# Umbrella break-even model handoff

Decision rule: expected cost. Carry the umbrella when C_soaked/C_umbrella > 1/P(get wet).

Forecast interpretation: 70% means rain occurs at the user's location at least once during a 12-hour window.

Models:
1. All-or-none daily event: P(get wet)=0.70.
2. Constant hazard: P(get wet)=1-(1-0.70)^(e/12).
3. Main model, continuous block: one rain block of d hours with random placement, P(get wet)≈0.70*(d+e)/12.

The main model is physically more defensible than constant hazard because rain is temporally clustered. It still depends on d, the typical rain duration. A provisional value d=2 hours is used as a middle scenario; it is unverified here and should be replaced with local climatology if available.

For d=1,2,4 hours:
- 20-minute exposure: ratios 12.86, 7.35, 3.96.
- 2-minute exposure: ratios 16.59, 8.43, 4.25.

The 2-, 20-minute values are computed from e=2/60 and 20/60 hours. The exact arithmetic is in umbrella_break_even_model.py.
Figure font: DejaVu Sans, an open-licensed Bitstream Vera derivative.
