How Fraction Product Distance Claim Works

Calculating the Score

Twelve independent bits, each equally likely to be 0 or 1, are revealed in order, one per step. They form three four-bit blocks. Decode each complete block as 0–15 and add 1 to obtain a, b, and c, each from 1 to 16. The raw score S is |a × c − b²| / gcd(a × c, b²), where gcd means greatest common divisor. The global minimum is zero, so subtracting it leaves S unchanged. The selected curve uses S, S², or S³ as the terminal reward weight.

Conditional Mean and Multiplier

The live gross multiplier is 0.97 × E[S^p | revealed bits] / E[S^p], with p = 1, 2, or 3. The conditional average includes every remaining possible completion and uses scores already raised to the selected power. Gross return in coins is captured stake times this multiplier; the number after × is not a coin amount or net profit. The multiplier can rise, fall, or reach zero.

Three Curves and Four Auto Options

Before starting, choose a stake of 10, 20, 50, or 100 coins; Linear, Square, or Cube; and Auto off or ×1.25, ×1.75, or ×2.50. Start the claim debits one stake. During the round, the main button becomes Collect current quote and is available immediately. Stake, curve, threshold, and restoration are locked until settlement; sound remains available.

Collection and Event Order

Automatic collection occurs at the first step whose live multiplier reaches or exceeds the chosen threshold. It uses that step's full multiplier, including any overshoot; it does not pay only ×1.25, ×1.75, or ×2.50. An earlier crossing settles before a later zero. If the multiplier is zero at the processed step, the round ends without return before collection at that step. At step 12, a positive quote is collected even if the threshold was never reached. There is no automatic queue of rounds.

Steps are scheduled every 450 milliseconds; step 12 corresponds to about 5.4 seconds. Visual updates can be delayed when the browser is busy. When advancing the round or receiving a collect click, the game processes all due steps in order with the same zero and first-crossing rules. A click does not preserve an older displayed quote from before an already due step.

An All-Zero Example

If all twelve bits are zero, a = b = c = 1 and S = 0. In Linear mode the multiplier is approximately ×0.9700 at the start, ×0.9468 after step 1, and ×0.1071 after step 6; at step 12 it is zero. With stake 20, immediate collection at ×0.97 gives 19.4 coins gross before carry and rounding. The example shows that a positive return can be smaller than the stake.

Expected Return and Settlement

There are 4,096 equally likely terminal combinations. Conditional means average all combinations consistent with the revealed bits. For supported collection policies, expected gross return is 97% of stake before whole-coin rounding. This includes returned stake; it is not 97% profit or a guaranteed result for a round or session. Reloading an unfinished round is outside those settlement policies.

The mathematical checks use all 4,096 terminal combinations and their conditional means. Fifteen combinations of three curves and five collection policies were simulated for one million rounds each. Measured gross returns ranged from approximately 96.769% to 97.121%. Those sample estimates support the exact 97% expectation without determining a session outcome.

At settlement, gross return is added to saved fractional carry from earlier rounds. The whole-coin part is credited to the balance and the remainder below one coin is saved for the next return. A zero-return round preserves existing carry. Carry does not change the gross multiplier. Balance and carry are stored in browser localStorage, including a zero balance.

Frequently asked questions