CHSH game example error: random.randint(0, 2) generates invalid inputs

[neeco1991]

URL to the relevant course

https://quantum.cloud.ibm.com/learning/en/courses/basics-of-quantum-information/entanglement-in-action/qiskit-implementation#qiskit-implementation-1

Select all that apply

• new content request
• typo
• code bug
• out-of-date content
• broken link
• other

Describe the fix or the content request.

I encountered an issue in the CHSH game code example where the input bits $x$ and $y$ are generated using an incorrect range. The code currently uses:

x, y = random.randint(0, 2), random.randint(0, 2)

But random.randint(0, 2) ranges from 0 to 2, which doesn't make sense for a bit.
in fact, if you run the whole code, you get:

Fraction of games won: 0.617

Which is wrong for my understanding. I believe the correct code sould be:

x, y = random.randint(0, 1), random.randint(0, 1)

With this fix, the code correctly outputs a win fraction of ~0.85.

For new content requests - if the request is accepted, do you want to write the content?

I will write (or already have written) a draft of the proposed content

[kalde]

@christopherporter1 It is possible that the randint method behaves differently when imported from the numpy library or standard Python random library. Perhaps, the pr related to this issue #4474 has introduced a bug depending on the imported library.
Currently the notebook (https://github.com/Qiskit/documentation/blob/main/learning/courses/basics-of-quantum-information/entanglement-in-action/qiskit-implementation.ipynb) mentions: from numpy import pi, random

from numpy: see https://numpy.org/doc/2.3/reference/random/generated/numpy.random.randint.html
Return random integers from low (inclusive) to high (exclusive).

from python standard: https://docs.python.org/3/library/random.html#random.randint
Return a random integer N such that a <= N <= b. Alias for randrange(a, b+1).