Twelve binary reveals
Twelve independent fair bits form three blocks of four bits. Each complete block represents 0–15; adding 1 gives a, b and c, each between 1 and 16. The reveals update the quote as more of the outcome becomes known.
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.
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.
A falling quote example
In Linear mode, twelve zero bits give a=b=c=1 and S=0. The quote is ×0.97 initially, about ×0.9012 after step 1, ×0.4529 after step 6 and zero at step 12. Collecting at step 6 would use that lower quote; waiting on this path reaches zero. It illustrates one path, not a forecast of the next round.
Frequently asked questions
Does Square mean squaring the Linear quote?
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.
What happens when the quote reaches zero?
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.
Can an unfinished round resume after reload?
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.
