Strict triangles from nine independent side draws
Triangle Proof draws three independent rows. Each row contains three independently uniform integer side lengths from one through four. A row scores only when all strict triangle inequalities hold: a+b greater than c, a+c greater than b and b+c greater than a. Equality is invalid and scores zero.
For a valid triangle of area A, raw score is16 times A squared, computed exactly as(a+b+c)(-a+b+c)(a-b+c)(a+b-c). Invalid rows have raw score zero. One spin has three rows and nine side-length draws. Each row uses one third of the captured total stake, and row returns add.
Check triangle validity and the raw area product
Sides1,1,1 form a valid equilateral triangle and raw score is3. Sides2,3,4 satisfy all strict inequalities and score135. Sides1,1,2 are invalid because one plus one equals two, so they score zero rather than a positive area prize.
The product formula gives16A squared, not A squared itself. Area is square root of the raw score divided by four. Side order does not change this geometric score, but each ordered random triple belongs to the equally likely row sample space. Validity and the raw score are checked before the chosen weighting.
Exact64-pattern means and one-third row shares
Choose Low, Medium or High before spinning. Positive raw scores receive square-root, identity or square weighting respectively; zero remains zero. Since raw score is16A squared, Low weight is4A, Medium16A squared and High256A to the fourth power. These weights are not final payout multipliers.
There are64 equally likely ordered triples per row. For each mode calculate its exact mean weight over all64 triples, including invalid zero-score triples. Each row credits one third of the captured total stake times0.96 times its weight divided by that mean. Add all three gross row credits. Every mode has96% exact expected gross virtual return.
The stake was deducted before settlement; gross credit includes its stake component and is not net profit. Modes change positive payout sizes after separate normalisation but leave validity and positive-score frequency unchanged. Neither96% nor a valid triangle guarantees a session outcome or describes a96% winning probability.
Captured rounds and the persisted wallet
A new browser wallet starts with1,000 free virtual coins. Settled balance and fractional-credit carry persist locally, so reload does not replenish settled funds. Fractional row returns accumulate before whole coins are credited rather than being discarded per row.
A spin captures one total stake and one mode for all three rows. Stake, mode 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 to1,000 rather than adding1,000 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 outside claims
This guide makes no licensing, legitimacy or safety verdict about a separate business. A search snippet, familiar name or logo cannot establish ownership or commercial authorisation. HTTPS encrypts transport to a selected host without authenticating the business behind it.
Triangle Proof calculations describe only this browser simulator. They cannot validate a commercial game, external app, payment or astronomical claim. No regulator listing, certified fairness seal or regional service availability is authenticated here.
Frequently asked questions
Is this an authenticated operator or astronomy source?
No. This independent guide supplies its own geometry simulator and establishes no external commercial affiliation or astronomical measurement.
When does a row score zero?
If any strict triangle inequality fails, including equality. Sides1,1,2 are invalid and score zero.
What is the raw score of a valid row?
Sixteen times squared triangle area, computed as(a+b+c)(-a+b+c)(a-b+c)(a+b-c).
Is Low weight the triangle area itself?
No. Square root of16A squared is4A. Weights are then normalised separately and are not final multipliers.
How many equally likely triples are there per row?
Exactly64 ordered triples: each of three lengths is independently uniform from one through four.
Are all three rows paid from separate full stakes?
No. Each row uses one third of the captured total stake; their gross returns add.
Do modes change the frequency of valid triangles?
No. The same strict validity rule and sample probabilities apply in every mode; only positive weights change.
Does96% guarantee a winning chance or session balance?
No. It is exact expected gross virtual return per stake under this simulator model.
When can I refill the wallet?
Only while idle with balance below ten. It sets balance to1,000 and preserves fractional-credit carry.
What does Stop do during automatic play?
It cancels future rounds while an already active round settles under its captured stake and mode.
Inspect the home-page geometry simulator with free virtual coins. Stop at your chosen time without chasing virtual losses.
Play the free demo