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.
Switch —Stay —Best odds 67%
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?