Fair signs update a retained three-state rotor
Begin rotor state r=1 and position x=0. Sample twelve independent equally likely signs −1/+1 once. For each sign, update r=(r+sign) modulo3 into 0,1,2, then x=x+(r−1). The rotor state persists between steps. These signs are generated by the program; there are no player direction choices. A move can be −1,0,+1, depending on the newly updated rotor.
Twelve +1 signs cycle rotor states 2,0,1, giving displacement +1,−1,0 repeated four times and final x=0, raw score0. Twelve −1 signs also return to0. Alternating +1,−1 signs cycle states2,1 and move +1,0, producing x=6 and raw score36. A fair input sign is not the same as the movement direction.
The raw score is x² after all twelve updates. The linear mode weights raw score; squared mode weights (x²)²=x⁴; cubed mode weights (x²)³=x⁶. These are not position powers1,2,3, nor raw score times2 or3. One whole captured stake prices the entire ball, with no row stake shares.
The complete law has 944 zero-score sequences and3152 positive-score sequences. Raw scores0,1,4,9,16,25,36 have respective counts944,1562,992,430,132,34,2. Mode weighting never changes positive-result frequency. Positive gross credit may be below its captured stake and need not be a net gain. Previous balls do not predict new independent input signs.
Square the final position before mode weighting
The raw score is x² after all twelve updates. The linear mode weights raw score; squared mode weights (x²)²=x⁴; cubed mode weights (x²)³=x⁶. These are not position powers1,2,3, nor raw score times2 or3. One whole captured stake prices the entire ball, with no row stake shares.
Separate exact means for each mode
For p=1,2,3, gross multiplier=0.96×rawScore^p/mean(rawScore^p). Exact means are3.03564453125,26.83056640625,376.89306640625. Each mode has96% expected gross credit of its captured stake. That figure is neither winning frequency, a final-wallet guarantee nor a profit strategy. Zero remains zero. Integer credit settles with saved fractional carry.
Six captured balls and future settings
A ball captures and debits its whole stake and mode before its880ms flight. At most6 priced balls run concurrently. Changing stake or mode affects later launches only. Auto schedules at most10 launches when balance permits. Stop cancels future launches; existing balls finish and settle. There is no early cashout. Refill locks until all active balls and the launch queue are empty.
Only when all balls and the queue are empty and balance is below10 can manual refill set balance to1000 while preserving fractional carry. It does not add1000, refill automatically or reset at any time. A saved zero remains zero after reload, with refill visible once idle.
Settled balance, already debited stake and fractional carry persist in localStorage. Reload does not resume unfinished balls, refund their stakes or pay pending credit. Keep active balls open until settlement. Clearing ordinary cache alone may leave localStorage; removing local data cannot recover progress or erase data already processed elsewhere.
Frequently asked questions
The G123 query and our own simulator?
G123 is a search topic in this independent guide. A matching name, logo, domain or app snippet does not establish a gaming business, official address, licence, app, account service or financial facility. Rotor Pegs is our original virtual-coin simulator, not a commercial replica, software test or representation of another publisher’s rules.
Fair signs update a retained three-state rotor?
Begin rotor state r=1 and position x=0. Sample twelve independent equally likely signs −1/+1 once. For each sign, update r=(r+sign) modulo3 into 0,1,2, then x=x+(r−1). The rotor state persists between steps. These signs are generated by the program; there are no player direction choices. A move can be −1,0,+1, depending on the newly updated rotor.
A repeated direction can return to zero?
Twelve +1 signs cycle rotor states 2,0,1, giving displacement +1,−1,0 repeated four times and final x=0, raw score0. Twelve −1 signs also return to0. Alternating +1,−1 signs cycle states2,1 and move +1,0, producing x=6 and raw score36. A fair input sign is not the same as the movement direction.
Square the final position before mode weighting?
The raw score is x² after all twelve updates. The linear mode weights raw score; squared mode weights (x²)²=x⁴; cubed mode weights (x²)³=x⁶. These are not position powers1,2,3, nor raw score times2 or3. One whole captured stake prices the entire ball, with no row stake shares.
