I have designed a lottery-style game and now need its full mathematical backbone. The core assignment is to calculate precise outcome probabilities so that the pay-table, player experience, and regulatory documents are all backed by solid numbers. Scope of work The game draws a fixed set of numbers from a larger pool, much like traditional lotteries, and awards several prize tiers. I need the complete breakdown of every winning combination, the exact jackpot odds, and the secondary prize probabilities. Alongside that, I want confirmation that the random number generator model delivers the expected statistical distribution across millions of simulated plays. Deliverables • A clear, step-by-step probability model of the draw mechanism • RTP / house-edge figure derived from the model • Separate tables for jackpot, mid-tier, and low-tier win odds • Verification notes (or a lightweight script) showing the RNG hits the theoretical targets • A short explanatory memo so non-technical stakeholders can follow the math Acceptance criteria The numbers must reconcile to 100 % total probability, the RTP must match the designed pay-table within ±0.01 %, and simulation outputs should remain inside a 95 % confidence interval of the theoretical curve after at least one million virtual plays. You may deliver the calculations in Excel, Google Sheets, or a well-commented Python or R notebook—whichever suits you best—as long as the logic is transparent and easy to audit.