The demo implements bounded diophantine solutions Claim, a game with specific mathematical rules, score functions, and payout structures described below. No external cashier, KYC, or payment method is implied.
Game Mechanics: Bounded Diophantine Solutions Claim
The game consists of twelve independent fair binary steps that reveal three four-bit blocks. Each completed block is decoded as a value from 0 to 15, and 1 is added to obtain integers a, b, and c, each ranging from 1 to 16.
The raw terminal statistic is the number of integer pairs (x, y) where 1 ≤ x, y ≤ 16 satisfying the equation a*x + b*y = 16*c. The score is calculated by subtracting the global minimum (0) from this statistic.
Before capturing a stake, players select a reward weight mode: linear, squared, or cubed. 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.
Settlement occurs via manual collection or preset first-crossing thresholds (1.25, 1.75, or 2.5). If zero is reached, it resolves before cashout. If an auto-threshold is crossed earlier than a zero event, the earlier crossing settles the round. The final step 12 collects the surviving current quote.
Controls, Modes & Stakes
Players can select stakes of 10, 20, 50, or 100 play coins, with 20 as the default. Settings, restoration, and starting a new round are locked while a round is active.
- Reward Weight: Choose linear, squared, or cubed before capturing the stake.
- Auto-Collection: Set to off, 1.25, 1.75, or 2.50. An earlier crossed auto threshold settles the round before a later zero event; a zero quote takes precedence over cashout if they occur at the same event.
- Scoring: The score function is defined as function score(mask){return statistic((mask>>8)+1,(mask>>4&15)+1,(mask&15)+1)-CFG.min;}
Wallet & Persistence
The demo wallet starts with an initial balance of 1000 virtual coins. Fractional carry persists in browser localStorage across settlement, refill, and reload; refilling does not clear it.
- Restoration: Manual idle-only restoration is eligible when the balance is below 10. It sets the balance to exactly 1000.
- Unfinished Reload: If the page reloads during an active round, the captured stake remains deducted. The round ends without refund, payout, continuation, or resume.
- Settled Balance: Persists locally, including zero. Controls after reload restore the default stake of 20 and the first preset.
Mathematical Evidence & RTP
The following table presents simulation measurements from one million rounds. These are supporting sample observations and not the mathematical payout law. The expected RTP is 97% for all modes, but measured values vary.
| Mode (Curve) | Policy | Expected RTP | Measured RTP | Std Error % |
|---|---|---|---|---|
| 0 (Linear) | Manual Step 6 | 97 | 96.9894 | 0.0373 |
| 0 (Linear) | Terminal 12 | 97 | 96.8616 | 0.1395 |
| 0 (Linear) | First-Cross 1.25 | 97 | 96.9612 | 0.0613 |
| 0 (Linear) | First-Cross 1.75 | 97 | 96.9308 | 0.0890 |
| 0 (Linear) | First-Cross 2.50 | 97 | 96.9083 | 0.1021 |
| 1 (Squared) | Manual Step 6 | 97 | 96.9489 | 0.0874 |
| 1 (Squared) | Terminal 12 | 97 | 96.8437 | 0.3743 |
| 1 (Squared) | First-Cross 1.25 | 97 | 96.9657 | 0.0672 |
| 1 (Squared) | First-Cross 1.75 | 97 | 97.0262 | 0.1002 |
| 1 (Squared) | First-Cross 2.50 | 97 | 97.2365 | 0.1317 |
| 2 (Cubed) | Manual Step 6 | 97 | 97.0121 | 0.1349 |
| 2 (Cubed) | Terminal 12 | 97 | 97.6186 | 0.6784 |
| 2 (Cubed) | First-Cross 1.25 | 97 | 97.0164 | 0.0744 |
| 2 (Cubed) | First-Cross 1.75 | 97 | 96.9790 | 0.1154 |
| 2 (Cubed) | First-Cross 2.50 | 97 | 97.2465 | 0.1365 |
Worked Example
For mask 0, the integers are [1, 1, 1]. The reward score is 15. The gross quotes progress as follows:
- Step 0: 0.9700
- Step 1: 1.0583
- Step 6: 0.7730
- Step 12: 11.5947
Privacy & Audience
This guide and its virtual-coin demo have an 18+ intended audience. Virtual-coin balance and fractional payout carry are stored in browser localStorage. The page template loads Google Fonts stylesheets and font files. Clearing cached files may leave local storage intact. The absence of account controls does not prove that no personal data are processed.
Frequently asked questions
Is 42c an official licensed operator?
The query name 42c does not establish an official company, account address, or verified app. This guide is independent, and the demo uses its own virtual wallet, not a regulated casino cashier.
How does the wallet restoration work?
When the balance is below 10 and the game is idle, manual restoration sets the balance to exactly 1000. Fractional carry persists across refills and reloads. Unfinished rounds ending on reload lose the stake without refund.
What happens if I reload during a round?
The captured stake remains deducted. The round ends without refund, payout, continuation, or resume. Default stake (20) and first preset are restored upon reload.
