6zk — Complement Rotation Echo

The core mechanic involves twelve labelled cyclic rotations of the bitwise complement of a 12-bit word. The score is derived from the common-prefix length between the original word and each rotated complement.

• Raw Score Calculation: For each of the 12 rotations, square the common-prefix length and sum these values.
• Score Powers: Players select one of three modes: Raw Score (Power 1), Squared Score (Power 2), or Cubed Score (Power 3).

The live gross bank quote is calculated as: 0.96 × captured whole stake × conditional expected terminal raw score (raised to selected power) ÷ unconditional mean for that power.

Twelve independent fair bits are revealed in order. The quote can rise or fall as more bits are revealed. If the conditional potential drops to zero, the round settles at zero. The expected gross return under supported stopping policies is exactly 96% before integer rounding.

• Stake: One whole captured stake per round.
• Auto-Cap: Preselect an automatic reveal cap of 4, 8, or 12 bits.
• Locking: Captured stake, power, and cap are locked during the live round.
• Manual Bank: Available immediately while live. No Auto10 queue.
• Sound: Remains available even when controls are locked.

• Settlement: Manual bank settles the current conditional quote. Auto-bank triggers at the selected cap (4, 8, or 12) or if conditional value hits zero.
• Fractional Carry: Persists across settlement, refill, and reload.
• Unfinished Reload: Reloading an unfinished trace loses the captured debit; it is not resumed.
• Idle Refill: If the balance is below 10 while idle, a manual refill sets the balance to exactly 1000, preserving fractional carry.

Twelve fair independent bits define 4,096 equally likely complete words. Select score, squared score or cubed score, each priced by its own exact unconditional mean. At each prefix the quote averages all remaining possible words, so it can rise or fall. Any bounded stopping rule has 96% expected gross return before integer rounding; fractional carry is saved. Auto-bank caps are 4, 8 or 12 revealed phases. Stake, power and cap are locked during a trace. Idle manual refill below 10 sets 1,000 and preserves carry. Reloading an unfinished trace loses its captured debit.

Wallet: Initial balance is 1000. Refill is manual and idle-only, setting balance to 1000 if below 10. Virtual coins have no cash value. Settled balance persists locally; unfinished rounds do not resume.

Virtual coins · no prizes