Game Mechanics and Scoring
The core mechanic of Return Arc Cover is defined by graph theory rather than physical peg bouncing. The game operates as follows:
- Structure: Twelve independent fair left/right bounces define thirteen signed positions, including the origin.
- Scoring Function: The score is calculated as the minimum vertex cover of a graph. The vertices of this graph are consecutive-return arcs, and the edges represent strict endpoint interlacing.
- Game Flow: One active ball is used per round. There is no auto-play, no stop button, and no early cash-out option. The whole stake is deducted when the round starts, and the gross return is credited when it finishes.
Stakes and Modes
The demo supports four specific stake levels. The mode determines which mathematical distribution applies to the scoring.
| Mode (Power) | Stake Options | Expected Gross Return |
|---|---|---|
| Power 1 | 10, 20, 50, 100 | 96% |
| Power 2 | 10, 20, 50, 100 | 96% |
| Power 3 | 10, 20, 50, 100 | 96% |
Each Power level (1, 2, and 3) uses its exact complete-path mean to calculate the expected gross return. The displayed multipliers reflect gross coin returns, not net profit.
Mathematical Expectation and Evidence
The expected return is fixed at 96% for all modes. However, simulation measurements show slight variance due to sample size and fractional carry. The table below details the source-bound mathematical evidence from 1,000,000 rounds per mode.
| Power | Expected RTP | Measured Return | Fractional Carry |
|---|---|---|---|
| 1 | 96% | 96.01775% | 0.21057934332301542 |
| 2 | 96% | 95.954455% | 0.67835051656931 |
| 3 | 96% | 95.893825% | 0.7963638915382214 |
Note: Measured percentages are supporting observations and do not constitute the mathematical payout law. The fractional carry persists through settlement.
Wallet and Balance Rules
The demo uses a local virtual wallet with specific persistence rules:
- Initial Balance: 1,000 virtual coins.
- Manual Restoration: If the idle balance drops below 10, you can manually restore it. This action sets the balance to exactly 1,000. It is not an addition of coins.
- Fractional Carry: Fractional payout carry persists through settlement, manual refill, and page reload.
- Unfinished Rounds: If you reload the page during an active round, the unfinished ball ends without refund and without resume capability. The settled balance (including zero) persists locally.
Controls and Limitations
During active play, the stake, mode, and refill controls are locked. Sound remains available. The demo does not have:
- Automatic replenishment.
- Account recovery or login flows.
- Real-money withdrawal or deposit mechanisms.
- Timer or network-synchronized account state.
Privacy and Storage
Local Storage: The game source uses localStorage for the settled balance and fractional carry. This does not establish anonymity, nor does it exclude other processing by third parties.
Third Parties: The template declares a Google Fonts stylesheet. Actual full-site network capture remains pending, so other data requests are not yet fully verified.
Age: This guide targets an 18+ audience policy. It is not a universal legal age or an implemented age gate.
The shared page builder also declares a Statinside counter script and a noscript pixel with identifier44. These declarations do not establish a complete network inventory or any guarantee about tracking, retention or other processing.
Frequently asked questions
How is the score calculated in Return Arc Cover?
The score is the minimum vertex cover of a graph where vertices are consecutive-return arcs and edges represent strict endpoint interlacing. This is determined by the outcome of twelve independent fair left/right bounces.
What happens if I refresh the page while a ball is active?
The unfinished round ends without refund. The balance remains at its current settled value, but the specific round progress is lost. There is no automatic resume.
Can I restore my balance automatically?
No. Restoration is manual. You must manually trigger the refill when your idle balance is below 10, which sets your balance to exactly 1,000.
