the Monty Hall game — win 💰, dodge 🐷
Your first pick is right only 1 time in 3. So 2 times in 3, the cash is behind a door you didn't pick.
Monty knows where the pigs are. He always opens a pig door from the ones you didn't pick. That doesn't change your 1-in-3 — it squeezes the other 2-in-3 onto one remaining door.
Stay = betting your first guess was right (1/3).
Switch = betting it was wrong (2/3). Switch wins twice as often.
Still not buying it? Imagine 100 doors. You pick one. Monty opens 98 pig doors and leaves one shut. Still feel good about your first pick?
Want to go deeper? Try the interactive Monty Hall simulators on Shodor's Interactivate — run thousands of trials and graph the results:
▸ Simple Monty Hall
▸ Advanced Monty Hall
▸ All Interactivate activities
Educational inspiration and further learning:
The Shodor Education Foundation,
a nonprofit advancing math & science education through computation,
founded by Dr. Robert M. Panoff.
This little game is an independent tribute — all credit for the deep-dive simulations and curricula goes to Shodor's Interactivate project.