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RNG Technical Specification: Crash Minimal

Cert-lab submission document for the Crash Minimal game. This spec accompanies packages/rng-core/src/index.ts (shared commit-reveal primitives), games/crash-minimal/src/outcome.ts (game-specific mapping), and the test artefacts under ./rng-test-vectors.md + ../fixtures/rng-test-vectors.json.

Certified against rng-core commit: <CERTIFIED-AGAINST-RNG-CORE: pending-first-submission> , filled in at GLI-11 submission time with the exact SHA of packages/rng-core/src/ this spec was certified against. Enforced by scripts/export-cert-packet.ts which pins the SHA into the submission zip.

Submission status: pre-cert. Not yet submitted to any lab. The derivations below track the production code path; the statistical test runs remain open before GLI-11 submission.

Audience: iTech Labs, BMM, GLI, internal security review, independent audit.

Companion documents:

1. Scope

This document specifies the random number generation used to determine round outcomes for Crash Minimal. It covers:

  • The shared commit-reveal scheme (inherited from packages/rng-core, documented in provably-fair.md).
  • The Crash-Minimal-specific derivation of crashMultiplier from the 52-bit uniform u.
  • The house-edge injection point.
  • The maxMultiplier clamp.
  • The statistical test plan a cert lab would run.

Primitives (HMAC-SHA256, roundHmac, generateSeedPair, verifyServerSeed) are shared with every other game and are specified in packages/rng-core + the platform-wide provably-fair doc; this spec does not re-derive them.

2. Classification

Attribute Value
RNG class Cryptographic pseudo-random (CSPRNG-seeded, deterministic-derived)
Entropy source Operating-system CSPRNG (shared with rng-core)
Entropy consumption per round 0 bytes, seed reused across rounds via incrementing nonce
Outcome bit-width 52 bits of HMAC output consumed per round
Outcome domain crashMultiplier ∈ [1.00, maxMultiplier], two-decimal precision
Player-influenced? Yes, player/operator may provide clientSeed

3. Derivation

Implemented in games/crash-minimal/src/outcome.ts.

hmac  = HMAC_SHA256(serverSeed, clientSeed || ':' || nonce)      // 256 bits
bits52 = first 52 bits of hmac as unsigned integer               // [0, 2^52)
u_raw  = bits52 / 2^52                                           // uniform[0, 1)

if u_raw < houseEdge:
  crashMultiplier := 1.00                                         // house-bust branch
else:
  u := (u_raw - houseEdge) / (1 - houseEdge)                      // rescale to uniform[0, 1)
  raw := floor(100 / (1 - u)) / 100                               // two-decimal multiplier
  crashMultiplier := clamp(raw, 1.00, maxMultiplier)

Why 52 bits: Number's safe-integer range is 2^53 - 1, so a 52-bit integer converted via Number(BigInt) is lossless. Using 53 bits would risk a precision edge case; using 32 bits would quantise the tail coarsely.

4. House-edge injection

The u_raw < houseEdge pre-roll branch is the standard Bustabit-family approach. It:

  1. Preserves the 1/K survival tail above the bust point, so RTP is identical for every cashout choice (see par-sheet.md).
  2. Keeps the proof verification one-branch-free for the non-bust path , external verifiers can recompute u_raw and check crashMultiplier without knowing the implementation.
  3. Is a visible single parameter (houseEdge), auditable from OperatorGameConfig.configJson at any time.

5. Bias analysis

  • 52-bit quantisation of uniform[0,1): the uniform is bits52 / 2^52, exact rational with 2^52 possible values. No rounding bias. Any implementation that uses Math.random() or JavaScript Number directly for entropy derivation is non-compliant.
  • floor(100 / (1 - u)) / 100 mapping: introduces two-decimal quantisation of the tail. At u → 1 the raw multiplier approaches infinity; the maxMultiplier clamp bounds this. Probability of clamp firing is (1 − houseEdge) / maxMultiplier, which at the default maxMultiplier = 1000 is < 0.001.
  • No modular reduction in the outcome path, unlike Ketapola Dice.

6. Statistical test plan

Test Tool Pass criterion
Bust-rate audit built-in |observed − houseEdge| / √(houseEdge·(1−houseEdge)/N) < 3σ, N = 10⁷
Tail goodness-of-fit chi-square p > 0.01, N = 10⁷, bucketed multipliers
RTP per cashout bucket tests/games/crash-minimal/rtp-regression.spec.ts each bucket within ±0.5 pp of 1 − houseEdge
Determinism tests/games/crash-minimal/rng-test-vectors.spec.ts (TBD) exact match on fixed vectors

7. Failure modes and mitigations

Failure Impact Mitigation
Entropy source not ready at boot randomBytes blocks /readyz fails closed; shared with every game via rng-core
serverSeed leaked pre-reveal Adversary can precompute for that session Seed is AES-GCM encrypted at rest; no raw seed in any log; session-bounded blast radius
floor() / Math.min drift across engines Divergent outcomes across JS runtimes games/crash-minimal/src/outcome.ts uses BigInt for the 52-bit read then a single Number cast; Math.floor and Math.min are IEEE-754-specified deterministic operations
maxMultiplier misconfigured at 1.01 Effectively constant-multiplier game Schema enforces maxMultiplier ≥ 1.01 (allowed but silly); operators should default to 1000+ per this spec

8. Reference implementation

Split across two files:

packages/rng-core/src/index.ts: shared primitives (roundHmac).

games/crash-minimal/src/outcome.ts: Crash-specific mapping:

  • determineCrashOutcome(ctx, config): the function specified in §3.
  • verifyCrashOutcome(ctx, config, claimed): symmetric to determineCrashOutcome, compares to floating-point tolerance.
  • RNG_VERSION = 'crash-minimal-rng-v1': stamped on every Round.

Both files are change-gated: CI rejects any PR touching packages/rng-core/src/ without a CERT-ATTEST-CORE: line, or any file under games/crash-minimal/src/{outcome,settle,config}.ts without a CERT-ATTEST-CRASH_MINIMAL: line. See change-management.md.

9. Artefacts for cert-lab submission

Artefact Location
Shared RNG primitives packages/rng-core/src/index.ts
Crash outcome mapping games/crash-minimal/src/outcome.ts
RNG spec (this doc) games/crash-minimal/docs/rng-spec.md
PAR sheet games/crash-minimal/docs/par-sheet.md + par-sheet.json
Test vectors games/crash-minimal/docs/rng-test-vectors.md + fixtures/rng-test-vectors.json (TBD)
Regression test tests/games/crash-minimal/rtp-regression.spec.ts
Commit-reveal spec (platform) docs/provably-fair.md
Change-management policy (platform) docs/change-management.md
Audit trail schema apps/rgs-server/prisma/schema.prisma (Round, GameSession, WalletCall models)

Run bun scripts/export-cert-packet.ts crash-minimal to assemble these into a single self-contained zip for GLI-11 submission.

10. Specification version

Field Value
Spec version 0.1.0-draft
Status Pre-cert, tracking games/crash-minimal/src/
Last reviewed 2026-04-24