Reel Mechanics and Score Calculation
The game features two independent uniform reels. Each reel displays a hexadecimal symbol ranging from 0 to F (where A=10, B=11, C=12, D=13, E=14, F=15). Each reel value is uniformly distributed between 0 and 15.
The core statistic is derived by reading the two reel values as digits in base 16. The integer n is calculated as:
- n = 16 × first_reel_value + second_reel_value + 1
This results in an integer n that is uniformly distributed between 1 and 256 inclusive.
The reward score is determined by counting the divisors d of n such that d > 1 and d can be written as b^k for integers b > 1 and k ≥ 2. These are divisors that are perfect powers (squares, cubes, etc.) greater than 1.
The final reward score is the count of such divisors minus the exact minimum statistic over all 256 outcomes. In this game, the exact subtracted minimum is 0.
Weight Modes and Multipliers
Before capturing the stake, the player must select one of three reward weight modes. These modes transform the raw reward score into a gross multiplier. The gross multiplier is calculated as:
Gross Multiplier = (0.96 × weight) / exact 256-outcome mean of that weight
- Linear Weight: The weight is equal to the reward score.
- Squared Weight: The weight is the reward score squared.
- Cubed Weight: The weight is the reward score cubed.
The entire game shares one stake amount. There are no row bets, bonus features, or interim collections.
Payout and Settlement
Each round uses a single captured stake. At settlement, the floor of the raw gross return plus any stored fractional carry is credited to the balance. Any remainder persists as fractional carry.
If a round results in a zero return, the fractional carry remains unchanged. The game does not offer intermediate collection; the stake is locked until the round settles.
Stakes and Controls
Players can select stakes of 10, 20, 50, or 100 play coins, with 20 as the default. Settings, restoration, and starting another round are locked while a round is active.
The weight mode (linear, squared, or cubed) must be chosen before the stake is captured. Once the round begins, controls remain locked until settlement.
Mathematical Evidence and RTP
The game has an exact expected RTP of 96% across all modes. Simulation measurements support this, though they are sample observations, not the mathematical law.
| Mode | Expected RTP | Exact Weight Sum | Exact Gross RTP |
|---|---|---|---|
| Linear (0) | 96% | 201 | 24/25 |
| Squared (1) | 96% | 597 | 24/25 |
| Cubed (2) | 96% | 2361 | 24/25 |
Fractional carry and gross-versus-net wording follow the actual contract. Simulation data shows measured RTPs close to 96%, with standard errors varying by mode.
Wallet and Persistence
The demo starts with an initial balance of 1000 virtual coins. The balance is stored in browser local storage. Fractional payout carry also persists in local storage across settlement, refill, and reload.
If the balance falls below 10 while idle, a manual restoration sets the balance to exactly 1000. This is a manual set, not an automatic replenishment or adding of coins.
If the page is reloaded during an unfinished round, the captured stake remains deducted. The round ends without refund, payout, or continuation. Controls after reload reset to the default stake of 20 and the first preset mode.
Frequently asked questions
How is the score calculated for Perfect Power Divisors Reels?
The score is based on the integer n generated from two hexadecimal reels (0-9, A-F). n ranges from 1 to 256. The score counts divisors of n that are perfect powers (>1) and subtracts the minimum possible statistic (which is 0). This count is then weighted by the selected mode (linear, squared, or cubed) to determine the multiplier.
What happens to fractional carry if I reload the page?
Fractional carry persists in browser local storage across settlement, refill, and reload. It is not cleared when you refill or reload. However, if you reload during an unfinished round, the stake is not refunded, and the round ends without payout.
Is there a difference in RTP between the linear, squared, and cubed modes?
No. The exact expected RTP is 96% for all three modes. The difference lies in the variance and the exact weight sums (201 for linear, 597 for squared, 2361 for cubed), which affect how scores are translated into multipliers, but the long-term expected return remains constant.
