Terms and Mechanics for Unique Start

Unique Start draws eight independent fair binary symbols, giving 256 equally likely words. For each starting position, examine contiguous factors of increasing length and choose the shortest one occurring exactly once anywhere in the whole word. Overlapping occurrences count. Add that length; a starting position with no unique factor contributes zero. The raw score is the sum of all eight contributions, not their maximum and not a player-selected starting position. All 256 words have positive raw scores, ranging from 8 to 35. All-zero and all-one words score 8; 01010101 scores 13.

One selected stake covers the entire word and is deducted when the draw starts. Choose Score, Score squared or Score cubed. Gross return = 0.96 × captured stake × raw score^p / mean_p, where p is 1, 2 or 3. The exact means are respectively 17.546875, 325.5 and 6401.640625. Each mode has a 96% expected gross return, not guaranteed net profit or a promised session result. The power changes payout magnitude without changing the drawn word or its raw score.

Choose a stake of 10, 20, 50, 100 or 200 coins and one of three modes before drawing. Auto ×10 starts at most ten draws and stops if balance is insufficient. Stop cancels future draws while the active draw settles. Stake, mode and refill are locked during active settlement and the queue; sound remains available. The animation normally settles after about 480 milliseconds and settles sooner with reduced motion. There is no early banking.

The initial wallet is 1000 virtual coins with no cash value. When no draw or queue is active and balance is below 10, Restore demo balance sets the wallet to exactly 1000; it does not add 1000 to the old balance. Fractional carry persists. Settlement pays floor(gross return + previous carry) and saves the new fractional remainder. Balance, including zero, and carry persist in localStorage. Reloading an unfinished draw keeps the stake deduction and ends the draw without refund or resume. Refilling balance is different from reloading the page.

The expected gross return is 96% for all modes. This is not a guaranteed net profit for any session. Simulation measurements are supporting sample observations, not the mathematical payout law.

Source: actual game.js pure score function. These examples illustrate how binary patterns affect the raw score.

The demo stores balance and fractional carry in browser localStorage. It has no account or payment form; this does not establish anonymity or exclude other processing. Pages request Google Fonts and Statinside counter 44; these may convey IP and browser request information to those services. Server retention and other processing are not established here. Clearing this site’s localStorage or site data removes balance and carry; clearing only cached files may leave them intact.