The displayed wallet begins with 1,000 free coins. Starting a round immediately deducts the selected stake, and that deducted balance persists if an unfinished round is reloaded. Restoration is a separate manual action while idle with a balance below 10.
Virtual Wallet and Persistence
The demo wallet tracks your virtual coins locally. It does not represent a real-money account.
| Feature | Behavior |
|---|---|
| Storage | Uses localStorage for settled balance and fractional carry. |
| Settlement | Local settled balance, including zero, persists across sessions. |
| Fractional Carry | Persists through settlement, manual refill, and reload. |
| Unfinished Round | Reloading the page ends an unfinished round without refund or resume. |
Manual Restoration and Idle Balance
When the wallet balance drops sufficiently while idle, you can restore it.
- Eligibility: The balance must be below 10.
- Action: A manual restoration sets the balance to exactly 1000.
- Fractional Carry: Any fractional change is preserved during this restoration.
- Not Automatic: The balance does not replenish automatically; it requires a manual action when idle.
Stake Controls and Modes
You can adjust the active stake for the Directed Hamilton Gate game.
- Stake Levels: 10, 20, 50, or 100 virtual coins.
- Busy Settings: Stake, mode, and refill options are locked while play is active.
- Refill Locks: Refill controls are also locked during active play.
Game Mechanics: Directed Hamilton Gate
The demo features the 'Directed Hamilton Gate' game with specific mathematical rules.
- Structure: Twelve fair switches form all directed nonloop edges on vertices 0..3.
- Reward: Counts directed Hamiltonian cycles starting at 0 and visiting each other vertex exactly once before returning.
- Reveal Order: Independent fair switches are revealed in row-major edge or matrix order.
- Gross Quote: The live gross quote is 0.97 times the conditional expected terminal reward, divided by its initial expected reward. It may rise or fall.
- Settlement: A zero quote ends the round immediately; a positive final quote settles automatically.
Stopping Rules and Auto Collection
After the first reveal, you can collect the current gross return in virtual coins while the round remains active.
- Manual Collection: Available after the first reveal.
- Auto Thresholds: Options are off, 1.2, 2, 3, or 5.
- First-Crossing Quote: Auto thresholds collect the actual full first-crossing quote. If a threshold is unreachable, it waits for the terminal result.
- Zero Event: A zero quote ends the round immediately, regardless of auto thresholds.
Expected Return and Evidence
The game has a fixed expected gross return.
- Expected RTP: Every policy using only revealed information has a 97% expected gross return.
- Deduction: The 3% opening deduction appears only once in the quote.
- Mathematical Evidence: Actual payout math and every mode are recorded in the source-bound mathematical evidence. Displayed multipliers are gross coin returns, not profit.
Frequently asked questions
Can I withdraw my virtual coins to a bank account?
No. This demo uses a virtual wallet with no cash value. There is no external cashier, deposit, or withdrawal process. The coins are for demonstration purposes only.
What happens if I refresh the page during a round?
An unfinished round ends without refund or resume. Any fractional carry persists, but the current round's progress is lost.
How do I restore my balance if it goes below 10?
You can perform a manual restoration when idle. This sets the balance to exactly 1000, preserving any fractional change.
