What quantity did you change?
Labs / Mathematics
Monty Hall
Pick a door hiding a prize. The host throws open the losing doors, then you either switch to the last closed door or stay put. Play by hand or auto-run thousands of rounds — the two bars track your real win rate against the odds probability predicts, and the surprise is that switching wins twice as often.
Labs / Mathematics / Monty Hall
Monty Hall
Pick a door hiding a prize. The host throws open the losing doors, then you either switch to the last closed door or stay put. Play by hand or auto-run thousands of rounds — the two bars track your real win rate against the odds probability predicts, and the surprise is that switching wins twice as often.
Why it matters
Why explore this?
Mathematics helps us describe patterns precisely and predict what comes next. This model turns an abstract relationship into something you can change and observe.
Explore
Try the model
Switch —Stay —Best odds 67%
Investigate
Questions to test
Predict first, try it in the model, then use what you observe to answer.
What to try
- Auto-run 2,000 rounds on Switch, then on Stay. Which strategy lands near 67% and which near 33%?
- Once you've committed to a door, does anything the host does actually change where the prize was hidden?
- Slide up to 10 doors. After the host opens 8 of them, how good does switching to that one lonely closed door look now?
- With only 3 doors, why doesn't staying give you a fair 50/50 once one loser is revealed?
- Play just five rounds by hand. Does such a small sample match the theory, and why does the auto-run of thousands hug it so tightly?
Explain
Make sense of what happened
State the pattern in words, test it with another example, and then connect it to the mathematical rule or representation shown in the model.
Check
Before you leave
What pattern did you observe?
Does the pattern work for another example?
If you can answer all three using evidence from the model, you understand the main idea. If not, return to Explore and change one setting at a time.