Triangle Proof Rules: Three Rows and Strict Triangle Inequalities

Scope of this independent guide

Wasp33.info is an independent query-information guide with its own Triangle Proof browser simulator. Queries containing WASP33b and astronomical wording do not establish a gaming operator. This guide provides no authenticated stellar measurements, planet characteristics or astronomical discovery claims.

A matching query or domain does not authenticate a casino, commercial affiliation, licence, app, account, payment method or outside catalogue. The simulator has original geometry rules and virtual pricing, with no commercial account, deposit, withdrawal or cash prize. Its calculations do not measure an astronomical object or validate a separate business.

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.