expected score 0.00)
With 0 rolls left and (2, 3, 3, 3, 3, 3) showing, we should keep (2, 3, 3, 3, 3, 3) (expected score 5.00)
With 0 rolls left and (2, 3, 3, 3, 3, 4) showing, we should keep (2, 3, 3, 3, 3, 4) (expected score 4.00)
With 0 rolls left and (2, 3, 3, 3, 3, 5) showing, we should keep (2, 3, 3, 3, 3, 5) (expected score 4.00)
With 0 rolls left and (2, 3, 3, 3, 3, 6) showing, we should keep (2, 3, 3, 3, 3, 6) (expected score 4.00)
With 0 rolls left and (2, 3, 3, 3, 4, 4) showing, we should keep (2, 3, 3, 3, 4, 4) (expected score 3.00)
With 0 rolls left and (2, 3, 3, 3, 4, 5) showing, we should keep (2, 3, 3, 3, 4, 5) (expected score 3.00)
With 0 rolls left and (2, 3, 3, 3, 4, 6) showing, we should keep (2, 3, 3, 3, 4, 6) (expected score 3.00)
With 0 rolls left and (2, 3, 3, 3, 5, 5) showing, we should keep (2, 3, 3, 3, 5, 5) (expected score 3.00)
With 0 rolls left and (2, 3, 3, 3, 5, 6) showing, we should keep (2, 3, 3, 3, 5, 6) (expected score 3.00)
With 0 rolls left and (2, 3, 3, 3, 6, 6) showing, we should keep (2, 3, 3, 3, 6, 6) (expected score 3.00)
With 0 rolls left and (2, 3, 3, 4, 4, 4) showing, we should keep (2, 3, 3, 4, 4, 4) (expected score 0.00)
With 0 rolls left and (2, 3, 3, 4, 4, 5) showing, we should keep (2, 3, 3, 4, 4, 5) (expected score 0.00)
With 0 rolls left and (2, 3, 3, 4, 4, 6) showing, we should keep (2, 3, 3, 4, 4, 6) (expected score 0.00)
With 0 rolls left and (2, 3, 3, 4, 5, 5) showing, we should keep (2, 3, 3, 4, 5, 5) (expected score 0.00)
With 0 rolls left and (2, 3, 3, 4, 5, 6) showing, we should keep (2, 3, 3, 4, 5, 6) (expected score 0.00)
With 0 rolls left and (2, 3, 3, 4, 6, 6) showing, we should keep (2, 3, 3, 4, 6, 6) (expected score 0.00)
With 0 rolls left and (2, 3, 3, 5, 5, 5) showing, we should keep (2, 3, 3, 5, 5, 5) (expected score 0.00)
With 0 rolls left and (2, 3, 3, 5, 5, 6) showing, we should keep (2, 3, 3, 5, 5, 6) (expected score 0.00)
With 0 rolls left and (2, 3, 3, 5, 6, 6) showing, we should keep (2, 3, 3, 5, 6, 6) (expected score 0.00)
With 0 rolls left and (2, 3, 3, 6, 6, 6) showing, we should keep (2, 3, 3, 6, 6, 6) (expected score 0.00)
With 0 rolls left and (2, 3, 4, 4, 4, 4) showing, we should keep (2, 3, 4, 4, 4, 4) (expected score 0.00)
With 0 rolls left and (2, 3, 4, 4, 4, 5) showing, we should keep (2, 3, 4, 4, 4, 5) (expected score 0.00)
With 0 rolls left and (2, 3, 4, 4, 4, 6) showing, we should keep (2, 3, 4, 4, 4, 6) (expected score 0.00)
With 0 rolls left and (2, 3, 4, 4, 5, 5) showing, we should keep (2, 3, 4, 4, 5, 5) (expected score 0.00)
With 0 rolls left and (2, 3, 4, 4, 5, 6) showing, we should keep (2, 3, 4, 4, 5, 6) (expected score 0.00)
With 0 rolls left and (2, 3, 4, 4, 6, 6) showing, we should keep (2, 3, 4, 4, 6, 6) (expected score 0.00)
With 0 rolls left and (2, 3, 4, 5, 5, 5) showing, we should keep (2, 3, 4, 5, 5, 5) (expected score 0.00)
With 0 rolls left and (2, 3, 4, 5, 5, 6) showing, we should keep (2, 3, 4, 5, 5, 6) (expected score 0.00)
