Twelve independent fair bits reveal three four-bit numbers. Each block represents 0 to 15; adding one gives a, b and c from 1 to 16. All 4,096 terminal triples have the same probability before the round begins.
Calculate the score and choose its weight
Let σ(n) be the sum of all positive divisors of n. The score S is |σ(abc) − σ(a)σ(b)σ(c)|. Its global minimum is zero, so subtracting the minimum leaves S unchanged.
For example, a = b = c = 2 gives σ(8) = 15 and σ(2)³ = 27, so S = 12. Linear uses S, Square uses S² and Cube uses S³. For a = b = c = 16, the score is 21,600.
The quote uses means, not totals
For your chosen curve, the current quote is 0.97 × (mean terminal weight among outcomes consistent with the revealed bits) ÷ (mean terminal weight among all 4,096 outcomes). Both quantities are means.
The full weight totals are 3,898,946 for Linear, 18,779,307,128 for Square and 165,684,883,545,248 for Cube. Divide each total by 4,096 to obtain its starting mean. At the terminal step, the numerator is the single remaining weight. Comparing a conditional mean directly with a full total would produce the wrong quote.
Before the first reveal, the two means are equal and the quote is ×0.97. Reveals occur roughly every 450 milliseconds. A quote may rise, fall or reach zero; a zero conditional mean means that every remaining outcome has zero weight.
Collection order and locked controls
Select stake 10, 20, 50 or 100 before starting. The default is 20. Starting deducts one stake and locks stake, curve, automatic threshold, restoration and another start. The sound button remains usable.
Auto off allows manual collection, including the initial ×0.97 quote. A collect click processes every step already due in order. Auto ×1.25, ×1.75 or ×2.50 settles at the first qualifying step and uses the actual quote, including overshoot.
At each step, zero settles before collection. An automatic collection at an earlier step ends the round before any later zero. If step twelve has a positive quote, it is collected even if the selected automatic level was never reached. On the all-zero-bit path, the Linear quote is already zero at step eight; that round ends there.
Worked payout with an automatic overshoot
Choose Linear and Auto ×1.25. If the first bit is 1, the step-one quote is approximately ×1.4540668067729072. That is the first threshold crossing and the round settles at this full quote.
With a 20-coin stake from 1,000 and previous carry zero, the stake first leaves 980. Raw gross return is approximately 29.081336135458144. Rounding down credits 29, leaves approximately 0.081336135458144 as fractional carry and gives a final balance of 1,009. The net change is +9, not +29.
Generally, payment = floor(stake × actual quote + previous carry). The new carry is the part remaining after this whole-coin payment. A zero return preserves a carry below one coin without crediting an extra coin.
Expected return and saved observations
The exact unrounded expected gross return is 97% for the tested curves and stopping policies. This refers to the probability-weighted gross return before whole-coin settlement. Saved carry preserves fractional parts for later rounds, while individual payments are whole coins.
Saved terminal-step simulations measured 96.7710% for Linear over 1,000,000 rounds, 96.8531% for Square over 1,000,000 and 97.5472% for Cube over 10,000,000. Their standard errors were approximately 0.1946, 0.4572 and 0.2564 percentage points respectively. These are observations from samples, not promised returns. The Cube sample had ten million rounds, unlike the other two.
Wallet restoration and reload
A new wallet starts with 1,000 virtual coins, which have no cash value. When idle and below 10, Restore balance sets the balance to 1,000. It is unavailable at 10 and does not clear carry.
Balance and carry persist in browser localStorage, including a zero balance. If you reload before settlement, the stake stays deducted and the unfinished round ends without refund, payment or resumption. Controls return to stake 20, Linear and Auto off. Completed rounds keep the selected controls until a reload or your next idle change.
Frequently asked questions
Does an automatic threshold cap my payment?
No. The first qualifying step pays its actual quote. If ×1.25 is selected and that step shows about ×1.4541, settlement uses the higher quote.
Does a zero terminal score always mean a zero return?
No. A round can have been collected at a positive earlier quote. Once it settles, later possible zero outcomes cannot change that payment.
Are the coins money or a withdrawable reward?
No. The wallet contains virtual play coins without cash value. The demo has no deposit, withdrawal or account-login flow.
