senior-game-math-engineer

name	senior-game-math-engineer
description	Design, audit, and tune casino game math for Stake-style game pipelines. Use when defining mode math, paytables, reel strips, feature frequencies, RTP/volatility/hit-rate targets, book weights, max-win controls, simulation plans, or release sign-off evidence.

Senior Game Math Engineer

Use this skill to produce simulation-backed math decisions and implementation guidance for slot-style games.

Workflow

1. Capture target spec before tuning.

• Collect game_id, mode list, target RTP by mode, volatility band, hit-rate band, max win cap, bonus frequency goals, and bet-unit assumptions.
• If constraints are missing, state assumptions explicitly and mark them as pending confirmation.

2. Build math model before runtime code.

• Break EV into components: base line wins, feature triggers, bonus rounds, multipliers, and retriggers.
• Keep currency-agnostic math in integer bet units and convert to display values only at UI/reporting layers.
• Check that each outcome path has bounded payout and deterministic trigger conditions.

3. Define mode architecture and RTP split.

• Allocate RTP contribution per mode and feature (base vs bonus).
• For selectable mode packs, verify weighted blend RTP remains within target range.
• Guard max win and tail-risk behavior with explicit caps or probability thresholds.

4. Run simulation and convergence checks.

• Use at least 1,000,000 spins for directional checks and 20,000,000+ for sign-off.
• Report standard error and confidence interval; reject sign-off if drift exceeds tolerance.
• Keep seeds reproducible and preserve run configuration for replay.

5. Validate generated artifacts.

• Verify book weights are positive, normalized, and mapped to valid state/outcome payloads.
• Recompute empirical RTP/hit-rate/volatility from generated books, not only from formula sheets.
• Confirm replay/event outputs do not mutate payout totals post-generation.

6. Prepare sign-off handoff.

• Deliver assumptions, math decomposition, simulation method, results table, and open risks.
• Include implementation deltas by file path and exact verification commands.

Project Commands

Use existing project verifiers first:

python3 Engine/scripts/verify_rtp.py <game_id> --spins 1000000
bash games/Darumas/verify_math.sh
bash games/Darumas/test_rtp_check.sh

When game-specific scripts differ, keep command shape the same and report the substituted paths.

Output Contract

When designing or auditing math, return:

1. Math Spec: assumptions, mode definitions, EV decomposition, target metrics.
2. Results: theoretical vs simulated RTP/hit-rate/volatility with deltas and pass/fail.
3. Patch Plan: exact files/functions to edit and why.
4. Verification: runnable commands and expected pass criteria.
5. Risks: unresolved constraints that block sign-off.

References

• references/workflow.md: detailed step-by-step execution order.
• references/metrics-and-thresholds.md: formulas, tolerances, and acceptance gates.
• references/signoff-template.md: final report template for handoff.

Execution Rules

• Distinguish theoretical RTP from simulated RTP in every report.
• Treat sub-million-spin conclusions as preliminary only.
• Flag contradictions between max-win marketing claims and math reality as blockers.
• Prefer deterministic, replayable evidence over narrative claims.