One seed, a thousand honest replays
Design notes on the simulator's randomness: why replication streams get their own hashed seeds, and why the gamma sampler throws instead of guessing.
The Monte Carlo layer needs 1,000 independent replications that reproduce bit-identically from one seed — the odds the game shows a player must be the same odds every time, on every machine. Two decisions worth recording.
Per-replication streams: hash, don't chain
Each replication i gets its own RNG stream seeded by a hash of (seed, i): add a golden-ratio Weyl stride (i times 0x9E3779B9), then a two-round avalanche mixer with low-bias constants.
Why not simpler options:
- Feeding seed+i directly into the base generator leaves adjacent replication streams correlated through its additive state increment — replication 5 and replication 6 would share structure exactly where independence matters most.
- Chaining (derive stream i's seed by drawing from stream i−1) makes replication i depend on having drawn i−1 first, which forecloses ever running replications in parallel.
The Weyl stride separates the indices; the avalanche decorrelates nearby inputs. Every number in the odds table reproduces from the seed, and any replication can be regenerated alone.
Fail loud in the samplers
Two guard decisions in the distribution code:
- The normal sampler draws from a half-open range that includes zero, and the log inside Box–Muller needs a strictly positive input — so it feeds 1−u, not u. A one-character bug class, eliminated by construction.
- The gamma sampler throws a RangeError below shape 1 rather than shipping the boost that would handle it. The Beta-PERT parameters the game uses guarantee the shape stays at or above 1 — and a silent wrong-tail bug in the luck distribution would be strictly worse than a crash. If the parameters ever change, the sampler refuses loudly instead of skewing the odds quietly.
The theme in both: in a simulation whose product is a probability, randomness infrastructure is a correctness surface, not plumbing.