Should you switch doors or stay?
The most contested puzzle in probability, as four spreadsheet rows. The host knows where the prize is, you always pick door 1, and the win formula encodes the logic. The flag column settles it.
School Starter Monte Carlo Pro engine
After you install, this is the model to open.
Switch or Stay? The Monty Hall Problem, Simulated
- In your spreadsheet, click the Sortia icon in the strip of icons down the right-hand edge. No strip? Click the arrow at the bottom-right to open it. You can also use Extensions, then Sortia, then Open Sortia.
- Click Start from a template and put that name in the search box.
- Pick the card with that name and click Load this template. It arrives on a new tab with real numbers already in it.
This one runs on a Pro engine, and every free install includes five full-quality runs on your own numbers, shared across all five Pro engines rather than five for each. After that, Pro is $199/year.
The answer
Twenty thousand games, switching:
- Win rate, switching
- 0.67
- Win rate, staying
- 0.33 set the cell to 0
Switching wins two games in three, exactly as the argument says and intuition refuses. The bigger lesson for a stats class: when probability arguments stall, build the game and play it twenty thousand times. Simulation checks reasoning; it does not replace it.
The model
The prize door is a discrete draw over 1, 2, 3. If you switch, you win exactly when your first pick was wrong; if you stay, exactly when it was right. One IF formula per game.
| Prize door | discrete 1/2/3, equal odds |
| Strategy | switch = 1, stay = 0 |
| Win rate | simulated |
Once it is in your sheet
- The model arrives with real numbers in it and runs as it stands, so you can press the button first and understand it second.
- Change the numbers to yours. The sheet marks which cells are inputs and which hold formulas, and most labels carry a note explaining the row.
- Press the run button at the bottom of the panel. It is labeled for the tool you are in, and the result lands on its own tab, with a written reading of it beside the figures.
Never used Google Sheets? Start here goes the whole way, in seven steps, and assumes nothing.
Next question
- Why does splitting the money cut the risk?Why Diversification Works
- Drill blind or pay to learn the odds first?Is the Test Worth Paying For?
- Why is the textbook schedule too optimistic?The Classic Project Network, Simulated
- Does discounting to fill the room ever work?What Does the Course Have to Charge?
- Is an equal share of the work actually fair?Share the Marking Fairly
- Did the course work or do the students just differ?Did the Course Move the Scores?
Every model like this one, and the method behind them: Monte Carlo simulation.