THE PROOF

A distribution, not a promise.

This is the shape of an answer in ExileCraft: one craft, run ten thousand times on practice copies, costed in chaos. The curve below is a labelled sample. Run your cursor along it.

[ 01 ] THE DISTRIBUTION — 10,000 RUNS

SAMPLE — SPEND TO FINISH “DOOM SONG”COST IN CHAOS

POSITION P50 SPEND 132c SAMPLE CURVE — ILLUSTRATIVE

[ 02 ] THE ROUTES — WHAT THE SOLVER HANDS BACK

Two ways in, priced side by side.

Same target, two legal paths. The cheaper route costs more steps; the faster route costs more orbs. The solver lays both on the bench and lets the budget decide. Sample numbers, drawn to show the shape of the answer.

SAMPLE ROUTE TABLETARGET: T1 %PHYS

ROUTE A — essence spam until the tier lands E[COST] 118c · P(HIT)/TRY 4.2% · 1 STEP

ROUTE B — fracture first, then the recomb ladder E[COST] 96c · 7 STEPS · BRICK RISK 3.1%

ROUTE C — alloy into the crafted slot E[COST] 142c · 2 STEPS · REMOVAL RISK NAMED

ILLUSTRATIVE NUMBERS — THE APP COMPUTES THESE FROM LIVE DATA

[ 03 ] THE SPLIT — HOW THE TEN THOUSAND ENDED

Where the runs landed.

Every simulated craft ends one of three ways: the target lands inside budget, the budget runs out first, or the item bricks on the way. The split is printed next to the curve so the chase is priced before it starts.

SAMPLE OUTCOME SPLIT — 10,000 RUNSSHARE OF RUNS

HIT IN BUDGET71.4%

BUDGET RAN OUT24.2%

BRICKED EN ROUTE4.4%

ILLUSTRATIVE NUMBERS — THE APP COMPUTES THESE FROM LIVE DATA

ENTER THE FORGE READ THE METHOD