How Prime Successor Mines Works

Which layouts are allowed?

Select three, four or five hazards on a four-by-four board labelled 1–16. Compute the least common multiple, or LCM, of the hazard labels. Count its positive divisors and add one. The layout is allowed if that result is prime. There are exactly 333 allowed three-hazard layouts, 969 four-hazard layouts and 2,003 five-hazard layouts. Each allowed complete layout has equal selection probability.

Safe observations and conditional chances

After every safe reveal, keep only layouts that have no hazard in any opened cell. A label’s safe probability is the number of those layouts where it is safe divided by the number of remaining layouts. A zero-chance cell is a known hazard and cannot be selected. A probability-one cell is certainly safe under the remaining layouts. The one-decimal percentage shown on a cell is a rounded display of the exact calculation.

The current value divided by the safe chance

The captured stake starts with a gross quote of 0.97 times stake. On a safe reveal with exact chance p, the new quote is current quote divided by p. This uses the current value, not a new multiplier applied to an already returned wallet balance. For three hazards, label 4 is initially safe in 252 of 333 layouts. At stake 20, the quote changes from 19.4 to approximately 25.635714 after that safe reveal. With zero previous carry, collecting credits 25 and saves the fraction.

Manual collection, automatic collection and cap

You may collect after at least one safe reveal. A hazard ends the round immediately with zero return. A choice whose safe result would exceed 1,000 times stake is disabled; exactly 1,000 is allowed. Automatic collection follows a safe reveal only when no eligible uncertain unopened choice remains. The greatest possible quote without the cap is 323.01 times stake for three hazards and 939.93 for four, so the cap cannot bind in those modes. With five hazards, narrowing to one layout would quote 1,942.91 times stake; such a transition is disabled.

Exact expectation and measured samples

The exact gross expectation is 97% for the nine checked collection policies. The saved simulations contain one million rounds per policy, nine million in total. For policies low-1, high-2 and first-4 respectively, the measured percentages are 96.9899, 96.8736 and 96.8045 with three hazards; 97.0696, 96.9705 and 96.9994 with four; and 96.9223, 97.0631 and 96.7128 with five. These are rounded sample results, not new measurements or a guarantee for a session.

Settlement, controls and persistence

At collection, the wallet receives the whole-number part of the full gross return plus the previous fractional carry. The remainder is saved for later settlements. Gross return includes the captured stake; it is not net profit. A hazard returns zero and preserves the carry. The wallet balance and a separate fractional payout carry are saved in this browser’s localStorage. A new wallet starts with 1,000 play coins only when no valid saved balance exists; a saved zero remains zero. While idle with fewer than 10 coins, Restore balance sets the wallet to exactly 1,000. It does not add 1,000 to the current balance, clear the fractional carry or resume a round. Reloading during a round preserves the stake deduction but abandons the unfinished board without refund, payout or continuation. Reloading selects stake 20 and three hazards; normal settlement keeps the selected stake and hazard count. The initial choices are stake 20 and three hazards; stake, hazard selectors and restore remain locked during the active round, while collection follows the rules above and sound remains available.

Frequently asked questions