One circle and five nonidentity shifts
One spin draws six independent symbols, each uniformly chosen from zero, one and two, and places them around one circle. The raw score counts nonidentity cyclic shifts that leave all six positions unchanged. Test shifts one through five; exclude identity shift zero. Reflections are not tested.
A shift qualifies only if every shifted symbol equals the original symbol at the corresponding position. This counts symmetry-preserving shifts, not the number of distinct rotations or matching adjacent pairs. The whole six-symbol circle uses one captured stake. There are no separately staked or paid rows.
Check periodic circles and their raw scores
The circle 000000 is unchanged by all five nonidentity shifts and scores five. The circle 012012 is unchanged only by shift three and scores one. The circle 010101 is unchanged by shifts two and four and scores two. A circle with no qualifying nonidentity shift scores zero.
All six comparisons must hold for each qualifying shift. A visually similar rotation with even one different position does not qualify. Mirroring the circle is a different operation and cannot add points. The identity operation always preserves a circle but is deliberately excluded from the score.
Exact 729-circle means and whole-stake credit
There are 729 equally likely ordered circles, since each of six independent symbols has three possible values. Choose Low, Medium or High before spinning. Positive raw scores receive square-root, identity or square weighting respectively; zero remains zero. These weights are not final payout multipliers.
For each mode compute its exact mean weight over all 729 circles, including zero scores. Gross credit is the captured whole stake times0.96 times the observed weight divided by that mean. Each mode therefore has 96% exact expected gross virtual return. There is one whole-circle return, not three separate row returns.
The stake was deducted before settlement, so gross credit is not net profit. Weighting changes positive payout sizes after separate normalisation but preserves the positive-score frequency. The 96% expectation neither guarantees a session balance nor means a 96% probability of winning.
Captured rounds 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. Fractional returns accumulate before whole coins are credited rather than being discarded after each spin.
A spin captures one total stake and one mode for its entire six-symbol circle. Settings and refill lock during settlement and an active automatic queue. Auto runs at most ten rounds; Stop prevents future rounds while an already active round settles. Optional free refill is available only while idle with balance below ten. It sets balance to 1,000 and preserves fractional carry. Coins cannot be bought, transferred, redeemed or withdrawn.
Local storage and third-party requests
Browser localStorage keeps the settled virtual balance and fractional-credit carry. Pages request Google Fonts and a Statinside analytics script. Hosting, CDN and third-party requests may expose IP address, browser, device, path and request details. No anonymity, particular retention period, cookie lifetime or complete processing profile is established.
This guide has no registration or identity-document form. That does not mean browsing produces no personal data or that records cannot be linked to someone. Cache clearing alone may leave localStorage intact. Removing site data can erase the wallet without deleting requests or records already held elsewhere. Free refill changes local game state; it is not a data-deletion tool.
Evidence limits for external claims
No external commercial operator, airline, licence or testing certificate is authenticated by this guide. A name, logo, search result or attractive page cannot establish affiliation. HTTPS encrypts transport to the selected host without certifying the business behind it.
Rotation Class calculations concern only this simulator. They cannot validate an outside game, app, transaction or aviation claim. This guide supplies no account of direct commercial testing, external commissions, certified industry approval or independently verified regional service availability.
Frequently asked questions
Does this guide represent an airline or casino operator?
No. This independent guide supplies its own browser simulator and establishes no external commercial affiliation.
How many symbols does a spin draw?
Six independent symbols, each uniformly chosen from zero, one and two, arranged around one circle.
What does the raw score count?
Nonidentity cyclic shifts one through five that leave all six positions unchanged. Identity and reflections are excluded.
What is the score of 000000?
Five: every nonidentity cyclic shift preserves all six positions.
Why does 012012 score one?
Only shift three preserves every position. Identity shift zero is excluded.
Why does 010101 score two?
Shifts two and four preserve all six positions; the other nonidentity shifts do not.
Are there separately paid rows?
No. One captured whole stake covers the entire six-symbol circle and its single return.
How many equally likely circles are there?
729 ordered circles, from three independent possibilities at each of six positions.
Do the modes change positive-score frequency?
No. They preserve zero and positivity while changing positive weights after separate normalisation.
Does 96% guarantee a win probability or final balance?
No. It is exact expected gross virtual return per stake in this simulator model.
When can the wallet be refilled?
Only while idle with balance below ten. Refill sets balance to 1,000 and preserves fractional-credit carry.
What does Stop do during automatic play?
It prevents future rounds while an already active round settles under its captured stake and mode.
Inspect the home-page circle simulator using free virtual coins. Leave at your chosen stopping time.
Play the free demo