Scores and controls in Cyclic Bridges

Select power 1, 2 or 3. The gross return is 0.96 times the ball’s captured whole stake times its raw score raised to that power, divided by that power’s own exact mean. The means are 0.38671875, 0.8701171875 and 2.4814453125, respectively. Each is calculated over all 4,096 equally likely words. The three modes preserve the same zero-score results but change the size of positive returns. Expected gross return is 96% of stake; this is not a promise of net profit.

Up to six balls can be active at once. Each ball captures its whole stake and selected power at launch, and the stake is debited then. Changing settings affects later launches. In normal motion, the animation runs for about 1,200 ms; reduced-motion preference can settle it earlier. There is no manual early collection. Auto schedules at most ten launches; Stop cancels future launches while existing balls finish. Sound remains available.

In normal motion, a launched ball’s animation runs for about 1,200 ms; reduced-motion preference can settle it earlier. The full twelve-choice word determines its rotation count; endpoint position is not the payout rule. Clicking Stop does not cancel balls already launched or refund their stakes.

A new wallet starts with 1,000 virtual coins. The current balance, including each stake debit at launch and any zero balance, and fractional carry persist in the browser where storage is available. When all balls have finished, the queue is empty and balance is below 10, manual refill sets the balance to 1,000 while keeping fractional carry. It is locked while any ball or queued launch remains. Reloading discards unfinished balls without refund or resume.

The page uses browser localStorage for current virtual balance and fractional carry. It also loads Google Fonts and a Statinside counter. A local wallet and absence of a demo login do not establish anonymity or exclude other processing. Clearing cached files may leave saved site storage intact. This description is not an exhaustive processing inventory.

All 4,096 twelve-choice words can be enumerated exactly. Each mode has 96% expected gross return by its own normalization. The one-million-round samples measured approximately 96.04%, 95.95% and 95.70%; these sample observations vary and do not replace the exact probability law. A positive gross return can still be smaller than the stake.