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  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)
  17. 	return total
  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
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Standard input is empty
stdout
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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,
https://ideone.com/RLAgsU
language:
Python (cpython 2.7.16)
created:
10 years ago
visibility:
public

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