https://www.notion.so/davidclarance/Stable-and-fast-randomization-using-hash-spaces-ce9357ae742b4e30b67a34fe87fee84e

stable_randomization.py

import hashlib

probability_assignments = {"Control": 50, "Variant 1": 30, "Variant 2": 20}

random_customer_ids = ["Customer1", "Customer2", "Customer3", "Customer4"]


def get_hash(customer_id):
    hash_object = hashlib.md5(customer_id.encode())
    return hash_object.hexdigest()[:10]


def get_integer_representation_of_hash(customer_id):
    hash_value = get_hash(customer_id)
    return int(hash_value, 16)


def get_assigned_bucket(customer_id, total_buckets):
    hash_value = get_integer_representation_of_hash(customer_id)
    return hash_value % total_buckets


def divide_space_into_partitions(prob_distribution):
    partition_ranges = []
    start = 0
    for partition in prob_distribution:
        partition_ranges.append((start, start + partition))
        start += partition
    return partition_ranges


def assign_groups(customer_id, partitions):
    hash_value = get_assigned_bucket(customer_id, 100)
    for idx, (start, end) in enumerate(partitions):
        if start <= hash_value < end:
            return idx
    return None


partitions = divide_space_into_partitions(
    prob_distribution=probability_assignments.values()
)

groups = {
    customer: [
        get_hash(customer),
        get_integer_representation_of_hash(customer),
        get_assigned_bucket(customer, 100),
        assign_groups(customer, partitions),
    ]
    for customer in random_customer_ids
}
groups

You can run a simulation to test if the distribution is correct:

import uuid
from collections import Counter

n_customers = 1000000

random_customer_ids = [uuid.uuid4().hex for _ in range(n_customers)]

partitions = divide_space_into_partitions(
    prob_distribution=probability_assignments.values()
)

groups = {
    customer: list(probability_assignments.keys())[assign_groups(customer, partitions)]
    for customer in random_customer_ids
}

{group: count / n_customers for group, count in Counter(groups.values()).items()}

This gives the following output: