- Game Name: Integer Hypotenuse Reels
- Reels: Two independent uniform reels showing hexadecimal symbols 0..9 and A..F (values 10..15).
- Scoring: Based on the number of positive integer pairs (x, y) with x≤y such that x² + y² = n², where n = 16*first + second + 1.
How is the score calculated?
The game generates an integer n uniformly distributed from 1 to 256. The statistic for n is the number of positive integer pairs (x, y) with x ≤ y such that x² + y² = n². The reward score is this statistic minus the exact minimum over all 256 outcomes (which is 0).
| Reel Values (Hex) | Integer n | Raw Statistic | Reward Score |
|---|---|---|---|
| 0, 0 | 1 | 0 | 0 |
The score function is: score(n) = statistic(n) - 0.
What are the betting modes and weights?
Before capturing a stake, you can choose one of three reward weight modes. The gross multiplier is calculated as 0.96 * weight / the exact mean over all 256 outcomes.
- Linear (Mode 0): Sum of weights is 169. Exact Gross RTP is 24/25 (96%).
- Squared (Mode 1): Sum of weights is 319. Exact Gross RTP is 24/25 (96%).
- Cubed (Mode 2): Sum of weights is 871. Exact Gross RTP is 24/25 (96%).
Stakes are selectable as 10, 20, 50, or 100 play coins (default is 20).
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.
How does the virtual wallet work?
The demo uses a virtual coin system stored in your browser's local storage.
- Initial Balance: 1000 coins.
- Restoration: If the balance falls below 10 while idle, you can manually restore it. This sets the balance exactly to 1000. It is not automatic replenishment.
- Fractional Carry: Any fractional carry from settlement persists across reloads and refills. It is stored in local storage.
- Persistence: Settled balances persist locally, including zero balances.
What happens if I reload the page?
- Unfinished Round: If you reload during an active round, the captured stake remains deducted. The round ends without refund, payout, or continuation.
- Controls: After reload, the default stake (20) and first preset are restored.
- Locked Controls: Stake, mode selectors, refill, and starting a second round are locked until settlement is complete.
Is there an account or login?
No. This demo has no account login flow and no payment flow. Virtual coins have no cash value. Balance and fractional carry are stored locally in your browser. Clearing cached files can leave localStorage intact. Deleting this site's stored browser data removes its saved balance and fractional carry.
What is the intended audience?
This guide and its virtual-coin demo have an 18+ intended audience. This is not a universal legal age or an implemented age gate. Responsible use is encouraged; the demo does not clinically train behavior or make losses safe.
Frequently asked questions
What is the exact payout for a score of 0?
If the reward score is 0, the raw gross return is 0. The floor of (0 + stored fractional carry) is credited. Because stored carry is less than one, the credited return is always zero for a zero-score round. The carry remains unchanged.
Can I resume an unfinished round after reloading?
No. If you reload during an active round, the captured stake remains deducted, and the round ends without refund or continuation. You must start a new round.
How do I restore my virtual coins?
You can manually restore your balance if it falls below 10 and you are idle. This action sets your balance exactly to 1000 coins. It is not automatic.
