找到骰子的分布

Question

Write a function called distribution_of_rolls that takes one number — the number of times to roll two dice — and prints the distribution of values of those rolls in the form shown below.
for example:

 Distribution of dice rolls 2: 7 ( 3.5%) ******* 3: 14 ( 7.0%) ************** 4: 15 ( 7.5%) *************** 5: 19 ( 9.5%) ******************* 6: 24 (12.0%) ************************ 7: 35 (17.5%) *********************************** 8: 24 (12.0%) ************************ 9: 28 (14.0%) **************************** 10: 18 ( 9.0%) ****************** 11: 9 ( 4.5%) ********* 12: 7 ( 3.5%) ******* ----------------------------- 200 rolls

My code somewhere is wrong. It can not print out.

def roll():
        return randrange(1,7) + randrange(1,7)

def distribution_of_rolls(n:int):
        result=({i,0} for i in range(2,13,1))
        c=''
        result=list(result)
        for i in range(n):
              a = roll()
              print(a)
              result[a]= result[a] + 1
              print(result)
        for i in range(2,13,1):
            b=(result[i]/float(n)) * 100
        for i in range(int(math.floor(n))):
            c = c + '*'
            d = "{0:0.1f}%".format(b)
        print("{0:2d}:   {1:5d} ({2:s})  {3:s}".format(i, result[i], d, c)
        print("-------------------------")
        print("{0:10d} rolls".format(n))


    distribution_of_rolls(20)

Answer 1

In probabilitic modelling, you can compute the sum of independant laws using caracteristic functions. Even with 50 dice, it's instantaneous on my computer using the OpenTurns platform.

import openturns as ot
d = 2 #number of dice

#define dice distribution with possible values: 1, 2, 3, 4, 5, 6
dice_distribution = ot.UserDefined([[i] for i in range(1,7)]) 

# create same distribution d times then sum
sum_distribution = sum([dice_distribution] * d) 

# create a sample of size 200
Sample = sum_distribution.getSample(200) 

If you want to count each realisation:

import numpy as np
unique, counts = np.unique(Sample, return_counts = True)
print(unique)
print(counts/200) # frequency

>>>[ 2.  3.  4.  5.  6.  7.  8.  9. 10. 11. 12.]
   [0.05  0.05  0.09  0.115 0.13  0.175 0.125 0.115 0.07  0.04  0.04 ]

You can also draw the probability density function (PDF) using OpenTurns viewer:

import openturns.viewer as otv 
graph = sum_distribution.drawPDF()
otv.View(graph)

You can also retrieve the values:

print(sum_distribution)
>>> UserDefined(
     {x = [2], p = 0.0277778},
     {x = [3], p = 0.0555556},
     {x = [4], p = 0.0833333},
     {x = [5], p = 0.111111},
     {x = [6], p = 0.138889},
     {x = [7], p = 0.166667},
     {x = [8], p = 0.138889},
     {x = [9], p = 0.111111},
     {x = [10], p = 0.0833333},
     {x = [11], p = 0.0555556},
     {x = [12], p = 0.0277778}
   )

With d = 50 dice, the density will be more like a Gaussian distribution:

Answer 2

Use more functions so that it becomes easier to debug. Eg,

def roll():
  return random.randrange(1,7) + random.randrange(1,7)

def create_data(nrolls):
  data = collections.defaultdict(int)
  for _ in range(nrolls):
    data[roll()] += 1
  return data

fmtstart = "{dsum:>2}:{count:>6} ({pct:4.1f}%)"

def format_data(data):
  result = []
  total = float( sum(data.values()) )
  tuples = sorted( data.items() )
  for k,v in tuples:
    start = fmtstart.format(dsum=k,count=v,pct=100*v/total)
    end = " " + "*"*v
    result.append(start + end)
  return "\n".join(result)

print( format_data( create_data(200) ) )

Answer 3

from random import randrange

def roll():
        return randrange(1,7) + randrange(1,7)

def distribution_of_rolls(n:int):
    results = {i:0 for i in range(2,13)}
    for i in range(n):
        results[roll()] += 1
    for i in range(2,13):
        occurrences = results[i]
        percentage = (occurrences/float(n)) * 100
        bar = occurrences * "*"
        print("{0:2d}: {1:5d} ({2:4.1f}%)  {3:s}".format(i, occurrences, percentage, bar))
    print("-------------------------")
    print("{0:9d} rolls".format(n))


distribution_of_rolls(200)