Five radii and an ordered closed contour
One spin draws five independent integer radii, each uniformly chosen from zero through three. In order, multiply them by the fixed vectors(1,0),(1,1),(0,1),(-1,0),(0,-1) to produce five points. Keep that point order and close the contour from its last point to its first.
Raw score is the absolute value of the sum of x_i times y_next minus y_i times x_next over all five edges, including the closing edge. This is doubled shoelace area, not area itself. A zero score returns zero. One whole captured stake covers the complete contour, without separately paid rows.
Check doubled area and zero-radius draws
All radii zero put every point at the origin and score zero. All radii one give points(1,0),(1,1),(0,1),(-1,0),(0,-1); the five edge cross-products each equal one, so raw score is five and area is 2.5.
A zero radius is a valid draw: it may repeat the origin or produce a degenerate contour. Such draws are not rerolled or removed from the probability space. Do not reorder points by magnitude, omit the closing edge or halve the raw score before weighting. The score is twice area, with absolute value applied to the completed sum.
Exact 1,024-sequence means and whole-stake credit
Five independent four-way radii give 1,024 equally likely ordered radius sequences. Choose Low, Medium or High before spinning. Positive raw scores receive square-root, identity or square weighting respectively; zero remains zero. Since raw score is2A for area A, the weights are square root of2A,2A and4A squared. These weights are not final multipliers.
For each mode calculate its exact mean weight over all 1,024 sequences, including zero scores. Gross credit equals the captured whole stake times0.96 times the observed weight divided by that mean. Each mode has 96% exact expected gross virtual return, with one whole-contour return.
The stake was deducted before settlement; gross credit is not net profit. Modes change positive credits after separate normalisation while preserving positive-score frequency. The 96% expectation guarantees neither a session balance nor a 96% chance 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 each spin.
A spin captures one total stake and mode for the complete contour. 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 spin 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.
Frequently asked questions
Does this guide represent a casino operator?
No. It supplies its own geometric simulator and authenticates no external commercial affiliation.
What are the random inputs?
Five independent integer radii, each uniformly chosen from zero through three.
Which vectors are scaled?
In order:(1,0),(1,1),(0,1),(-1,0),(0,-1). Keep the resulting point order.
What does the raw score measure?
The absolute completed shoelace sum, including the closing edge. It is twice the contour area.
What is the score when all radii are one?
Five, corresponding to area 2.5 for the fixed ordered points.
What happens when all radii are zero?
Every point is the origin, giving raw score and return zero.
Are zero radii rerolled?
No. Repeated origins and degenerate contours remain valid random outcomes in the probability space.
Does each edge or row use a separate stake?
No. One whole captured stake covers the entire contour and its single return.
How many equally likely radius sequences exist?
1,024, from four possibilities at each of five independent positions.
Do modes change positive-score frequency?
No. They change positive weights after separate normalisation and preserve zero and positivity.
Does 96% guarantee a win or final balance?
No. It is exact expected gross virtual return per stake in this simulator model.
What does Stop do during automatic play?
It prevents future rounds while an already active spin settles under its captured settings.
When can the wallet be refilled?
Only while idle below ten. Refill sets balance to 1,000 and preserves fractional carry.
Inspect the home-page Radial Area simulator using free virtual coins. Leave at your chosen stopping time.
Play the free demo