Pak365: Independent Convex Subsequence Demo

Twelve steps and a convex subsequence

A round samples one of 4,096 equally likely twelve-step left/right paths. Starting at position zero, each left step subtracts one and each right step adds one. The board displays thirteen row-position points, indexed 0 through 12. Select any subsequence in increasing row order: the slopes between consecutive selected points must be strictly increasing. The score is the greatest possible number of selected points minus two. Collinear triples do not meet the strict condition. The score is computed automatically; there is no point-selection control.

Reward powers and gross return

Choose reward power 1, 2 or 3 before starting. If the path score is s and the chosen power is p, the gross multiplier is 0.96 × s^p ÷ the mean of s^p across all 4,096 paths. The exact means for powers 1, 2 and 3 are 2.7822265625, 8.2744140625 and 25.87841796875. All three have 96% model expected gross return before whole-coin settlement. Power changes the payout distribution, not that expectation. Zero score returns zero; a positive score can still return less than the stake. The four-decimal multiplier display is rounded; settlement uses the unrounded value. Expected return is not a win probability or a session promise.

Starting and completing one draw

Select a virtual stake of 10, 20, 50 or 100 and a reward power, then press Drop one ball. The stake and power are captured, and the whole stake is deducted and saved immediately. One draw runs at a time. Stake, reward power, start and restoration are locked while busy; sound remains available. The sampled path settles after the short animation. There is no Auto, Stop, pause or early cash-out control, and no automatic queue. To take a break, finish a draw and leave the next one unstarted.

Whole coins and separate carry

A new local wallet starts with 1,000 virtual coins. A completed draw credits floor(stake × unrounded gross multiplier + previous fractional carry). The remainder is saved separately for later settlement; it is not a decimal wallet balance. Stored wallet zero and carry persist. When idle below 10, manual restoration sets the wallet to exactly 1,000 while retaining carry; it does not add 1,000 or happen automatically. Reloading an unfinished draw retains the stake deduction, with no refund or resume. Previously stored carry remains.

Browser storage and external resources

The game uses localStorage for the virtual wallet and separate fractional carry. These are browser entries rather than a synchronized account. Clearing this site’s stored data can remove them; clearing only cached files may leave them intact. The font configuration declares Google Fonts, and the published page includes Statinside counter 44. These observations do not establish anonymity, exclusive local processing, an exhaustive request inventory, retention periods or no sale. The absence of account and payment fields does not establish an absence of personal-data processing.

Frequently asked questions