Ode to the Monty Hall Problem

Lyrics

[Intro]
Three doors.
Just three.
The lights are hot enough to melt greasepaint.
Studio 33. Ninety degrees under the Fresnels.
And you. You have to choose.

[Verse 1]
You point a trembling finger.
Door Number One.
It feels right. A gut feeling.
The first is always lucky, or so they say.
The host smiles. A practiced, patient smile.
He knows something you don't.
He always knows.

[Chorus]
And he walks to Door Number Three.
He opens it slow.
Just a goat.
Now he turns to you.
The smile is wider now.
He says, "Behind your door, or the other one... is a brand new car."
"Do you want to switch?"

[Verse 2]
Your mind screams no.
It's fifty-fifty now. A coin flip.
To switch is to doubt yourself. To look weak.
Ten thousand letters to Marilyn vos Savant.
From PhDs in statistics.
From men who signed their names with all their titles.
All of them shouting, "Don't switch. She's wrong."
September 9, 1990. Parade magazine.
They all trusted their gut.

[Chorus]
And he walks to Door Number Three.
He opens it slow.
Just a goat.
Now he turns to you.
The smile is wider now.
He says, "Behind your door, or the other one... is a brand new car."
"Do you want to switch?"

[Bridge]
But your first choice wasn't a fifty-fifty guess.
It was one in three.
A two-in-three chance you were wrong from the start.
He didn't open a door at random.
He opened a door he knew was empty.
All that probability...
All that two-thirds chance you were wrong...
It doesn't disappear.
It pools behind the last closed door.
Steve Selvin tried to tell them in 1975.
The host's knowledge changes everything.

[Outro]
The audience is quiet.
The lights feel hotter.
You look at your door. Number One.
You look at his smile.
You look at Door Number Two.
And you say the word.
"Switch."
You always switch.