Curvature Keys Rules: Three Rows and Equal Differences

Three rows and three second differences

Curvature Keys displays three independent rows. Each row contains five independent uniform digits from zero through three. For a row a0,a1,a2,a3,a4, calculate d0=a2-2a1+a0, d1=a3-2a2+a1 and d2=a4-2a3+a2. These are second differences, rather than differences between adjacent digits.

Count the equal unordered pairs among d0,d1,d2. Three distinct values score zero; exactly two equal values score one; all three equal values score three. A score of two is impossible because equality is transitive. The displayed differences allow you to check the score directly.

Check the equal-pair score

For the row 0,1,2,3,3, the second differences are 0,0,-1. One equal pair gives raw score one. For 0,0,0,0,0, all three differences are zero and there are three equal pairs, giving raw score three. For 0,0,1,0,0, the differences are 1,-2,1 and score one.

Negative differences are ordinary inputs to the equality test. Their magnitude, sum and sign do not directly pay coins. Five matching digits are not a separate jackpot: the score follows the same second-difference rule. Compare all three unordered pairs, rather than counting only adjacent matches.

Exact row weights and total gross return

Choose Low, Medium or High before the round. Positive raw scores receive square-root, identity or square weighting respectively; zero remains zero. A raw score three therefore has weight square root of three, three or nine. These are weights, not the final payout multipliers.

Each row has 4 to the fifth power, or 1,024, equally likely digit patterns. For each mode calculate its exact mean weight over those patterns. A row credits one third of the captured total stake times 0.96 times its weight divided by that mean. Add the three row returns. The total expected gross virtual return is 96% of the stake in every mode.

The stake was deducted before settlement, so credited gross return includes its stake component and is not net profit. Modes change positive payout sizes and their distribution, but leave the positive-score frequency unchanged. Expected return is not a guaranteed session result or a 96% winning chance.

Captured rounds and the persisted virtual wallet

A new browser wallet starts with 1,000 free virtual coins. Settled balance and fractional-credit carry persist locally. Reloading does not replenish the settled wallet. Fractional returns accumulate before whole coins are credited, avoiding separately discarding each fractional payout.

A round captures one total stake and one mode for all three rows. Settings and refill lock during settlement. Auto queues at most ten rounds; Stop prevents future rounds while an already active round settles. Free refill is optional, available only while idle with balance below ten, and sets balance to 1,000 while preserving fractional carry. Coins cannot be purchased, transferred, redeemed or withdrawn.

Scope of this independent guide

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