With 0 rolls left and (2, 3, 4, 5, 6, 6) showing, we should keep (2, 3, 4, 5, 6, 6) (expected score 0.00)
With 0 rolls left and (2, 3, 4, 6, 6, 6) showing, we should keep (2, 3, 4, 6, 6, 6) (expected score 0.00)
With 0 rolls left and (2, 3, 5, 5, 5, 5) showing, we should keep (2, 3, 5, 5, 5, 5) (expected score 0.00)
With 0 rolls left and (2, 3, 5, 5, 5, 6) showing, we should keep (2, 3, 5, 5, 5, 6) (expected score 0.00)
With 0 rolls left and (2, 3, 5, 5, 6, 6) showing, we should keep (2, 3, 5, 5, 6, 6) (expected score 0.00)
With 0 rolls left and (2, 3, 5, 6, 6, 6) showing, we should keep (2, 3, 5, 6, 6, 6) (expected score 0.00)
With 0 rolls left and (2, 3, 6, 6, 6, 6) showing, we should keep (2, 3, 6, 6, 6, 6) (expected score 0.00)
With 0 rolls left and (2, 4, 4, 4, 4, 4) showing, we should keep (2, 4, 4, 4, 4, 4) (expected score 0.00)
With 0 rolls left and (2, 4, 4, 4, 4, 5) showing, we should keep (2, 4, 4, 4, 4, 5) (expected score 0.00)
With 0 rolls left and (2, 4, 4, 4, 4, 6) showing, we should keep (2, 4, 4, 4, 4, 6) (expected score 0.00)
With 0 rolls left and (2, 4, 4, 4, 5, 5) showing, we should keep (2, 4, 4, 4, 5, 5) (expected score 0.00)
With 0 rolls left and (2, 4, 4, 4, 5, 6) showing, we should keep (2, 4, 4, 4, 5, 6) (expected score 0.00)
With 0 rolls left and (2, 4, 4, 4, 6, 6) showing, we should keep (2, 4, 4, 4, 6, 6) (expected score 0.00)
With 0 rolls left and (2, 4, 4, 5, 5, 5) showing, we should keep (2, 4, 4, 5, 5, 5) (expected score 0.00)
With 0 rolls left and (2, 4, 4, 5, 5, 6) showing, we should keep (2, 4, 4, 5, 5, 6) (expected score 0.00)
With 0 rolls left and (2, 4, 4, 5, 6, 6) showing, we should keep (2, 4, 4, 5, 6, 6) (expected score 0.00)
With 0 rolls left and (2, 4, 4, 6, 6, 6) showing, we should keep (2, 4, 4, 6, 6, 6) (expected score 0.00)
With 0 rolls left and (2, 4, 5, 5, 5, 5) showing, we should keep (2, 4, 5, 5, 5, 5) (expected score 0.00)
With 0 rolls left and (2, 4, 5, 5, 5, 6) showing, we should keep (2, 4, 5, 5, 5, 6) (expected score 0.00)
With 0 rolls left and (2, 4, 5, 5, 6, 6) showing, we should keep (2, 4, 5, 5, 6, 6) (expected score 0.00)
With 0 rolls left and (2, 4, 5, 6, 6, 6) showing, we should keep (2, 4, 5, 6, 6, 6) (expected score 0.00)
With 0 rolls left and (2, 4, 6, 6, 6, 6) showing, we should keep (2, 4, 6, 6, 6, 6) (expected score 0.00)
With 0 rolls left and (2, 5, 5, 5, 5, 5) showing, we should keep (2, 5, 5, 5, 5, 5) (expected score 0.00)
With 0 rolls left and (2, 5, 5, 5, 5, 6) showing, we should keep (2, 5, 5, 5, 5, 6) (expected score 0.00)
With 0 rolls left and (2, 5, 5, 5, 6, 6) showing, we should keep (2, 5, 5, 5, 6, 6) (expected score 0.00)
With 0 rolls left and (2, 5, 5, 6, 6, 6) showing, we should keep (2, 5, 5, 6, 6, 6) (expected score 0.00)
With 0 rolls left and (2, 5, 6, 6, 6, 6) showing, we should keep (2, 5, 6, 6, 6, 6) (expected score 0.00)
With 0 rolls left and (2, 6, 6, 6, 6, 6) showing, we should keep (2, 6, 6, 6, 6, 6) (expected score 0.00)
With 0 rolls left and (3, 3, 3, 3, 3, 3) showing, we should keep (3, 3, 3, 3, 3, 3) (expected score 6.00)
