Hash Bucket A/B Assignment

Background

Deterministic A/B assignment hashes each unit (user, session, cookie) into a stable bucket. The same unit always gets the same arm — that's what makes the experiment persistent for each user across visits, sessions, devices.

Problem statement

Implement assign(unit_id, experiment_id, pct_a=0.5). Hash the tuple (unit_id, experiment_id) deterministically; treat the first byte of the SHA-256 digest as a uniform value in $[0, 256)$; assign to "A" if the byte / 256 < pct_a, otherwise "B".

Input

• unit_id — str, the assignment unit.
• experiment_id — str, identifies the experiment.
• pct_a — float in $[0, 1]$, fraction of traffic to arm A (default 0.5).

Output

Returns "A" or "B".

Examples

Example 1 — same input → same arm

Input:  ("user_1", "exp_1")
Output: same arm every call

Example 2 — different experiments give different arms

Input:  fixed user, varying experiment_id
Output: across 20 experiments, both arms are observed

Example 3 — roughly 50/50 at default pct_a

Input:  1000 distinct users
Output: count in each arm ≈ 500 (within ±100)

Example 4 — pct_a = 0 → all B; pct_a = 1 → all A

Constraints

• Deterministic: same (unit_id, experiment_id) → same arm across runs.
• Hashing scheme: SHA-256(unit_id + "|" + experiment_id), take first byte.
• pct_a in $[0, 1]$.

Notes

• Why include experiment_id in the hash. Without it, the same user would land in the same arm for every experiment — destroying the independence between concurrent experiments.
• Bucketing granularity. Using only the first byte gives 256 buckets — enough for any reasonable split. For very fine splits (0.01% canaries), use more bytes.