Testing the human random number generator algorithm
I came across the "Human RNG" blog post today. Its author analyzes the distribution of random numbers given by 8500 students and proposes the following algorithm for generating approximately random numbers when querying humans for random numbers:
- Ask a person for a random number, n1.
- n1=1,2,3,4,6,9, or 10:
- Your random number is n1
- If n1=5:
- Ask another person for a random number (n2)
- If n2=5 (12.2%):
- Your random number is 2
- If n2=10 (1.9%):
- Your random number is 4
- Else, your random number is 5
- If n1=7:
- Ask another person for a random number (n2)
- If n2=2 or 5 (20.7%):
- Your random number is 1
- If n2=8 or 9 (16.2%):
- Your random number is 9
- If n2=7 (28.1%):
- Your random number is 10
- Else, your random number is 7
- If n1=8:
- Ask another person for a random number (n2)
- If n2=2 (8.5%):
- Your random number is 1
- Else, your random number is 8
In this blog post, I propose to use this algorithm and verify that it works as advertised by the author.
To do this, we will first generate random numbers according to how humans generate random numbers (using our computer). Then, we will implement the algorithm and see if it yields a uniform distribution of random numbers between 1 and 10.
Generating random numbers like a human, using a computer¶
Let's start by downloading the same data than the blog writer and extract the counts for each number.
import pandas as pd
def load_data():
"""Loads the data and returns counts for each number."""
df = pd.read_csv("https://git.io/fjoZ2")
s = df.pick_a_random_number_from_1_10.dropna().map(int)
s = s[~((s < 1) | (s > 10))]
counts = s.value_counts().sort_index()
percentage_counts = (counts / counts.sum() * 100)
return percentage_counts
import hvplot.pandas
percentage_counts = load_data()
percentage_counts.hvplot.bar(width=500)
Let's use scipy.stats to sample random numbers from the above arbitrary distribution.
We first build a discrete distribution object.
from scipy.stats import rv_discrete
xk, pk = percentage_counts.index.values, percentage_counts.values / percentage_counts.values.sum()
human_rn_distribution = rv_discrete(values=(xk, pk))
And then we can sample from this distribution:
human_rn_distribution.rvs(size=100)
array([9, 8, 1, 7, 1, 3, 7, 8, 7, 6, 5, 8, 7, 9, 8, 8, 7, 5, 7, 8, 4, 6,
1, 7, 2, 1, 7, 4, 3, 3, 1, 7, 6, 4, 5, 3, 7, 7, 1, 7, 7, 6, 9, 1,
1, 7, 6, 1, 8, 7, 7, 7, 6, 6, 3, 7, 8, 4, 3, 6, 9, 4, 5, 7, 1, 7,
2, 8, 6, 5, 6, 8, 5, 4, 7, 7, 7, 7, 7, 8, 8, 1, 2, 3, 7, 4, 7, 2,
8, 4, 7, 7, 7, 7, 7, 7, 7, 4, 7, 8])
We can now define a human_RNG function that returns a single number that follows the above number distribution:
def human_RNG():
return int(human_rn_distribution.rvs(size=1))
human_RNG()
2
To verify that this works correctly, we can sample a large number of values and check that our constructed histogram is similar to the data we started with.
pd.Series([human_RNG() for _ in range(10000)], name='counts').value_counts().sort_index().hvplot.bar(width=500)
This looks like the original distribution, so we can move on and implement the human random generator rule.
Implementing the human RNG rule¶
The rule stated above can be transcribed in the following function:
def random_number_1_10():
"""Generates random numbers, assuming it gets input numbers generated by humans."""
n1 = human_RNG()
if n1 in [1, 2, 3, 4, 6, 9, 10]:
return n1
elif n1 == 5:
n2 = human_RNG()
if n2 == 5:
return 2
if n2 == 10:
return 4
else:
return 5
elif n1 == 7:
n2 = human_RNG()
if n2 in [2, 5]:
return 1
elif n2 in [8, 9]:
return 9
elif n2 == 7:
return 10
else:
return 7
elif n1 == 8:
n2 = human_RNG()
if n2 == 2:
return 1
else:
return 8
random_number_1_10()
3
Now the interesting part: we evaluate the procedure by drawing a large amount of numbers from it and will (hopefully) find a flat distribution of numbers between 1 and 10.
pd.Series([random_number_1_10() for _ in range(50000)], name='counts').value_counts().sort_index().hvplot.bar(width=500)
Neat. We find something that is almost flat. So the advertised procedure works as announced by the author.
This is good to know if you ever run out of pseudo random number generators and computers ^^.
This post was entirely written using the Jupyter Notebook. Its content is BSD-licensed. You can see a static view or download this notebook with the help of nbviewer at 20190703_HumanRandomNumbers.ipynb.
