Game Mechanics: Directed Hamilton Gate
The demo features the Directed Hamilton Gate game. The board consists of twelve fair switches that form all directed nonloop edges on vertices 0 through 3. The reward counts the number of directed Hamiltonian cycles starting at vertex 0, visiting each other vertex exactly once, and returning to the start.
Switches are revealed in row-major edge or matrix order. The live gross quote is calculated as 0.97 times the conditional expected terminal reward, divided by its initial expected reward. This quote may rise or fall during the round. A zero quote ends the round immediately, while a positive final quote settles automatically.
Settlement, Stopping, and Auto-Cashout
Manual collection is available only after the first reveal. Auto-cashout thresholds are set at 1.2, 2, 3, or 5. These thresholds collect the actual full first-crossing quote. If a threshold is unreachable, the system waits for the terminal result. Every policy using only revealed information has a 97% expected gross return.
| Audit collection policy | Expected gross return | Measured gross return |
|---|---|---|
| Collect after reveal 1 | 97.00% | 97.03% |
| Collect after reveal 6 | 97.00% | 96.96% |
| Collect after reveal 12 | 97.00% | 96.93% |
| First crossing 1.2× | 97.00% | 96.97% |
| First crossing 2× | 97.00% | 97.13% |
| First crossing 3× | 97.00% | 97.10% |
| First crossing 5× | 97.00% | 96.98% |
Each measurement uses 1,000,000 simulated rounds. Reveal-depth policies are audit examples of manual collection, not selectable stop modes. The automatic options are off, 1.2×, 2×, 3× and 5×. Results are rounded for readability; measured returns are sample observations, not session promises.
Wallet, Balance, and Restoration
The demo wallet begins with an initial balance of 1000 virtual coins. If the balance drops below 10 while idle, it may be manually restored to exactly 1000. This restoration preserves any fractional change from previous settlements. Fractional carry persists through settlement, manual refill, and reload.
The settled balance, including zero, persists locally. However, reloading the page during an unfinished round ends the round without refund or resume capability. Busy settings (stake, mode, refill) are locked during active play, though sound and the current-quote collection button remain available after the first reveal while the round survives.
Stake and Mode Limits
Players select one active stake from the available options: 10, 20, 50, or 100. The gross quote includes a 3% opening deduction that appears only once in the quote calculation. The demo does not support external cash withdrawals or deposits; all values are internal to the virtual wallet.
Privacy and Storage Observations
Game source data uses localStorage for settled balance and fractional carry. This local storage usage does not establish anonymity or exclude other data processing. The template declares a Google Fonts stylesheet, but actual full-site network capture remains pending. No account login or payment flow is implemented in this demo.
Audience and Responsibility
This guide is intended for an 18+ audience. This is a policy guideline, not a universal legal age or an implemented age gate. Responsible use includes observing personal time and virtual-coin limits. The demo does not clinically train behavior or make losses safe, nor does it offer account-level blocking or self-exclusion tools.
Frequently asked questions
Does the virtual coin have cash value?
No. The virtual coins in this demo have no cash value and cannot be redeemed for real currency. They are used solely for demonstrating game mechanics.
How is the balance restored if it drops below 10?
The balance can be manually restored to exactly 1000 when idle. This process preserves any fractional change from previous settlements. Automatic replenishment does not occur.
What happens to an unfinished round if I reload the page?
An unfinished round ends without refund or resume. The settled balance persists, but the specific round state is lost upon reload.