With 0 rolls left and (3, 3, 3, 3, 3, 4) showing, we should keep (3, 3, 3, 3, 3, 4) (expected score 5.00)
With 0 rolls left and (3, 3, 3, 3, 3, 5) showing, we should keep (3, 3, 3, 3, 3, 5) (expected score 5.00)
With 0 rolls left and (3, 3, 3, 3, 3, 6) showing, we should keep (3, 3, 3, 3, 3, 6) (expected score 5.00)
With 0 rolls left and (3, 3, 3, 3, 4, 4) showing, we should keep (3, 3, 3, 3, 4, 4) (expected score 4.00)
With 0 rolls left and (3, 3, 3, 3, 4, 5) showing, we should keep (3, 3, 3, 3, 4, 5) (expected score 4.00)
With 0 rolls left and (3, 3, 3, 3, 4, 6) showing, we should keep (3, 3, 3, 3, 4, 6) (expected score 4.00)
With 0 rolls left and (3, 3, 3, 3, 5, 5) showing, we should keep (3, 3, 3, 3, 5, 5) (expected score 4.00)
With 0 rolls left and (3, 3, 3, 3, 5, 6) showing, we should keep (3, 3, 3, 3, 5, 6) (expected score 4.00)
With 0 rolls left and (3, 3, 3, 3, 6, 6) showing, we should keep (3, 3, 3, 3, 6, 6) (expected score 4.00)
With 0 rolls left and (3, 3, 3, 4, 4, 4) showing, we should keep (3, 3, 3, 4, 4, 4) (expected score 3.00)
With 0 rolls left and (3, 3, 3, 4, 4, 5) showing, we should keep (3, 3, 3, 4, 4, 5) (expected score 3.00)
With 0 rolls left and (3, 3, 3, 4, 4, 6) showing, we should keep (3, 3, 3, 4, 4, 6) (expected score 3.00)
With 0 rolls left and (3, 3, 3, 4, 5, 5) showing, we should keep (3, 3, 3, 4, 5, 5) (expected score 3.00)
With 0 rolls left and (3, 3, 3, 4, 5, 6) showing, we should keep (3, 3, 3, 4, 5, 6) (expected score 3.00)
With 0 rolls left and (3, 3, 3, 4, 6, 6) showing, we should keep (3, 3, 3, 4, 6, 6) (expected score 3.00)
With 0 rolls left and (3, 3, 3, 5, 5, 5) showing, we should keep (3, 3, 3, 5, 5, 5) (expected score 3.00)
With 0 rolls left and (3, 3, 3, 5, 5, 6) showing, we should keep (3, 3, 3, 5, 5, 6) (expected score 3.00)
With 0 rolls left and (3, 3, 3, 5, 6, 6) showing, we should keep (3, 3, 3, 5, 6, 6) (expected score 3.00)
With 0 rolls left and (3, 3, 3, 6, 6, 6) showing, we should keep (3, 3, 3, 6, 6, 6) (expected score 3.00)
With 0 rolls left and (3, 3, 4, 4, 4, 4) showing, we should keep (3, 3, 4, 4, 4, 4) (expected score 0.00)
With 0 rolls left and (3, 3, 4, 4, 4, 5) showing, we should keep (3, 3, 4, 4, 4, 5) (expected score 0.00)
With 0 rolls left and (3, 3, 4, 4, 4, 6) showing, we should keep (3, 3, 4, 4, 4, 6) (expected score 0.00)
With 0 rolls left and (3, 3, 4, 4, 5, 5) showing, we should keep (3, 3, 4, 4, 5, 5) (expected score 0.00)
With 0 rolls left and (3, 3, 4, 4, 5, 6) showing, we should keep (3, 3, 4, 4, 5, 6) (expected score 0.00)
With 0 rolls left and (3, 3, 4, 4, 6, 6) showing, we should keep (3, 3, 4, 4, 6, 6) (expected score 0.00)
With 0 rolls left and (3, 3, 4, 5, 5, 5) showing, we should keep (3, 3, 4, 5, 5, 5) (expected score 0.00)
With 0 rolls left and (3, 3, 4, 5, 5, 6) showing, we should keep (3, 3, 4, 5, 5, 6) (expected score 0.00)
With 0 rolls left and (3, 3, 4, 5, 6, 6) showing, we should keep (3, 3, 4, 5, 6, 6) (expected score 0.00)
