One permutation and disjoint nontrivial cycles
One spin draws a uniformly random permutation of six labelled positions zero through five. Read each position as pointing to its permuted label. Follow these pointers until returning to the starting position to identify a disjoint cycle, then continue from an unvisited position.
Raw score counts cycles of length at least two. Fixed points, which point to themselves, are excluded. Count cycles rather than moved positions or adjacent label matches. One whole captured stake covers the six-position permutation; there are no separate row shares. All 720 permutations are equally likely.
Fixed points and cycles of different lengths
Identity [0,1,2,3,4,5] consists only of fixed points and scores zero. The permutation [1,0,3,2,5,4] has three two-position cycles and scores three. The permutation [1,2,3,4,5,0] has one six-position cycle and scores one.
The permutation [1,2,0,4,3,5] has a three-position cycle, a two-position cycle and one excluded fixed point; its score is two. A cycle contributes one regardless of its length. Every position belongs to exactly one cycle; the same cycle cannot be counted again from a different starting position.
Exact 720-permutation means and whole-stake credit
There are 720 equally likely permutations of six distinct labels. Choose Low, Medium or High before spinning. Positive raw scores receive square-root, identity or square weighting respectively; zero remains zero. These are weights rather than final payout multipliers.
For each mode calculate the exact mean weight over all 720 permutations, including the zero-score identity. Gross virtual credit equals the whole captured stake times 0.96 times its observed weight divided by that mean. Every mode has 96% exact expected gross return. One whole-permutation return is paid, without separately paid rows.
The stake is deducted before settlement, so gross credit is not net profit. Modes change positive credits after separate normalisation but preserve positive-score frequency. Neither a nontrivial cycle nor 96% expectation guarantees a session balance or a 96% winning chance.
Captured round 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. Fractions accumulate before whole coins are credited rather than being discarded per spin.
A spin captures one total stake and mode for its permutation. Settings and refill lock during settlement and an active automatic queue. Auto runs at most ten rounds; Stop prevents future rounds while an active spin settles. Optional manual refill is available only while idle with balance below ten. It sets balance to 1,000 and preserves carry. Coins cannot be purchased, 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
This guide authenticates no external operator, airport, official domain, licence, support contact, app publisher or commercial safety verdict. A name, aviation-related query, logo or attractive interface cannot establish affiliation. HTTPS encrypts transport to a selected host without certifying its business.
Cycle Cabinet results describe only this browser simulator. They cannot test outside game interfaces, airport services, funds or transactions. No commercial testing history, payout record, regulator endorsement or regional authorisation is established here.
Adult use and a chosen stopping time
The site rule limits this guide and simulator to adults aged 18 or older. That rule establishes no regional gambling age or commercial service eligibility. Choose a stopping time outside the game and leave when it arrives.
Free virtual losses do not need recovery; refill can remain unused. If play displaces other activities or causes distress, pause and seek qualified local support. No diagnostic threshold, treatment promise or authenticated local helpline is supplied here.
Pause without recovering virtual losses
Stop cancels future automatic rounds while an active spin settles under its captured settings. Closing the page ends participation. A result creates no obligation to recover the starting virtual balance or continue.
Modes do not change symbol probabilities or positive-score frequency. Raising the stake scales debit and possible credit without improving expected return per coin. Previous sequences do not make a palindrome due to appear. Leave at a stopping time chosen independently of the last result.
Frequently asked questions
Does this guide represent a casino or airport?
No. It supplies its own simulator and authenticates no outside commercial affiliation.
What does a spin draw?
One uniformly random permutation of six distinct labels zero through five.
What does raw score count?
Disjoint permutation cycles of length at least two, excluding fixed points.
Does a six-position cycle score six?
No. Each nontrivial cycle contributes one, regardless of its length.
What does the identity permutation score?
Zero. All six positions point to themselves and are excluded fixed points.
What does [1,0,3,2,5,4] score?
Three. It consists of three disjoint two-position cycles.
What does [1,2,3,4,5,0] score?
One. It has one cycle containing all six positions.
How many equally likely permutations exist?
720, the factorial of six distinct labels.
Are there separate row stakes?
No. One whole captured stake covers the permutation and its single return.
Do modes change positive-score frequency?
No. They preserve zero and positivity while changing positive weights after separate normalisation.
Does 96% guarantee a profit or winning chance?
No. It is exact expected gross virtual return per stake in this simulator model.
What do Stop and refill do?
Stop prevents future automatic rounds while the active spin settles. Manual refill only while idle below ten sets balance to 1,000 and preserves carry.
Inspect the home-page Cycle Cabinet simulator using free virtual coins. Leave at your chosen stopping time.
Play the free demo