The scoring mechanism relies on the sum of the greatest common divisors (GCD) of all unordered hazard pairs being a perfect square. Probabilities are calculated using exact posterior safe probabilities, and gross returns are divided by these probabilities upon a safe reveal.
How does the scoring and probability work?
The game selects a subset of hazards from the 16 printed labels. The support is restricted to complete subsets where the sum of the GCD of all label pairs is a perfect square.
- Initial Value: The initial quoted value is 97% of the captured stake.
- Reveal: Each successful safe reveal divides the current gross value by its exact posterior safe probability.
- Probability 1: If a reveal has a probability of 1, the gross value remains unchanged.
For each complete hazard subset, sum the greatest common divisor of every unordered pair of printed labels. Only a perfect-square sum qualifies; layouts are sampled uniformly from these qualifying subsets.
What are the controls and modes?
The demo offers specific controls and modes for Pair Gcd Square Mines:
- Stakes: Selectable stakes are 10, 20, 50, or 100 play coins. The default stake is 20.
- Hazards: Before a round, you must choose 3, 4, or 5 hazards.
- Collection: You can collect only after at least one safe reveal.
- Auto-Bank: A choice is disabled if its gross return exceeds 1000 times the captured stake, but equality is allowed. The bank automatically triggers only when no eligible uncertain choice remains.
How is the wallet managed?
The virtual wallet in this demo has specific persistence and restoration rules:
- Initial Balance: 1000 virtual coins.
- Restoration: A manual idle-only restoration sets the balance to exactly 1000. This is eligible only while idle, and only if the balance is below 10.
- Fractional Carry: Fractional carry persists in browser localStorage across settlement, refill, and reload. Refilling does not clear it.
- Settlement: At settlement, floor(raw gross return + stored fractional carry) is credited. The remainder persists.
- Zero Return: Zero-return rounds leave the fractional carry unchanged.
What happens on reload or interruption?
If you reload the page during a round:
- The captured stake remains deducted.
- The unfinished round ends without refund, payout, continuation, or resume.
- Controls reset to the default stake (20) and the first preset.
- Stake, mode selectors, refill, and starting a second round remain locked until settlement.
What is the expected return (RTP)?
The expected RTP is 97% for all modes. Simulation measurements support this but are not the mathematical law. The exact policy gross mean is consistently near 0.97.
| Hazards | Policy | Expected RTP | Measured RTP |
|---|---|---|---|
| 3 | low-1 | 97% | 97.0133% |
| 3 | high-2 | 97% | 97.0956% |
| 3 | first-4 | 97% | 96.9050% |
| 4 | low-1 | 97% | 96.9772% |
| 4 | high-2 | 97% | 97.1247% |
| 4 | first-4 | 97% | 96.8795% |
| 5 | low-1 | 97% | 97.0125% |
| 5 | high-2 | 97% | 97.1654% |
| 5 | first-4 | 97% | 97.0981% |
What about privacy and storage?
The demo stores the virtual-coin balance and fractional payout carry in browser localStorage. The page template loads Google Fonts stylesheets and font files. No account login or payment flow is present in the demo. Clearing cached files may leave local storage intact.
The deployed guide also loads the Statinside44 counter script and sends visit-counter requests. Network requests can include connection and page information; the absence of login does not establish that no personal data are processed.
Frequently asked questions
How do I restore my balance?
You can manually restore your balance to exactly 1000 virtual coins. This is only eligible while you are idle and your balance is below 10. Refilling does not clear the fractional carry.
Can I resume a round after reloading?
No. If you reload the page, the unfinished round ends without refund or payout. The captured stake remains deducted, and you start a new round with default settings (stake 20).
When does the bank automatically trigger?
The bank automatically triggers only when no eligible uncertain choice remains. A choice is disabled if its gross return exceeds 1000 times the captured stake, but equality is allowed.
