Board Layout and Hazard Constraints
The game uses a 4 by 4 grid containing 16 cells numbered 1 through 16 in row-major order. A fixed number of hazards are hidden uniformly among all complete layouts satisfying a specific constraint. The constraint is defined by a queen hazard graph: cells are joined if they share the same row, same column, or a chess diagonal. This graph must have exactly one connected component of size three, with all other components being isolated single cells.
One complete hazard layout is sampled uniformly from the published constraint support of the selected hazard count at round start and stays fixed for that round. It is never redrawn. After each safe pick, the set of compatible layouts shrinks, and each cell updates to show its exact conditional safety probability based on the remaining consistent layouts.
Pricing and Gross Value Calculation
Each selected safe cell is priced from the exact posterior over consistent layouts. The gross value starts at 0.97 times the original stake and updates as the game progresses. The current value is calculated as the current value divided by the safe probability of the selected cell.
Known-safe cells leave the value unchanged, while proven hazards are disabled and cannot be selected. The live gross quote is calculated as 0.97 times the original support count divided by the surviving support count. This quote represents the gross coin return, not profit. A hazard returns zero, ending the round.
Controls, Modes and Settlement Rules
Capturing a stake locks settings and refill until settlement. The available stakes are 10, 20, 50, or 100 virtual coins. Collection is allowed after at least one safe reveal. If a choice has a prospective quote above 1,000 times the original stake, it is blocked without changing state. Automatic settlement occurs only when no eligible uncertain move remains after a safe pick.
If no uncertain cell remains after a safe pick, settlement is automatic. Every revealed-information strategy has a 97% expected gross return in the fair support model, which is a mathematical expectation, not a win probability. The hidden layout is never redrawn during the round.
Expected Return and Math Evidence
The expected return is exactly 97% across various hazard counts and collection depths. Simulation data supports this mathematical expectation:
- 3 hazards: 1,000,000 rounds show an exact return of approximately 97.0000%, with measured results around 96.97%.
- 4 hazards: 1,000,000 rounds show an exact return of approximately 97.0000%, with measured results around 96.97%.
- 5 hazards: 1,000,000 rounds show an exact return of 97.0000%, with measured results around 97.10%.
These measured percentages are sample observations from specific strategies and may vary slightly from the exact theoretical value due to simulation variance.
Local Wallet and Balance Management
The demo uses a local wallet with an initial balance of 1,000 virtual coins. The balance persists through settlement, manual refill, and reload. Fractional changes are preserved. If the idle balance falls below 10 coins, you can manually restore it to 1,000 coins, preserving any fractional change.
Unfinished rounds receive no refund upon reload. During active play, stake, mode, and refill controls are locked, but sound and specific game-specific choices remain available. The settled balance includes zero and persists locally.
Privacy and Site Facts
This demo uses localStorage for settled balance and fractional carry. This does not establish anonymity or exclude other processing. The template declares a Google Fonts stylesheet; actual full-site network capture remains pending. There is no account flow, no payment flow, and virtual coins have no cash value. The intended audience is 18+, which is a guide policy, not a universal legal age or implemented age gate.
Frequently asked questions
How is the hazard layout determined?
One complete 4x4 hazard layout is sampled uniformly from the published constraint support of the selected count at the start of the round. The layout stays fixed and is never redrawn. The constraint requires the queen hazard graph to have exactly one connected component of size three, with all other components being single cells.
When can I collect my winnings?
You can collect after at least one safe pick. If no uncertain cell remains after a safe pick, settlement is automatic. Choices with a prospective quote above 1,000 times the original stake are blocked until the state changes.
What happens to my balance if I reload the page?
An unfinished round ends without refund or resume. The settled balance persists, including any fractional carry. If your idle balance drops below 10 coins, you can manually restore it to 1,000 coins, preserving the fractional change.
