THE MONTY HALL PROBLEM

three doors and a host who opens an empty one: why switching wins twice as often, and what actually decides it

Built as a memo rather than a table: the thing worth hanging it up for reads across the room, with the full reference in smaller type below it.

Three sizes in one archive — from a sheet on the fridge to a poster on the wall.

Formats: A4 · A3 · A2
What you get: Print-ready PDFs, one per size, with every letterform converted to outlines — nothing to install, nothing to shift.
Subject: maths · everyone · memo · study

The figures are computed for one game: the host knows where the prize is, always opens an empty door and always offers the swap. Change one of those and the answer changes.

WHAT SETTLES IT IS WHAT THE HOST KNOWS

The whole force of the puzzle lies in what the host knows, not in how many doors there are. If the host does not know where the prize is and opens one of the two doors at random, then in 1 game in 3 he reveals the prize himself and the game is over. And in the games where his hand happened to land on an empty door, the odds really are even: 1 in 2 for switching and the same for staying.

The picture on the screen is identical either way: three doors, one of them open, nothing behind it. The only difference is whether the host could have opened the prize — and that difference is worth 2 in 3 against one half. So “always switch” is not a rule about doors; it is a rule about a host who knows.

On the sheet

The figures are computed for one game: the host knows where the prize is, always opens an empty door and always offers the swap. Change one of those and the answer changes.
Colour carries meaning, but meaning never rests on colour alone — the sheet reads in black and white.
Nothing about how it was made: the sheet carries only what the reader needs.

Printing

Three sizes in the archive: A4 — 210×297 mm, A3 — 297×420 mm, A2 — 420×594 mm.
All text is converted to outlines. No fonts to install, and nothing shifts on another machine.
White background and sparing fills — it prints on a home printer without draining the cartridge.
Margins of at least 10 mm: a home printer cannot print to the edge.
No stroke thinner than 0.3 mm, so nothing disappears in print.

Why the numbers can be trusted. Every countable number here is computed from data rather than typed in, and the sheet must pass 9 independent checks before it is allowed to build — how many items there are, the order they come in, and the claim in the highlighted box itself. If one fails, there is no file.

THE MONTY HALL PROBLEM

WHAT SETTLES IT IS WHAT THE HOST KNOWS

On the sheet

Printing

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