With 0 rolls left and (3, 3, 4, 6, 6, 6) showing, we should keep (3, 3, 4, 6, 6, 6) (expected score 0.00)
With 0 rolls left and (3, 3, 5, 5, 5, 5) showing, we should keep (3, 3, 5, 5, 5, 5) (expected score 0.00)
With 0 rolls left and (3, 3, 5, 5, 5, 6) showing, we should keep (3, 3, 5, 5, 5, 6) (expected score 0.00)
With 0 rolls left and (3, 3, 5, 5, 6, 6) showing, we should keep (3, 3, 5, 5, 6, 6) (expected score 0.00)
With 0 rolls left and (3, 3, 5, 6, 6, 6) showing, we should keep (3, 3, 5, 6, 6, 6) (expected score 0.00)
With 0 rolls left and (3, 3, 6, 6, 6, 6) showing, we should keep (3, 3, 6, 6, 6, 6) (expected score 0.00)
With 0 rolls left and (3, 4, 4, 4, 4, 4) showing, we should keep (3, 4, 4, 4, 4, 4) (expected score 0.00)
With 0 rolls left and (3, 4, 4, 4, 4, 5) showing, we should keep (3, 4, 4, 4, 4, 5) (expected score 0.00)
With 0 rolls left and (3, 4, 4, 4, 4, 6) showing, we should keep (3, 4, 4, 4, 4, 6) (expected score 0.00)
With 0 rolls left and (3, 4, 4, 4, 5, 5) showing, we should keep (3, 4, 4, 4, 5, 5) (expected score 0.00)
With 0 rolls left and (3, 4, 4, 4, 5, 6) showing, we should keep (3, 4, 4, 4, 5, 6) (expected score 0.00)
With 0 rolls left and (3, 4, 4, 4, 6, 6) showing, we should keep (3, 4, 4, 4, 6, 6) (expected score 0.00)
With 0 rolls left and (3, 4, 4, 5, 5, 5) showing, we should keep (3, 4, 4, 5, 5, 5) (expected score 0.00)
With 0 rolls left and (3, 4, 4, 5, 5, 6) showing, we should keep (3, 4, 4, 5, 5, 6) (expected score 0.00)
With 0 rolls left and (3, 4, 4, 5, 6, 6) showing, we should keep (3, 4, 4, 5, 6, 6) (expected score 0.00)
With 0 rolls left and (3, 4, 4, 6, 6, 6) showing, we should keep (3, 4, 4, 6, 6, 6) (expected score 0.00)
With 0 rolls left and (3, 4, 5, 5, 5, 5) showing, we should keep (3, 4, 5, 5, 5, 5) (expected score 0.00)
With 0 rolls left and (3, 4, 5, 5, 5, 6) showing, we should keep (3, 4, 5, 5, 5, 6) (expected score 0.00)
With 0 rolls left and (3, 4, 5, 5, 6, 6) showing, we should keep (3, 4, 5, 5, 6, 6) (expected score 0.00)
With 0 rolls left and (3, 4, 5, 6, 6, 6) showing, we should keep (3, 4, 5, 6, 6, 6) (expected score 0.00)
With 0 rolls left and (3, 4, 6, 6, 6, 6) showing, we should keep (3, 4, 6, 6, 6, 6) (expected score 0.00)
With 0 rolls left and (3, 5, 5, 5, 5, 5) showing, we should keep (3, 5, 5, 5, 5, 5) (expected score 0.00)
With 0 rolls left and (3, 5, 5, 5, 5, 6) showing, we should keep (3, 5, 5, 5, 5, 6) (expected score 0.00)
With 0 rolls left and (3, 5, 5, 5, 6, 6) showing, we should keep (3, 5, 5, 5, 6, 6) (expected score 0.00)
With 0 rolls left and (3, 5, 5, 6, 6, 6) showing, we should keep (3, 5, 5, 6, 6, 6) (expected score 0.00)
With 0 rolls left and (3, 5, 6, 6, 6, 6) showing, we should keep (3, 5, 6, 6, 6, 6) (expected score 0.00)
With 0 rolls left and (3, 6, 6, 6, 6, 6) showing, we should keep (3, 6, 6, 6, 6, 6) (expected score 0.00)
With 0 rolls left and (4, 4, 4, 4, 4, 4) showing, we should keep (4, 4, 4, 4, 4, 4) (expected score 0.00)
