How to calculate distance (similarity) between two continuous random samples with different length using python?

Question

I want to calculate similarity or distance between two sample sets.
Each set indicates game play times of a user.
For example, suppose there are two users and the first user (X1) play five times, and the other one play four times as four times as follows.

X1={1,2,3,1,2}
X2={1,2,3,4}

I want to calculate similarity or distance between X1 and X2 using python. How can I calculate it?

Note 1. the order is not important.
I mean, {1,2,3,4} and {4,1,2,3} should be considered as the same set.

Note 2. element (ie, 1, 2, 3, 4) is not fixed. I mean, the play time is a continuous variable.

Answer 1

Well, you could use Kolmogorov-Smirnov 2 samples test, from https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.ks_2samp.html , described here

It should work for samples of different size.

In Python, eg

import scipy.stats as st    

x = np.random.normal(0,1,1000)
y = np.random.normal(0,1,1000)
z = np.random.normal(1.1,0.9,1000)

st.ks_2samp(x, y)
st.ks_2samp(x, z)

It returns D statistics (as well as p-value), which is the absolute max distance (supremum) between the CDFs of the two samples. This is your distance. See here for details