Board and Hazard Logic
The 4×4 board hides a fixed number of hazards uniformly among complete layouts satisfying a specific graph rule. The queen hazard graph, joining equal rows, equal columns, or chess diagonals, has exactly one connected component of size three, with all other components having size one. Cells are numbered row-major 1–16. A complete layout is sampled uniformly from the published constraint support of the selected count and stays fixed for the round.
Pricing and Probability
Each selected safe cell is priced from the exact posterior over consistent layouts. The gross value starts at 0.97 times stake and becomes the current value divided by that cell's safe probability. Known-safe cells leave value unchanged; proven hazards are disabled. After safe picks, only compatible layouts remain, and each cell shows its exact conditional safety probability. The live gross quote is 0.97 times the original support count divided by the surviving support count.
Controls and Modes
The demo uses a captured virtual stake of 10, 20, 50, or 100. Settings and refill are locked while active. You may collect after at least one safe reveal. Individual prospective values above 1,000 times the original stake are disabled. A choice with a prospective quote above 1,000× is blocked without changing state. If no uncertain cell remains after a safe pick, settlement is automatic.
Payout and Settlement
A hazard returns zero. The displayed multipliers are gross coin returns, not profit. Every revealed-information strategy has a 97% expected gross return in the fair support model; this is not a win probability. The exact payout math and every mode are recorded in the source-bound mathematical evidence. Fractional carry persists through settlement, manual refill, and reload.
Wallet and Restoration
The demo starts with an initial balance of 1000 virtual coins. If the idle balance drops below 10, you can manually restore it to exactly 1000, preserving any fractional change. An unfinished round ends without refund or resume upon reload. The settled balance, including zero, persists locally.
Mathematical Evidence
The following table shows exact expected returns and simulation measurements for various hazard counts and depths. Simulation measurements are supporting sample observations, not the mathematical payout law.
| Hazards | Depth | Exact RTP | Measured RTP |
|---|---|---|---|
| 3 | 1 | 97.00000000000017% | 96.974125% |
| 4 | 2 | 96.99999999999996% | 96.893985% |
| 5 | 3 | 97% | 97.248705% |
Frequently asked questions
How is the hazard layout determined?
One complete 4×4 hazard layout is sampled uniformly from the published constraint support of the selected count and stays fixed. It is never redrawn during the game.
What happens if the balance is low?
If the idle balance is below 10, you can manually restore it to exactly 1000, preserving any fractional change. This is a manual action, not automatic replenishment.
Is the 97% return guaranteed?
Every revealed-information strategy has a 97% expected gross return in the fair support model; this is not a win probability. Simulation measurements are supporting sample observations, not the mathematical payout law.
