Python Build a Reproducible Monte Carlo Estimate

Estimate a probability with a reproducible Monte Carlo simulation.

What It Does and Why It Matters

A Monte Carlo simulation repeats an experiment using pseudorandom inputs and estimates a quantity from the observed frequency. Set a seed on a dedicated Random instance so tests are reproducible. Larger samples usually reduce sampling error, but they do not correct an invalid model or guarantee exact results.

The fixed seed is appropriate for reproducibility, not for generating secrets.

Step-by-Step Example

Start with the complete example below. Read the inputs and predict what the final print statement will show before you run it.

import random
rng = random.Random(2026)
trials = 10_000
inside = 0
for _ in range(trials):
    x = rng.random()
    y = rng.random()
    if x*x + y*y <= 1:
        inside += 1
print(3.0 < 4 * inside / trials < 3.3)

How the Code Works

The imports make these standard-library tools available: random.
The name rng receives the value of random.Random(2026). Changing this input lets you explore a different case.
The loop advances through values one at a time. Note when the condition is checked and when the state changes.
The print calls display the results. Compare these results with the method’s documented return type and the input used.

Expected output:

True

For the demonstrated inputs, Python displays 'True'. This result follows from the operation described above; change one input at a time to understand which rule matters.

What to Notice

Pay attention to the accepted input types, the returned value and the boundary behavior. Predict what changes if you replace the example input with an empty, zero, negative or missing value, where that value is meaningful for this operation.

If the task uses a library function, inspect its documented exceptions and return type before reusing it inside a larger function.

Where You Would Use This

Use the technique when it makes a real task easier to understand or safer to maintain. Check input and output behavior with small tests before combining it with larger application code.

Practice Exercise

Run the experiment with 100, 1,000, and 10,000 trials; compare estimates of pi.

Before running your edited example, write down the result you expect. Then test at least one valid boundary or deliberately invalid value, using appropriate exception handling where necessary.

Reference: official Python documentation for the complete API contract and version notes.

Common Beginner Mistakes

Treating one simulation estimate as an exact analytical answer.
Overlooking the documented condition: larger samples usually reduce sampling error, but they do not correct an invalid model or guarantee exact results.

Key Takeaways

Estimate a probability with a reproducible Monte Carlo simulation.
A Monte Carlo simulation repeats an experiment using pseudorandom inputs and estimates a quantity from the observed frequency.
Run the experiment with 100, 1,000, and 10,000 trials; compare estimates of pi.