Route 168: Compass trace rules

Start at coordinate(0,0) facing east. A complete hidden sequence of twelve independent fair left/right choices is sampled once. On each choice, turn the current heading 90 degrees left or right BEFORE moving one unit in that new heading. Subsequent heading is relative to the previous heading rather than a fresh east direction. Animation reveals only the actual trace reached so far, without future path information or redraws.

Twelve left turns repeat a one-by-one rectangle and score0. Alternating left/right turns form a north/east staircase with width6 and height6, scoring35. Width and height are coordinate differences without an extra one, not cell counts or enclosed trace area.

There are4 zero-score paths and4092 positive-score paths. Power weighting changes gross-credit amounts but never positive-result frequency. A positive credit may be below its captured stake and is not necessarily profit. Previous traces do not predict independent future choices.

Include the origin and every reached coordinate. Width is maximum x minus minimum x; height is maximum y minus minimum y. Neither extent includes an extra one. Raw score is max(0,width×height−1). It is the area of that axis-aligned rectangle minus one, not the area enclosed by the path or the number of visited cells. A completed trace confined to a one-by-one rectangle scores zero. Alternating L/R turns form a north/east staircase with width and height six, giving score 35.

Select linear, squared or cubed positive-score weighting. Gross multiplier is 0.96 times raw score raised to selected power divided by that power’s exact unconditional mean. The means are 8.37890625,93.80859375 and 1322.578125. Four of 4096 equally likely paths have score zero;4092 are positive. Zero remains zero. Every mode has 96% exact unrounded expected gross credit, not winning frequency or a session promise. Mode changes do not change an already captured drop.

At most six priced drops can be active concurrently. Each captures and debits its own whole stake and selected mode once. Settings affect later launches rather than drops already active. Auto schedules ten drops. Stop cancels future launches while active drops complete and settle. There is no early collection or row-share stake. Refill remains locked until every ball and queued launch has settled or been cancelled.

The wallet begins with 1000 free virtual coins. Settled wallet and fractional-credit carry persist in browser localStorage. Only while idle below ten coins can manual refill set balance to 1000 preserving carry; it does not add 1000. Saved debited wallet and carry survive reload, but unfinished drops are not recovered or refunded. Keep active drops open until settlement. The guide has no customer account, deposit, withdrawal, cash prize or coin exchange.

Refill locks until all active drops and queued launches finish or are cancelled. Only while idle below10 can manual refill set balance to1000 preserving carry. It does not add1000, refill automatically or reset at any time. Saved zero remains zero after reload with the refill button visible.

Saved debited balance and fractional carry survive reload. Unfinished drops are not resumed or refunded. Keep active drops open until settlement. Clearing ordinary cache may not clear localStorage; removing local data cannot recover prior progress or remove data already processed elsewhere.