Comprehensive Calculator Guide
This calculator gives the chance of winning by switching or staying in the Monty Hall puzzle, for any number of doors. With 3 doors, switching wins 66.67% of the time against 33.33% for staying. It explains why the host’s knowledge is what makes switching better.
Why switch
Your door keeps its 1/3; the host knowingly opens empty doors, so the other 2/3 gathers on the remaining door. With 100 doors and 98 opened, switching wins 99%. If the host opened doors at random, it would be 50/50.
How to Use
- Enter the doors.
- Enter how many empty doors the host opens.
- Press “Calculate” to compare switching and staying.
Formula Used
Stay = 1/doors | Switch = (doors − 1) ÷ (doors × (doors − opened − 1))
Practical Examples
- Example 1
- 3 doors: 66.67% vs 33.33%.
- Example 2
- 100 doors, 98 opened: 99% vs 1%.
Important Tips
- Try it with three cards.
- Picture 100 doors.
- The host must know where the prize is.
Common Mistakes to Avoid
- Thinking two doors means 50/50.
- Ignoring the host’s knowledge.
- Staying to avoid a “trick”.
Frequently Asked Questions
- Always switch?
- Yes, if the host knows and always opens an empty door.
- Why not 50%?
- The opening wasn’t random.
- Link to Bayes?
- It’s an update on new information.