The game samples three independent uniform four-bit values and reveals their twelve bits in order. Each value is from 0 to 15; adding one gives a, b and c from 1 to 16. Before any reveal, all 4,096 triples are equally likely.
Count three directed divisibility relations
Test a divides b, b divides c and c divides a, meaning the corresponding divisions have no remainder. The score S is the number of true statements. Its minimum is zero, so subtracting that minimum leaves S unchanged.
For a = 2, b = 4 and c = 8, the first two statements are true but 8 does not divide 2, giving S = 2. If all three numbers equal 1, all statements are true and S = 3. Linear uses S, Square uses S² and Cube uses S³; the curve weights rather than changes the score.
Calculate the current quote from means
For the selected curve, quote = 0.97 × (mean terminal weight among triples consistent with revealed bits) ÷ (mean terminal weight among all 4,096 triples). Both quantities are means.
The full weight totals are 2,400 for Linear, 3,060 for Square and 4,476 for Cube. Divide each by 4,096 for its starting mean. At step twelve the numerator is the single remaining weight. Comparing a conditional mean directly with a full total would produce the wrong quote.
The initial quote is ×0.97 because the two means are equal. Reveals are due every 450 milliseconds, up to twelve steps, although browser scheduling can delay their processing. The panel shows partial binary prefixes and progress out of four bits, not decoded integers. Quotes display four decimals; the calculation uses the unrounded value.
Manual, automatic and zero settlement
Manual collection is available immediately after starting, including before the first reveal. A click processes all steps already due in chronological order, then collects if the round remains active. It does not bypass a due zero or earlier automatic crossing.
Auto off leaves manual collection available. Auto ×1.25, ×1.75 or ×2.50 collects at the first step reaching the level, using the full current quote including overshoot. At a step, zero settles before collection. An earlier automatic crossing settles before any later zero. A positive step-twelve quote is collected even below the selected automatic level.
Choose stake 10, 20, 50 or 100 before starting. The default is 20, Linear and Auto off. A round deducts one stake and locks stake, curve, threshold, restoration and another start. The sound control remains usable.
A full terminal payment example
With Linear and Auto off, twelve zero bits decode to a = b = c = 1. The terminal score is 3, and quote = 0.97 × 3 ÷ (2,400/4,096) = 4.9664. The quote stays positive along this path; no earlier manual collection is assumed.
For stake 20 from balance 1,000 with carry zero, starting leaves 980. Raw gross return is 20 × 4.9664 = 99.328. Settlement credits 99, saves 0.328 as carry and leaves 1,079. The net balance change is +79, rather than +99.
If Auto ×1.25 were selected on this same path, it would instead settle at step two, whose quote is about ×1.3838666667. Later quotes would not affect the completed payment. An immediate manual collection at ×0.97 with stake 20 and carry zero pays 19 and saves 0.4, giving net change −1.
Whole coins, restoration and reload
Generally, payment = floor(stake × actual unrounded quote + previous carry). The remainder becomes the new carry. A zero return preserves existing carry below one coin without crediting an extra coin.
A first-time wallet starts at 1,000 virtual coins without cash value. When idle and strictly below 10, Restore balance sets the total to 1,000 and preserves carry. Exactly 10 is not eligible. Balance and carry persist in browser localStorage, including zero.
If you reload before settlement, the stake stays deducted and the unfinished round ends without refund, payout or resumption. Controls return to stake 20, Linear and Auto off. Completed rounds keep your chosen controls until you change them while idle or reload.
Exact expectation and sample measurements
The exact unrounded expected gross return is 97% for the tested curves and stopping policies. This is the probability-weighted raw return, not a promised session result or the same whole-coin credit every round.
Fifteen saved simulations each used one million rounds. Terminal-step measurements were 97.0241% for Linear, 96.7427% for Square and 97.2858% for Cube, with standard errors approximately 0.1052, 0.1475 and 0.2271 percentage points. These are sample observations, separate from the exact payout expectation.
Frequently asked questions
Does the quote always rise until a crash?
No. It follows the mean terminal weight remaining after the bits revealed so far and can rise, fall or become zero.
Does Auto ×1.25 cap the return at ×1.25?
No. It triggers at the first qualifying step and pays that step’s actual quote, including overshoot.
Is Auto off required to reach the terminal example?
The example assumes Auto off and no earlier manual collection. With an automatic threshold, an earlier crossing can settle before step twelve.
