Rotating Ternary Register: Mechanics and Demo

Start with three base-three digits 000. Twelve independent fair bits are revealed in order. A zero increments the register modulo 27, wrapping from 222 to 000; a one moves the last digit to the front. Convert the final register to a decimal raw score from 0 to 26. Choose Score, Score squared or Score cubed before starting. All 4096 twelve-bit words are equally likely.

The live gross quote equals 0.96 × captured stake × the average terminal powered score over all completions of the revealed prefix, divided by the unconditional mean for that power. Raise each completed word’s raw score to the selected power BEFORE averaging; do not raise the average raw score. The exact means are 13.595947265625, 236.730712890625 and 4612.481689453125 for powers one, two and three respectively.

The quote may rise or fall. Bank live value settles it immediately; Auto-bank phase 4, 8 or 12 banks at that many exposed bits, or earlier if no positive future value remains. Gross includes the original stake; net change subtracts the stake. At the empty prefix every mode quotes 0.96 times the stake: stake 20 quotes 19.2. With zero prior carry, immediate banking credits 19 and saves 0.2; a wallet starting at 1000 then holds 999.

A new local wallet starts with 1000 virtual coins. Starting deducts and immediately saves one whole stake. Settlement credits floor(gross quote + previously saved fractional carry) and saves the remaining fraction. Zero gross retains the prior carry. Carry survives settlement, restoration and reload. Reloading unfinished leaves the stake deducted: no payout, refund, continuation or new carry is created. Prior saved carry remains. Controls reset to stake 20, Score and cap 12. While idle below 10 coins, Restore demo balance sets exactly 1000 and preserves carry. A saved zero stays zero until restored. These coins have no cash value.

Saved samples comprise one million traces for each of nine power/cap combinations, nine million total. Each banks at its cap or earlier zero potential. These measurements support the exact calculation; they do not determine a personal result.

Independent checks cover all 4096 terminal scores and all conditional tree values. Each conditional value averages the two fair next-bit values. Supported stopping decisions based only on revealed information preserve 96% expected gross before integer rounding. This is an expectation, not a win probability or guaranteed net profit. Carry retains unpaid fractions across settlements.

For word 000000000000, twelve increments produce decimal score 12. For 000000001100, eight zeros produce register 022; two rotations give 202 and then 220; two increments give 222, decimal score 26. For 111111111111, rotations leave 000, score zero. The selected power is applied after this raw score is calculated.

The demo uses browser localStorage for wallet balance, including the saved stake deduction, and fractional carry. It does not save an unfinished trace or the selected stake, power and cap for continuation. Built pages load Google Fonts resources and the Statinside44 visit counter; these requests are separate from the local wallet. No account login or payment form is present, but this does not establish anonymity or exclude personal-data processing. Clearing cached files alone may leave localStorage; browser site-data controls can remove the saved wallet. An outside data controller, retention schedule or encryption guarantee is not established here.