Twelve fair directions and ten lag-two products
One drop samples twelve independent fair directions, each minus one or plus one. Label them d0 through d11. Raw score is the absolute value of the sum of d_i times d_(i-2) for i from two through eleven: ten lag-two products.
Each product compares a direction with the direction two bounces earlier, rather than its immediate predecessor. Take absolute value after completing the sum. The raw score is an even integer from zero through ten. It is not the final landing position, an edge-slot prize, adjacent reversal count or sum of absolute products. One captured stake covers the whole twelve-bounce path and its terminal return.
Exact4,096-path means for powers one, two and three
Choose power one, two or three before the drop. The weight is raw score raised to that selected power; zero remains zero. These choices are identity, square and cube, not square-root, identity and square. There are4,096 equally likely twelve-direction paths.
Exact mean weights over all4,096 paths are2.4609375 for power one,10 for power two and49.21875 for power three. Gross credit equals the captured stake times0.96 times observed weight divided by the corresponding exact mean. All three powers have 96% exact expected gross virtual return.
The stake was deducted before settlement, so gross credit is not net profit. Powers change positive credits after separate normalisation but preserve the positive-score frequency. The 96% expectation guarantees neither a session balance nor a 96% winning probability. The absolute correlation score has a positive mean even though the signed lag-two sum has mean zero.
One active ball 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 drop.
Available stakes are10,20,50 and100. Only one ball can be active. Stake, power, start and refill lock during the active drop; there is no automatic queue or Stop control. The complete twelve-bounce path settles at its end. Optional manual 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 Coins cannot be bought, transferred, redeemed or withdrawn.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 path simulator and authenticates no outside commercial affiliation.
What are the random inputs?
Twelve independent fair directions, each minus one or plus one.
What does the raw score measure?
Absolute value of the completed sum of ten products d_i times d_(i-2), for zero-based indices two through eleven.
Is this an adjacent reversal or endpoint score?
No. Each product compares directions two positions apart; the landing position alone does not determine the reward.
What do identical or alternating directions score?
Ten. In both cases all ten lag-two products equal plus one.
What does repeating plus,plus,minus,minus score?
Ten. All ten lag-two products equal minus one and their sum has absolute value ten.
Which powers are available?
One, two and three: identity, square and cube. There is no square-root weighting mode.
What are the exact mean weights?
2.4609375,10 and49.21875 for powers one, two and three respectively, over all4,096 paths.
Do powers change positive-score frequency?
No. They change positive credits after separate normalisation while preserving zero and positivity.
Does 96% guarantee a win or final balance?
No. It is exact expected gross virtual return per stake, not a win probability or session guarantee.
Can I use multiple balls, automatic play or cashout?
No. This simulator runs one active ball, locks its controls and credits only the terminal path result.
When can the wallet be refilled?
Only manually while idle below ten. Refill sets balance to 1,000 and preserves fractional-credit carry.
