The core mechanic relies on a specific mathematical score: the number of integer pairs (x, y) between 1 and 16 that satisfy the equation a*x + b*y = 16*c. The global minimum is subtracted to determine the raw terminal statistic. This distinguishes the scoring from conventional game categories by anchoring payouts to a Diophantine solution count rather than standard paylines or reels.
Game Mechanics and Controls
The game proceeds through twelve steps. After each step, a four-bit block is revealed. Once all three blocks are revealed, the score is calculated.
- Stakes: Selectable stakes are 10, 20, 50, or 100 play coins. The default stake is 20.
- Reward Modes: Before capturing the stake, you must choose a reward weight curve: Linear, Squared, or Cubed.
- Controls: Settings, restoration, and starting another round are locked while a round is active.
The live gross quote is calculated as 0.97 times the conditional expected terminal weight divided by the initial expected terminal weight. This quote may rise, fall, or become zero during the process.
Scoring and Settlement
The score function is defined as: function score(mask){return statistic((mask>>8)+1,(mask>>4&15)+1,(mask&15)+1)-CFG.min;}
Settlement occurs under specific conditions:
- Manual Collect: You can collect the current quote at any time.
- Auto Collect: You can preset thresholds at 1.25, 1.75, or 2.50. The first crossing of these thresholds triggers settlement.
- Zero Event: If the quote hits zero, it resolves before cashout at the same event.
- Terminal Step: At step 12, the surviving current quote is collected.
At settlement, the floor of (raw gross return + stored fractional carry) is credited to your balance. Any remainder persists as fractional carry. Zero-return rounds leave the fractional carry unchanged.
Mathematical Evidence and RTP
The following table presents simulation measurements from 1,000,000 rounds for each mode. These are supporting observations, not the mathematical payout law.
| Curve | Policy | Expected RTP | Measured RTP | Std Error % |
|---|---|---|---|---|
| 0 (Linear) | Manual Step 6 | 97 | 96.989 | 0.037 |
| 0 (Linear) | Terminal 12 | 97 | 96.862 | 0.140 |
| 0 (Linear) | First-Cross 1.25 | 97 | 96.961 | 0.061 |
| 0 (Linear) | First-Cross 1.75 | 97 | 96.931 | 0.089 |
| 0 (Linear) | First-Cross 2.50 | 97 | 96.908 | 0.102 |
| 1 (Squared) | Manual Step 6 | 97 | 96.949 | 0.087 |
| 1 (Squared) | Terminal 12 | 97 | 96.844 | 0.374 |
| 1 (Squared) | First-Cross 1.25 | 97 | 96.966 | 0.067 |
| 1 (Squared) | First-Cross 1.75 | 97 | 97.026 | 0.100 |
| 1 (Squared) | First-Cross 2.50 | 97 | 97.236 | 0.132 |
| 2 (Cubed) | Manual Step 6 | 97 | 97.012 | 0.135 |
| 2 (Cubed) | Terminal 12 | 97 | 97.619 | 0.678 |
| 2 (Cubed) | First-Cross 1.25 | 97 | 97.016 | 0.074 |
| 2 (Cubed) | First-Cross 1.75 | 97 | 96.979 | 0.115 |
| 2 (Cubed) | First-Cross 2.50 | 97 | 97.246 | 0.137 |
Wallet and Persistence
The demo uses a virtual wallet stored in browser localStorage. The initial balance is 1000 coins.
- Restoration: A manual idle-only restoration sets the balance to exactly 1000 if the balance is below 10 and the user is idle. This is not automatic replenishment.
- Fractional Carry: Persists in browser localStorage across settlement, refill, and reload. It is not cleared by refill.
- Unfinished Reload: If you reload during a round, the captured stake remains deducted. The round ends without refund, payout, continuation, or resume.
- Controls After Reload: Default stake (20) and first preset are restored.
Example Scenario
A worked example from the contract:
- Mask: 0
- Integers (a,b,c): [1, 1, 1]
- Reward Score: 15
- Quotes:
- Step 0: 0.970
- Step 1: 1.058
- Step 6: 0.773
- Step 12: 11.595
Privacy and Audience
This guide has an 18+ intended audience. The demo has no account or payment flow. Virtual coins have no cash value.
Storage includes the virtual-coin balance and fractional payout carry in browser localStorage. The page template loads Google Fonts stylesheets and font files. Clearing cached files may leave local storage intact.
Frequently asked questions
How is the score calculated?
The score is the number of integer pairs (x,y) between 1 and 16 satisfying a*x+b*y=16*c, where a,b,c are derived from three four-bit blocks incremented by 1. The global minimum is subtracted.
What happens if I reload the page mid-round?
The captured stake remains deducted. The round ends without refund, payout, continuation, or resume. Controls reset to default stake (20) and first preset.
Does fractional carry reset on refill?
No. Fractional carry persists in browser localStorage across settlement, refill, and reload. Refill does not clear it.
