Monty Hall Simulator

Stay vs switch, simulated and exact

About this calculator

The Monty Hall Simulator solves the famous stay-or-switch puzzle exactly and by simulation, for the classic game and generalized versions with N doors and K revealed goats. It reports the exact win probabilities as reduced fractions — P(stay) = 1/N and P(switch) = (N−1)/(N(N−1−K)) — plus the switching advantage, then plays thousands of seeded, reproducible games to show the empirical win rates converging on theory, with 1σ standard errors on both rates.

How to use the Monty Hall Simulator calculator

  1. Enter the values for your problem into the input fields.
  2. Read the result — it updates instantly as you type.
  3. Check the formula and the visual explanation to follow how the answer was found.
  4. Copy the page URL to share the exact calculation.

Common examples

  • Classic 3 doors, 1 reveal → stay wins 1/3, switch wins 2/3; 10,000 games: 33.61% vs 66.39%
  • 100 doors with 98 goats revealed → switching wins 99/100 = 99% of the time
  • 10 doors, 5 revealed → stay 1/10, switch 9/40 = 22.5%, a 2.25× advantage; simulation ≈ 22.48%
  • The advantage ratio simplifies to (N−1)/(N−1−K) — always > 1, so switching never hurts

Frequently asked questions

How does the Monty Hall Simulator calculator work?

Enter your values and the calculator applies the exact mathematical method for this problem, showing the result together with the formula it used. Everything is computed with high-precision arithmetic, so the answer you see is not limited by ordinary floating-point rounding.

When would I use the Monty Hall Simulator calculator?

It is useful for homework and exam preparation, for checking work done by hand, and whenever a step in a larger problem needs this calculation done quickly and reliably.

How accurate are the results?

Calculations run at 30 significant digits of precision internally. Displayed values are rounded for readability, but the underlying result is far more precise than a typical hand or pocket-calculator computation.

Can I share a specific calculation with someone else?

Yes. Every value you enter updates the URL, so copying the address bar and sharing the link reopens the exact same calculation for whoever clicks it.