The game uses a unique mathematical structure based on directed graphs. Below, you will find the exact rules, scoring mechanics, and settlement behavior observed in this specific guide's implementation. Simulation data supports but does not replace the mathematical evidence.
Game Structure and Scoring
Directed Route Census operates on a graph with vertices 0 through 3. The game utilizes twelve fair switches that form all directed nonloop edges on these vertices.
- Objective: The reward counts the number of simple directed paths from vertex 0 to vertex 3, ensuring no repeated vertices.
- Reveal Order: Independent fair switches are revealed in row-major edge or matrix order.
- Quote Calculation: 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.
The 3% opening deduction appears only once in the quote. Every policy using only revealed information has a 97% expected gross return.
Settlement and Stopping Rules
Settlement depends on the behavior of the live gross quote and the chosen stopping mode.
- Zero Quote: If the quote hits zero, the round ends immediately.
- Positive Final Quote: If the round reaches the finite trace cap with a positive quote, it settles automatically.
- Manual Collection: Available after the first reveal while the round is active. It collects the current quote at the time of collection.
- Auto Thresholds: Settings at 1.2, 2, 3, or 5 collect the actual full first-crossing quote. If a threshold is unreachable, the system waits for the terminal result.
Controls and Modes
The demo supports specific stake levels and settings that lock during active play.
| Feature | Details |
|---|---|
| Active Stakes | 10, 20, 50, or 100 virtual coins. |
| Settings Lock | Stake, mode, and refill settings are locked during active play. |
| Availability | Sound controls remain available. Manual collection is available after the first reveal while the round remains active. |
Wallet and Persistence
This demo uses a local virtual wallet with specific persistence rules.
- Initial Balance: 1000 virtual coins.
- Restoration: An idle balance below 10 may be manually restored to exactly 1000. This is a manual set, not an automatic refill.
- Fractional Carry: Fractional values persist through settlement, manual refill, and reload.
- Unfinished Rounds: Reloading the page ends an unfinished round without refund or resume.
- Storage: Game source uses localStorage for settled balance and fractional carry. This does not establish anonymity or exclude other processing.
Expected Return and Evidence
The following table displays the exact expected return and measured simulation data for various modes. Note that simulation measurements are supporting sample observations, not the mathematical payout law.
| Stop (Reveal Depth) | Auto Threshold | Expected RTP (%) | Measured RTP (%) |
|---|---|---|---|
| 1 | 0 | 97.00000000000163 | 96.98492620143719 |
| 6 | 0 | 96.99999999999969 | 96.88573399966499 |
| 12 | 0 | 96.99999999999818 | 96.97959119967501 |
| 12 | 1.2 | 96.9999999999983 | 97.02915820106917 |
| 12 | 2 | 96.99999999999835 | 96.89948859951859 |
| 12 | 3 | 96.99999999999802 | 97.04943119971443 |
| 12 | 5 | 96.99999999999818 | 97.038411999678 |
Identity and Privacy Scope
Identity: The queried identity is unverified. This demo belongs to this independent guide and does not certify or reproduce any outside product. No operator, licence, or verified app is established.
Privacy: Clearing cached files may leave local storage. The absence of account controls does not prove no personal data is processed. Template declarations include Google Fonts stylesheet; actual full-site network capture remains pending.
Audience: This guide is intended for an 18+ audience. This is not a universal legal age or an implemented age gate.
Frequently asked questions
What is the exact expected return for this game?
Every policy using only revealed information has a 97% expected gross return. The live gross quote is 0.97 times the conditional expected terminal reward, divided by its initial expected reward.
How does the wallet restoration work?
If your idle balance falls below 10, you may manually restore it to exactly 1000. This sets the balance; it does not add coins or trigger automatic replenishment. Fractional carry is preserved during this process.
What happens if I reload the page during a round?
An unfinished round ends without refund or resume. The local settled balance persists, but any active quote or pending settlement is lost.
Third-party requests
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