With 0 rolls left and (4, 4, 4, 4, 4, 5) showing, we should keep (4, 4, 4, 4, 4, 5) (expected score 0.00)
With 0 rolls left and (4, 4, 4, 4, 4, 6) showing, we should keep (4, 4, 4, 4, 4, 6) (expected score 0.00)
With 0 rolls left and (4, 4, 4, 4, 5, 5) showing, we should keep (4, 4, 4, 4, 5, 5) (expected score 0.00)
With 0 rolls left and (4, 4, 4, 4, 5, 6) showing, we should keep (4, 4, 4, 4, 5, 6) (expected score 0.00)
With 0 rolls left and (4, 4, 4, 4, 6, 6) showing, we should keep (4, 4, 4, 4, 6, 6) (expected score 0.00)
With 0 rolls left and (4, 4, 4, 5, 5, 5) showing, we should keep (4, 4, 4, 5, 5, 5) (expected score 0.00)
With 0 rolls left and (4, 4, 4, 5, 5, 6) showing, we should keep (4, 4, 4, 5, 5, 6) (expected score 0.00)
With 0 rolls left and (4, 4, 4, 5, 6, 6) showing, we should keep (4, 4, 4, 5, 6, 6) (expected score 0.00)
With 0 rolls left and (4, 4, 4, 6, 6, 6) showing, we should keep (4, 4, 4, 6, 6, 6) (expected score 0.00)
With 0 rolls left and (4, 4, 5, 5, 5, 5) showing, we should keep (4, 4, 5, 5, 5, 5) (expected score 0.00)
With 0 rolls left and (4, 4, 5, 5, 5, 6) showing, we should keep (4, 4, 5, 5, 5, 6) (expected score 0.00)
With 0 rolls left and (4, 4, 5, 5, 6, 6) showing, we should keep (4, 4, 5, 5, 6, 6) (expected score 0.00)
With 0 rolls left and (4, 4, 5, 6, 6, 6) showing, we should keep (4, 4, 5, 6, 6, 6) (expected score 0.00)
With 0 rolls left and (4, 4, 6, 6, 6, 6) showing, we should keep (4, 4, 6, 6, 6, 6) (expected score 0.00)
With 0 rolls left and (4, 5, 5, 5, 5, 5) showing, we should keep (4, 5, 5, 5, 5, 5) (expected score 0.00)
With 0 rolls left and (4, 5, 5, 5, 5, 6) showing, we should keep (4, 5, 5, 5, 5, 6) (expected score 0.00)
With 0 rolls left and (4, 5, 5, 5, 6, 6) showing, we should keep (4, 5, 5, 5, 6, 6) (expected score 0.00)
With 0 rolls left and (4, 5, 5, 6, 6, 6) showing, we should keep (4, 5, 5, 6, 6, 6) (expected score 0.00)
With 0 rolls left and (4, 5, 6, 6, 6, 6) showing, we should keep (4, 5, 6, 6, 6, 6) (expected score 0.00)
With 0 rolls left and (4, 6, 6, 6, 6, 6) showing, we should keep (4, 6, 6, 6, 6, 6) (expected score 0.00)
With 0 rolls left and (5, 5, 5, 5, 5, 5) showing, we should keep (5, 5, 5, 5, 5, 5) (expected score 0.00)
With 0 rolls left and (5, 5, 5, 5, 5, 6) showing, we should keep (5, 5, 5, 5, 5, 6) (expected score 0.00)
With 0 rolls left and (5, 5, 5, 5, 6, 6) showing, we should keep (5, 5, 5, 5, 6, 6) (expected score 0.00)
With 0 rolls left and (5, 5, 5, 6, 6, 6) showing, we should keep (5, 5, 5, 6, 6, 6) (expected score 0.00)
With 0 rolls left and (5, 5, 6, 6, 6, 6) showing, we should keep (5, 5, 6, 6, 6, 6) (expected score 0.00)
With 0 rolls left and (5, 6, 6, 6, 6, 6) showing, we should keep (5, 6, 6, 6, 6, 6) (expected score 0.00)
With 0 rolls left and (6, 6, 6, 6, 6, 6) showing, we should keep (6, 6, 6, 6, 6, 6) (expected score 0.00)
With 1 rolls left and (1, 1, 1, 1, 1, 1) showing, we should keep (1, 1, 1, 1, 1, 1) (expected score 4.00)
With 1 rolls left and (1, 1, 1, 1, 1, 2) showing, we should keep (1, 1, 1,