Scoring Mechanics and Modes
The core statistic for any outcome n is the count of positive integer pairs x ≤ y where x² + y² = n². The reward score is calculated by subtracting the exact minimum statistic over all 256 outcomes from this count. For the outcome n=1, the raw statistic is 0, and the subtracted minimum is 0, resulting in a reward score of 0.
Before capturing a stake, players select one of three weight modes for the reward score:
- Linear (Mode 0): Sum of weights is 169.
- Squared (Mode 1): Sum of weights is 319.
- Cubed (Mode 2): Sum of weights is 871.
The gross multiplier is calculated as 0.96 × weight / mean, where the mean is derived from the exact 256-outcome distribution for the selected mode.
The sums of weights over all 256 equally likely outcomes are 169, 319 and 871; their means are respectively 169/256, 319/256 and 871/256. The gross multiplier is 0.96 × 256 × weight / sum of weights. Gross return includes any returned stake, and 96% is an expected value rather than a guaranteed session return.
Stake and Control Structure
Each round uses a single captured stake. There are no row bets, interim collections, or bonus features. The available stake presets are 10, 20, 50, or 100 play coins, with 20 as the default.
Controls for stake selection, mode switching, and starting a new round are locked once a round is active. Settlement occurs after the reels stop, crediting the floor of the raw gross return plus any stored fractional carry to the balance.
Mathematical Evidence and RTP
The exact gross RTP for all modes is 24/25 (96%). Simulation measurements support this but are not the mathematical law. The following table shows the exact parameters and observed simulation data:
| Mode | Sum of Weights | Exact Gross RTP | Measured RTP (1M rounds) | Std Error (%) |
|---|---|---|---|---|
| 0 (Linear) | 169 | 24/25 | 95.86% | 0.13 |
| 1 (Squared) | 319 | 24/25 | 96.11% | 0.24 |
| 2 (Cubed) | 871 | 24/25 | 96.45% | 0.35 |
Wallet and Persistence
The demo wallet starts with an initial balance of 1000 play coins. Fractional carry persists in browser localStorage across settlement, refill, and reload. Refilling the balance does not clear this carry.
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 deposit. Unfinished rounds ending on reload keep the stake deducted without refund or continuation. After reload, controls reset to a default stake of 20 and the first preset.
Privacy and Data Storage
Virtual-coin balance and fractional payout carry are stored in browser localStorage. The page loads Google Fonts stylesheets and font files, and includes the Statinside counter script with counter identifier 44. No account login or payment flow is present in this demo. The absence of account controls does not prove that no personal data are processed elsewhere.
Audience and Responsibility
This guide and its demo have an 18+ intended audience. This is not a universal legal age or an implemented age gate. Responsible use includes optional pauses and setting personal time or virtual-coin limits. The demo does not clinically train behavior or make losses safe.
Frequently asked questions
How is the reward score calculated?
The score is the number of positive integer pairs x≤y where x²+y²=n², minus the exact minimum statistic over all 256 outcomes. For n=1, the score is 0.
What happens if I reload the page during a round?
The captured stake remains deducted. The round ends without refund, payout, or continuation. Controls reset to default stake 20 and the first preset.
Does the demo require a deposit?
No. The demo uses virtual coins with no cash value. Refill is a manual set when the balance is below 10, setting it to exactly 1000. It is not an external payment.
