The labelled board and restricted layouts
The board has four rows and four columns, labelled 1–16 in row order. Choose 3, 4 or 5 hazards before starting. A complete hazard set is eligible only when the sum of the positive-divisor counts of its labels is a perfect square. For example, label 6 has four positive divisors: 1, 2, 3 and 6. Layouts are sampled uniformly from the eligible sets, not from all ordinary grids.
Exact probabilities change after safe reveals
There are 93 eligible layouts with 3 hazards, 228 with 4 and 650 with 5. Revealing a safe cell removes every layout in which that cell was hazardous. The next safe probability is the number of remaining layouts where a cell is safe divided by the total remaining layouts. The displayed percentage is rounded to one decimal place; pricing uses the exact fraction. Printed labels define the restriction, rather than independent equal cell risks.
Current value divided by the next safe probability
One stake is captured when a round starts, and the initial quoted gross value is 97% of it. A successful reveal with exact safe probability q changes the current value to current value / q. A probability-one reveal leaves it unchanged. Hitting a hazard returns zero. At stake 20 with 3 hazards, label 3 is initially safe in 77 of 93 layouts; a successful reveal changes 19.4 to 19.4 × 93/77, about 23.431 play coins.
Collection and the per-choice cap
Collect becomes available after at least one safe reveal. You may collect the current gross value or choose another eligible cell. A cell is disabled if it is already open, certainly hazardous or would produce more than 1,000 times the captured stake; equality is allowed. Automatic collection occurs only when no eligible uncertain cell remains. Merely touching a cap is not a separate automatic-collection rule.
Gross credit and fractional carry
At settlement the wallet receives floor(raw gross return + stored fractional carry). The remaining fraction is saved for later settlements; a zero-return round leaves it unchanged. Gross return includes any returned stake, so it differs from net profit. The expected raw gross-return benchmark is 97% for completed valid stopping policies; it does not promise a winning session or a particular integer credit.
An unfinished round is not resumed
Reloading or closing during an active round ends it without refund, payout or continuation. The captured stake remains deducted, while carry from earlier settlements remains stored. The revealed cells and hidden layout are not saved for resumption. On loading again, stake 20 and 3 hazards are restored as defaults.
Frequently asked questions
Are all cells equally likely to be safe?
No. Hazard layouts obey the square divisor-sum restriction, and safe reveals filter the remaining layouts. Each cell uses its own exact posterior probability.
Does the cap itself trigger automatic collection?
No. Automatic collection occurs when no eligible uncertain cell remains. Choices above 1,000 times the captured stake are disabled; equality is allowed.
Can an unfinished round resume after a reload?
No. The captured stake stays deducted, and the unfinished round ends without refund or payout. The default stake is 20 and the default hazard count is 3.
