ZA9 demo: practical questions

Proper divisors and the score

Let u(n) be the sum of the positive divisors of n smaller than n. For example, u(6)=1+2+3=6 and u(1)=0. The score is S=|u(a)−2u(b)+u(c)|. Its global minimum is 0, so subtracting that minimum leaves S unchanged.

Three reward weights

Linear uses S, Square uses S² and Cube uses S³. With power p=1, 2 or 3, the live gross quote is 0.97 × E[Sᵖ | revealed bits] / E[Sᵖ]. The power applies to terminal scores before averaging; it does not square or cube a finished Linear quote. The quote begins at ×0.97 and can rise, fall or reach zero.

Choose before starting

Choose 10, 20, 50 or 100 play coins; the default is 20. Select the reward weight and turn automatic collection off or choose ×1.25, ×1.75 or ×2.50. Starting deducts one stake. Stake and mode controls, balance restoration and a second round are locked until settlement.

Collection and event order

Manual collection first processes any reveals already due, then collects the surviving current quote. Automatic collection settles at the first quote at or above its threshold, using that quote. Zero resolves first at the same event, with no return; an earlier automatic settlement is unaffected by a later zero. Step 12 collects a surviving quote if the round has not ended.

Whole coins and fractional carry

Settlement credits floor(stake × collected quote + saved carry). The part below one coin is saved for the next settlement. For a stake of 20, quote ×1.25 and carry 0.4, the credit is 25 coins and the carry remains 0.4. A zero-return round leaves existing carry unchanged. This is a gross return, including any stake returned, rather than pure profit.

What a reload preserves

Balance, including zero, and fractional carry are saved in browser localStorage. Reloading an unfinished round keeps the stake deducted and gives no refund, payout or resume. Controls return to stake 20, Linear and Auto off. Saved carry survives a reload and balance restoration.

Frequently asked questions