Two symbols make one integer
Each of two independent reels selects one of sixteen equally likely hexadecimal symbols: 0 through 9, then A through F. The letters have values 10 through 15. Calculate n = 16 × first value + second value + 1, giving each integer from 1 to 256 equal probability. Symbols 0 and B give 12; F and F give 256. Both reels share one stake. There are no separate row bets, matching-symbol prizes or bonus rounds.
Use every positive divisor
List all positive divisors of n, including 1 and n itself, and let k be the number of divisors. Calculate k × the sum of their squares − the square of their sum. The minimum across the 256 starting integers is 0, so the reward score equals this statistic. It also equals the sum of squared differences over all unordered pairs of divisors. The game does not divide by k or k²: its score is not a normalized statistical variance. No proper-divisor chain or repeated replacement is involved.
Choose before spinning
Choose a stake of 10, 20, 50 or 100 virtual coins and a reward curve: Linear, Square or Cube. The defaults are stake 20 and Linear. For score s, the curve weights are s, s² and s³ respectively. Starting deducts one stake for both reels. Stake, curve, restoration and another start are locked until settlement; sound remains available. There is no interim collection or automatic sequence of spins. Settlement keeps your chosen stake and curve.
Gross return and fractional carry
The gross multiplier is 0.96 × selected weight ÷ that curve’s exact mean weight. The sums across all 256 integers are 29,753,529 for Linear, 11,204,376,612,271 for Square and 7,113,856,702,189,995,795 for Cube. Divide each sum by 256 to get its mean. Multiply the captured stake by the multiplier for the raw gross return. Add stored fractional carry, credit the whole-number part and save the remaining fraction. Net whole-coin change is the credit minus the stake already deducted. Carry is added before rounding down, and zero raw return leaves existing carry unchanged.
Four scores and a small-return example
For n = 1, the divisor list is [1] and the score is 0. For n = 2, [1, 2] gives 2 × 5 − 3² = 1. For n = 6, [1, 2, 3, 6] gives 4 × 50 − 12² = 56. For n = 12, [1, 2, 3, 4, 6, 12] gives 6 × 210 − 28² = 476. At stake 20 on Linear with n = 12 and no prior carry, raw return is about 0.078633872 coins: credit 0 whole coins and save that fraction as carry. Positive raw return can therefore produce zero whole-coin credit. Carry does not compensate for the stake already deducted.
Local wallet and manual restoration
A fresh wallet starts with 1,000 virtual coins. The balance, including zero, and fractional carry are saved in browser localStorage. When no round is active and the balance is below 10, Restore balance sets it to exactly 1,000. It does not add 1,000 or run automatically. Restoration preserves carry, the selected stake and the selected curve. It is available whenever those conditions are met. Coins have no cash value and cannot be withdrawn.
Frequently asked questions
Which divisors are included?
All positive divisors, including 1 and the integer itself. With k divisors, the score is k × sum of squared divisors − square of their sum; the subtracted minimum is 0.
Can a positive raw return credit zero coins?
Yes. If raw return plus existing carry is below 1, the whole-number credit is zero and the fraction is retained as carry. This differs from a zero raw return, which leaves existing carry unchanged.
Is 96% the chance of a winning spin?
No. It is exact average raw gross return as a percentage of stake across all 256 integers for each curve. Individual returns and session results vary.
