#Vault Breakers: Super Score — Exact Results, draft-v0.1

SUPERSEDED by draft-v0.2. Retained unchanged. This document records the APPROVED unbalanced reference baseline of 2026-08-19, including the two Bonus Buy prices that deliberately did not balance. Nothing in it is rewritten by later tuning.

DEV ONLY · NOT FOR PRODUCTION · NOT FOR CERTIFICATION. Everything in this document is a closed form. Nothing here is sampled, and nothing sampled appears in it. Monte Carlo results live in ../simulation/draft-v0.1.md and are never mixed in here.

#Command

cd /Users/admin/kiro/backend
go test -count=1 -v -run TestExactSnapshotReport \
    ./libs/mathengine/games/vault_breakers_super_score

#Method boundary — what is exact, and why

The draw model is what makes any of this exact. DrawModel: independent_cells draws all 30 cells independently from one weight table, on the initial grid and on every refill alike. Two consequences follow from that alone, not from any approximation:

1. The number of copies of a symbol on a snapshot is Binomial(30, p).
2. Conditional on a snapshot holding n scatter-class symbols, the number of Super Scatters among them is Binomial(n, q) with q the Super share of the class.

So the first snapshot's regular-symbol RTP, its hit rate, the trigger probability and the instant-prize expectation are sums, not samples. No simulation can make them more true.

What is NOT exact, and is not claimed here. A later cascade snapshot holds survivors from the one before it, so its composition is no longer i.i.d.; charge values are drawn after the initial grid; and free spins are a stochastic sequence. mathengine.CheckEnumerable refuses this config for exactly those reasons, and that refusal is respected rather than worked around. Everything involving the cascade or the feature is measured.

#Per-cell probabilities

Weights are out of 50,000, read from the strips the engine executes.

Scatter class = SCATTER + SUPER_SCATTER = 1,140 / 50,000 = 0.022800. Super share of the class q = 16 / 1,140 = 0.01403509.

#Exact results, one i.i.d. snapshot

The hit rate is computed by walking the joint distribution of the eight symbols' counts, not by multiplying per-symbol probabilities: the counts are multinomial and negatively correlated, and an independence approximation would be quietly wrong in the third decimal.

#Charge pools

#What this does and does not establish

• These are the engine's own arithmetic, produced by a calculator written against the same config the engine executes. They are internally exact. They are not independent verification, and this document is not certification.
• The exact figures above cover one snapshot. A spin is one or more snapshots, so the whole-game figures are strictly larger and are measured, not derived from these.
• The Super Scatter expectation per snapshot is exact; its contribution per spin depends on how many snapshots a spin produces, which is measured.