I44: One uniform permutation and complete stack passes

Draw one uniformly random permutation of1,2,3,4,5 from all120 possibilities. Read a pass left to right. Before pushing an incoming number, repeatedly pop any smaller stack top into output; then push that number. After the input is exhausted, pop the remaining stack into output. Feed the complete output into the next pass until ascending. Raw score=number of COMPLETE passes−1. One whole captured stake prices the entire permutation, without row shares.

Starting2,3,4,5,1, complete outputs are2,3,4,1,5; then2,3,1,4,5; then2,1,3,4,5; finally1,2,3,4,5. Four passes give score3. A permutation sorted on its first pass scores0, including5,4,3,2,1. An individual pop or a temporarily empty stack is not a complete pass. Players do not choose permutations or stop sorting for a different payout.

Scores0,1,2,3 have counts42,49,23,6. Powers do not change positive frequency. Positive gross credit may be smaller than captured stake and is not guaranteed profit. Fresh uniform permutations are independent of previous stack outputs or wallet history.

For p=1,2,3, gross multiplier=0.96×rawScore^p/mean(rawScore^p). Exact unconditional means are0.9416666666666667,1.625,3.2916666666666665. Each mode has96% expected unrounded gross credit, not winning frequency, strategy or guaranteed final wallet. Zero stays zero. Square and cube are powers, not multiplication by2 or3. Capture mode before drawing, not after seeing score.

Capture stake and mode and debit once before480ms settlement. Settings and refill lock during settlement and an active Auto queue. Auto schedules at most10 rounds when coins permit; this is per Auto request, not a lifetime or session limit. Stop cancels future rounds while an already active round settles. No early cashout or resampling is offered.

A new browser wallet starts at 1000 virtual coins. Settled integer balance and fractional payout carry are saved in localStorage. A gross credit is added to any saved fraction; the integer part is credited and the remaining fraction is carried forward. These coins have no cash value, deposits, withdrawals or prizes. Storage belongs to this browser and origin, not to an account or an external payment balance.

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.

For p=1,2,3, gross multiplier=0.96×rawScore^p/mean(rawScore^p). Exact unconditional means are0.9416666666666667,1.625,3.2916666666666665. Each mode has96% expected unrounded gross credit, not winning frequency, strategy or guaranteed final wallet. Zero stays zero. Square and cube are powers, not multiplication by2 or3. Capture mode before drawing, not after seeing score.

A new browser wallet starts at 1000 virtual coins. Settled integer balance and fractional payout carry are saved in localStorage. A gross credit is added to any saved fraction; the integer part is credited and the remaining fraction is carried forward. These coins have no cash value, deposits, withdrawals or prizes. Storage belongs to this browser and origin, not to an account or an external payment balance.

Capture stake and mode and debit once before480ms settlement. Settings and refill lock during settlement and an active Auto queue. Auto schedules at most10 rounds when coins permit; this is per Auto request, not a lifetime or session limit. Stop cancels future rounds while an already active round settles. No early cashout or resampling is offered.