zbus.info: Queens on Open Cells Rules and Probability

The actual simulator rules

One spin draws sixteen independent fair open/closed cells in a four-by-four board. Raw score counts complete placements of four queens on open cells, with exactly one queen in each row and column and no shared diagonal. The software counts all qualifying placements; the player does not choose a placement after seeing the board. One whole stake covers the board.

These are this guide's original rules. Visual resemblance, game-category names and search snippets provide no evidence about an external commercial game.

Worked scoring examples

A completely open board permits two placements and scores two. A board containing only its main diagonal scores zero. A board opening only columns [1,3,0,2] in rows zero through three permits one placement and scores one. Queen conflicts include both diagonal directions.

Exact expected gross return

Enumerate all 65536 equally likely outcomes and calculate a separate exact mean for each weighting mode. Choose Low, Medium or High before a round. Positive raw scores receive square-root, identity or square weighting respectively; zero remains zero.

Gross virtual credit equals the whole captured stake times 0.96 times observed weight divided by the corresponding exact mean. Every mode has 96% exact expected gross return. There are no separately paid row shares. The stake was deducted at launch, so gross credit includes the stake component and is not net profit.

Modes preserve positive-score frequency while changing positive credits after normalisation. The expectation is neither a 96% chance of winning nor a session-balance guarantee. Past results do not make a favourable next outcome due.

Captured settings and the persisted wallet

A new browser wallet starts with 1,000 free virtual coins. Settled balance and fractional-credit carry persist in localStorage. Reload does not replenish settled funds; clearing cache may leave localStorage intact. Fractions accumulate before whole coins are credited.

A spin captures one whole stake and mode. Controls and refill lock during settlement and an active automatic queue. Auto launches at most ten rounds; Stop cancels future launches while active results settle. Refill remains locked until all active results and queued launches finish. Optional manual refill is available while idle with balance below ten; it sets balance to 1,000 and preserves carry. It is not automatic and does not add 1,000.

Local storage and external requests

The browser retains settled balance and fractional-credit carry as local game state. These records are not an online account and provide no recovery or device synchronisation service. Clearing site storage can remove them; cache deletion alone may not do so.

Pages request Google Fonts and a Statinside analytics script. Server/CDN logs and external requests may expose IP address, browser, device and request details. No anonymity, cookie lifetime, absence of profiling or complete third-party processing description is established. Having no personal-information form does not establish that browsing creates no personal data record.

Limits of external claims

No outside business identity, official domain, commercial safety verdict, licence, financial service or support channel is authenticated here. A logo, search ranking, name or professional interface does not establish these facts. HTTPS encrypts transport to a selected host; it does not certify the host business.

The simulator cannot test external responsiveness, commercial payouts, accounts, funds or transactions. No commercial testing history, regulator endorsement or named editorial team with verified contacts has been established for these pages.