代写Discrete Math、histograms留学生代做、代写Java/c++程序语言、代做Python

日期：2019-05-13 10:17

5/10/2019 Spring 2019 Discrete Math/Reference Materials/Pigs.sagews

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Spring 2019 Discrete Math/Reference Materials/Pigs.sagews

Date 2019-05-10T23:11:26

Project aa288497-fcac-43f6-91ba-dfd1aa1c10ed

Location Spring 2019 Discrete Math/Reference Materials/Pigs.sagews

Original file Pigs.sagews

1 ### Pass the Pigs

2 #Frequencies from the histograms made on Monday 5/6/2019

3 ## Dot, NoDot, Razor,Trottor, Sounter, Leaning Jowler, Other

4 F=matrix([[7,8,26,5,2,0,3], [37, 52, 55, 9, 4, 1,4], [30,22, 29, 3, 0, 0,0], [33, 44, 34, 4, 0,0,0], [29, 34, 40, 12, 1, 0,0],

6 ## Score function: Feel free to modify or reimplement this code however you want to.

8 def Score (x, roll):

9 if roll == [1,1]: ## sider with dots showing

10 return x+1

11 elif roll == [2,2]: ## sider with nodots showing

12 return x+1

13 elif roll == [3,3]: ## double razor

14 return x+ 20

15 elif roll == [4,4]: ## double trotter

16 return x+20

17 elif roll == [5,5]: ## double snouter

18 return x+40

19 elif roll == [6,6]: ## double leaning jowler

20 return x+60

21 elif roll == [1,2]: #pig out

22 return 0

23 elif roll == [1,3]: # razor

24 return x + 5

25 elif roll == [1,4]: # trotter

26 return x + 5

27 elif roll == [1,5]: #snouter

28 return x + 10

29 elif roll == [1,6]: # leaning jowler

30 return x + 15

31 elif roll == [2,3]: # razor

32 return x + 5

33 elif roll == [2,4]: # trotter

34 return x + 5

35 elif roll == [2,5]: #snouter

36 return x + 10

37 elif roll == [2,6]: # leaning jowler

38 return x + 15

39 elif roll == [3,4]: # razor plus trotter

40 return x + 5+5

41 elif roll == [3,5]: #razor plus snouter

42 return x + 5+10

43 elif roll == [3,6]: #razor plus leaning jowler

44 return x + 5+ 15

45 elif roll == [4,5]: #trotter plus snouter

46 return x + 5+10

47 elif roll == [4,6]: #trotter plus leaning jowler

48 return x + 5+ 15

49 elif roll == [5,6]: #trotter plus leaning jowler

50 return x + 10+ 15

51 elif (roll[0] == 7) or (roll[1] == 7 ): #other rolled, reroll with no penalty

52 return x

5/10/2019 Spring 2019 Discrete Math/Reference Materials/Pigs.sagews

file:///Users/billey/Downloads/Pigs.sagews.html 2/5

53 elif roll[0]>roll[1]:

54 return Score(x,[roll[1],roll[0]])

55 counts=[sum(F.column(j)) for j in range(6)] # not counting other rolls

56 counts

[276, 363, 413, 109, 35, 6]

57 P=[counts[j]/sum(counts) for j in range(6)]

58 [float(p) for p in P]

[0.22961730449251247, 0.3019966722129784, 0.34359400998336104, 0.09068219633943428, 0.029118136439267885, 0.004991680532445923]

59 sum(P)

60 random()

0.7302587689166408

61 CDF = [sum(P[i] for i in range(j)) for j in range(7)]

62 [float(c) for c in CDF] #cumulative distribution function for 7 possibilities is given by list of 7 numbers

[0.0, 0.22961730449251247, 0.5316139767054908, 0.8752079866888519, 0.9658901830282862, 0.9950083194675541, 1.0]

63 def pigroll():

64 x = random()

65 roll =-1

66 for i in range(7):

67 if x>CDF[i]:

68 roll = roll + 1

69 return roll

70 [pigroll() for i in range(100)]

[1, 2, 4, 2, 1, 1, 1, 0, 2, 2, 1, 3, 2, 1, 1, 2, 1, 1, 3, 2, 1, 1, 0, 1, 2, 0, 1, 0, 0, 1, 3, 2, 1, 1, 0, 2, 3, 0, 1, 3, 1, 1, 0, 1, 1

4, 1, 1, 2, 1, 2, 0, 0, 0, 1, 2, 0, 0, 2, 2, 2, 2, 4, 3, 1, 2, 1, 1, 2, 0, 2, 2, 2, 1, 1, 5, 5, 1, 1, 2, 2, 0, 3, 1, 2, 3, 0, 2, 0, 2,

1, 1, 2, 2, 4, 3, 2, 3]

71 Test = [0 for i in range(6)] ## Looks like we are getting some numbers larger and some smaller than they should be

72 for i in range(1000):

73 temp = pigroll()

74 Test[temp] = Test[temp]+1

75 Test

[247, 307, 321, 95, 27, 3]

76 [float(p) for p in P]

[0.22961730449251247, 0.3019966722129784, 0.34359400998336104, 0.09068219633943428, 0.029118136439267885, 0.004991680532445923]

77 Test2 = [0 for i in range(6)] ## looks better!

78 for i in range(10000):

79 temp = pigroll()

80 Test2[temp] = Test2[temp]+1

81 Test2

[2257, 3060, 3444, 862, 339, 38]

82 roll = [pigroll()+1, pigroll()+1]

83

84 roll, Score(3, roll)

([1, 2], 0)

85 Record_Scores=[]

86 for i in range(100):

87 ## simulation of rolling two pig dice

88 roll = [pigroll()+1, pigroll()+1]

89 Record_Scores.append(Score(0, roll))

90 max(Record_Scores)

20

91 Record_Scores[3]

0

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92 Totals = [0 for i in range(61)]

93 for i in Record_Scores:

94 Totals[i]=Totals[i]+1

95 Totals

[12, 17, 0, 0, 0, 45, 0, 0, 0, 0, 7, 0, 0, 0, 0, 2, 0, 0, 0, 0, 17, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

96 Q=[Totals[i]/100 for i in range(61)]

97 ## probability of +0, +1, +2 ,...

98 Q

[3/25, 17/100, 0, 0, 0, 9/20, 0, 0, 0, 0, 7/100, 0, 0, 0, 0, 1/50, 0, 0, 0, 0, 17/100, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

99 x=var('x')

102 ##What is the formula for expected score?

103 ### E[NextScore(x)]= sum over all possible values of Score(x, roll) times prob it occur.

104 ExpectedScore=0+sum((x+i)*Q[i] for i in range(1,61))

105 L=ExpectedScore

106 L

22/25*x + 341/50

107 plot(L , (x,0,50))

108 plot(L, (x,0,60))+ plot(x , (x,0,60), color='red')

5/10/2019 Spring 2019 Discrete Math/Reference Materials/Pigs.sagews

file:///Users/billey/Downloads/Pigs.sagews.html 4/5

109 float((341/50)*(25/3))

(19, 23.54)

5/10/2019 Spring 2019 Discrete Math/Reference Materials/Pigs.sagews

file:///Users/billey/Downloads/Pigs.sagews.html

116 def sara_billey_slow_and_steedy (opponentscore, myscore, myturnscore,round):

117 if myturnscore>10:

122 sara_billey_slow_and_steedy (99,10,2,4)

123 [sara_billey_slow_and_steedy(99,10,i,4) for i in range(5,15)]

[True, True, True, True, True, True, False, False, False, False]

generated 2019-05-10T23:11:26 on CoCalc