Game Mechanics and Scoring
The core mechanic involves twelve independent fair switches. These switches form all directed non-loop edges on vertices 0, 1, 2, and 3. The reward is the count of directed Hamiltonian cycles that start at vertex 0, visit every other vertex exactly once, and return 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 as switches are revealed. The 3% opening deduction appears only once in the quote.
Payout and Settlement
Every policy using only revealed information has a 97% expected gross return. Actual payout math and every mode are recorded in the source-bound mathematical evidence. Displayed multipliers are gross coin returns, not profit.
A zero quote ends the round immediately. A positive final quote settles automatically at the finite trace cap. Manual collection is available after the first reveal.
Stopping Rules and Auto Modes
Select automatic collection before starting a round: off, 1.2×, 2×, 3× or 5×. A threshold settles the actual full quote at its first crossing. If it is not reached, the game continues until a zero quote or the terminal result.
With automatic collection off, the current quote can be collected after at least one reveal. There are no selectable stop-depth 1, 6 or 12 buttons: those values identify simulation audit policies. A zero quote ends immediately, and a positive quote at reveal twelve settles automatically.
Virtual Wallet and Balance
The initial balance is 1000. If the idle balance drops below 10, it may be manually restored to exactly 1000 with fractional change preserved. This is a manual set, not an automatic replenishment.
Fractional carry persists through settlement, manual refill, and reload. The local settled balance, including zero, persists. Reload does not refund an unfinished round.
Controls and Settings
Select a stake of 10, 20, 50 or 100 virtual coins before the round. Stake, automatic setting and restoration are locked while active. Sound remains available. The collection button becomes available after the first reveal while the round survives.
Mathematical Evidence and Modes
The following table shows simulation measurements for various modes. Expected RTP is not a promised session result.
| 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.
Frequently asked questions
How is the reward calculated?
The reward counts directed Hamiltonian cycles starting at vertex 0, visiting each other vertex exactly once, and returning to 0. There are twelve fair switches forming all directed non-loop edges on vertices 0-3.
What determines the live 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 as switches are revealed.
When does a round end?
A zero quote ends the round immediately. A positive final quote settles automatically. Manual collection is available after the first reveal.
How do auto thresholds work?
Auto thresholds off, 1.2, 2, 3, or 5 settle the actual full first-crossing quote. An unreachable threshold waits for the terminal result.
What is the expected return?
Every policy using only revealed information has a 97% expected gross return. This is distinct from measured simulation results.
How is the wallet restored?
If the idle balance is below 10, it may be manually restored to exactly 1000. Fractional change is preserved. This is not an automatic replenishment.
Does reload refund an unfinished round?
No. Reload does not refund an unfinished round. An unfinished round ends without refund or resume.
What stakes are available?
One active stake is selected from 10, 20, 50, or 100. Settings and refill are locked during active play.
Where is balance stored?
Game source uses localStorage for settled balance and fractional carry. This does not establish anonymity or exclude other processing.
Is there an account login?
No. The demo has no account-login flow. Virtual coins have no cash value.
Is fractional carry fixed by the automatic threshold?
No. The remainder depends on the stake, gross quote and carry from earlier settlements. The demo credits whole coins and preserves a separate fractional remainder below one coin. A final carry reported in a simulation is a sample state, not a fixed property of an automatic setting.
What is the intended audience?
18+ is this guide's own intended audience policy, not a universal legal age or implemented age gate.
