Every morning is a departure.

You said eight minutes.

Isha's shower. It's what she always says.

It took twelve.

It usually does. People plan from the plan, not from last time.

Only 30% finish on time.

When students predicted when they would finish, about 3 in 10 made it by then.

Buehler, Griffin and Ross, 1994: the planning fallacy.

And it's never one person.

Her overrun lands on everyone's door. Three mornings, one gate.

A step is a range, not a number.

Each person's step is a log-normal distribution: never negative, sometimes long. What they say is where it starts.

Every morning teaches it.

Each real "I'm done" pulls the curve towards what happens. Five mornings in, her shower is planned at twelve, and the spread knows she underestimates.

Add the steps together.

A morning is a sum of steps. One distribution with the same mean and variance stands in for the sum (Fenton–Wilkinson), so the answer has a closed form.

Then ask the door.

The share of the curve before the gate is her chance of being ready. Tested against 100,000 simulated mornings: within 2 points.

P = Φ((ln g − μ) / σ)

A slow start is a slow morning.

Isha's shower ran 21 minutes today. Someone who starts slow usually stays slow: tired, distracted, a step behind.

So the rest moves with it.

Every finished step is a reading of today's pace. Her next steps are planned longer, and the board says so.

A shared pace per person, updated exactly; the step still running counts too.

When it says 85%, it means 85%.

Forty thousand simulated mornings, looked at mid-step. Treat the steps as unrelated and the chances drift off the line; with the pace they stay on it.

Calibration error 0.39% with the pace, 2.44% without.

"She's still in the shower."

Ten more minutes, at 7:26. Her chance of making 7:52 falls through the floor.

Gentlest changes first.

Breakfast to go costs 1. Dad packing her bag costs 2. The dishwasher waiting costs 3. It searches cheapest first, and only what the family allowed.

The cheapest plan that works.

An exact search, checked against brute force on 1,000 random mornings. Alexa says what changed; one word undoes it.