Game Board and Layout Constraints
The King Closed Tour game is played on a 4 by 4 board, consisting of 16 cells arranged in row-major order from 1 to 16. A fixed number of hazards are hidden within this grid. Unlike games that redraw the board randomly after every turn, the hidden layout is sampled once from the published constraint support and remains fixed for the entire round. This means the relative positions of the hazards do not change during gameplay.
The selection of valid layouts is governed by a strict geometric rule. The hazards must form a Hamiltonian cycle on the eight-neighbour king graph. This means that if you were to connect the hazard cells, they would form a continuous loop that visits every hazard exactly once and returns to the start, moving only horizontally, vertically, or diagonally to adjacent cells. At least three hazards are required to satisfy this rule. The game samples one complete layout uniformly from all possible layouts that satisfy this constraint, ensuring that every valid configuration has an equal chance of being the active layout.
Pricing Mechanics and Exact Posterior
Each cell on the board has a specific value, or gross quote, which represents the return you receive if that cell is safe. The pricing is dynamic and based on the exact posterior probability. When you start a round, the gross value starts at 0.97 times your original stake. As you reveal safe cells, the value of the remaining uncertain cells adjusts. The new value is calculated by dividing the current total value by the conditional probability that the cell is safe, given the information revealed so far.
Proven-safe cells can be inferred without being revealed. Both proven-safe and already revealed cells are disabled. Proven hazards, cells that are mathematically determined to contain a hazard based on the remaining layouts, are disabled and cannot be selected. The current gross multiplier is 0.97 times the original support count divided by the surviving support count. A prospective safe pick divides this multiplier by that cell’s conditional safety probability. This ensures that the pricing accurately reflects the changing odds as you eliminate invalid layouts by revealing safe cells.
Controls, Modes, and Settlement
The game offers specific controls for managing your virtual stake. You can choose from whole stake amounts of 10, 20, 50, or 100 coins. Once a stake is selected and the round begins, your settings and refill options are locked until the round concludes. You can collect your winnings after at least one safe pick has been revealed. If you choose not to collect manually, the game will automatically settle when no eligible uncertain move remains, meaning all remaining cells are either proven safe or proven hazards.
A unique rule applies to high-value prospects. If a single cell has a prospective quote above 1,000 times the original stake, that choice is blocked without changing the state of the board. This is a mechanical quote cap; it does not establish that any choice is safe or advantageous. A hazard returns zero, ending the round. The layout is never redrawn, so the probabilities are static relative to the fixed layout, but dynamic relative to the revealed information.
Wallet, Restoration, and Fractional Carry
The demo uses a local wallet system with an initial balance of 1,000 virtual coins. These coins have no cash value and are used solely for the demo. The whole-coin balance and separate fractional carry persist in the browser’s local storage. If your idle balance drops below 10 coins, you can manually restore it to 1,000 coins. This restoration preserves any fractional change in your balance, meaning you do not lose the precise decimal value of your remaining coins. A valid saved balance is loaded, including zero; 1,000 coins is used only when no valid saved balance is available.
It is important to note that an unfinished round does not receive a refund if you refresh or reload the page. The restoration process is manual and does not add the reset amount automatically. Furthermore, restoring your balance does not resume an unfinished round; it simply replenishes your coin supply for a new session. The fractional carry persists through settlement, manual refill, and reload, ensuring that your precise balance is maintained across interactions.
Expected Return and Mathematical Evidence
The expected gross return for every revealed-information strategy in the fair support model is 97%. This figure represents a mathematical expectation over many rounds, not a win probability for a single session. Simulations with one million rounds confirm this expectation. For example, with 3 hazards, the exact expected return is 97%, and measured simulation percentages hover around 96.99% to 97.05% depending on the depth of the strategy. Similar consistency is observed with 4 and 5 hazards, with support counts of 61 and 116 respectively.
The measured percentages from simulations are sample observations and may vary slightly from the exact theoretical values due to random sampling variance. The exact expected return is calculated based on the uniform distribution of layouts within the constraint support. This means that over a large number of rounds, the average return will converge to 97% of the total stake captured at the start of the rounds.
Browser Demo and Identity Context
This demo runs entirely in your browser, meaning no application download or installation is required. There is no verified APK, package name, or sideloading procedure associated with this specific demo instance. The identity of the operator is unverified in this context, as the demo is a self-contained mathematical simulation. The game uses local storage to save your balance and fractional carry, but this does not guarantee anonymity or the absence of other data processing.
The intended audience for this guide is 18+, which is a policy guideline for the demo experience rather than a strictly enforced legal age gate. There is no account flow, login requirement, or payment cashier in this demo. The virtual coins used are for demonstration purposes only and do not represent real money. The game caps and resets are mechanical features designed to balance the risk and reward structure of the King Closed Tour variant.
Frequently asked questions
How is the hazard layout determined in King Closed Tour?
The hazard layout is determined by sampling uniformly from all possible 4x4 configurations that satisfy the Hamiltonian cycle constraint on the eight-neighbour king graph. This layout is fixed for the entire round and is not redrawn. At least three hazards are required to form a valid cycle.
What happens if my balance drops below 10 coins?
If your idle balance drops below 10 coins, you can manually restore it to 1,000 coins. This restoration preserves any fractional change in your balance. The process is not automatic, and an unfinished round will not receive a refund if you refresh the page.
Is the 97% expected return a guarantee of winning?
No, the 97% expected gross return is a mathematical expectation over many rounds, not a win probability or a guarantee for a single session. Simulations with one million rounds confirm this average, but individual results can vary significantly.
