You run a retirement risk simulation with 100 iterations and get a success rate of 87%. You run it again. This time it says 81%. Again: 90%. The plan did not change. The inputs did not change. So why does the answer keep moving?
Because 100 iterations is not enough.
Monte Carlo is a statistical sampling method. Each iteration is one randomly generated future for your portfolio. The success rate is the percentage of those futures where your money lasted. With too few samples, you are measuring noise, not signal.
The Convergence Problem
Think of it like polling before an election. If you ask 50 people how they will vote, your margin of error is huge. Ask 1,000 and the picture stabilizes. Ask 10,000 and you can be quite confident in the result.
Monte Carlo works the same way. Each iteration is one "respondent" drawn from the universe of possible market return sequences. The success rate is your poll result. And like any poll, the margin of error shrinks as you increase the sample size.
At 100 iterations, the standard deviation of your success rate estimate can be 3-5 percentage points. That means an 85% result could easily be 80% or 90% in reality. The number is almost meaningless.
At 1,000 iterations, the standard deviation drops to about 1-1.5 percentage points. Much better. You can start to trust the ballpark.
At 10,000 iterations, it drops below 0.5 percentage points. The success rate you see is very close to what you would get with infinite iterations.
At 50,000 iterations, running it again gives a result within a few tenths of a point of the previous run.
See it for yourself - pick a success rate and a number of simulated futures:
Try it
How precise is a success rate?
A simulation with more futures gives a steadier answer. Pick a success rate and a number of futures to see how far the result could move just by chance.
With 1,000 futures, a 85% result could really be anywhere from 82.8% to 87.2% (±2.2 points).
95% range, the same formula the simulator shows under your result. Free runs 1,000 futures, Pro 50,000.
Why Percentile Bands Need Even More Iterations
The success rate is an average measure. It converges relatively quickly. But the percentile bands showing the range of portfolio outcomes are harder to pin down, especially at the extremes.
The median (50th percentile) outcome converges almost as fast as the success rate. But the 5th percentile (your worst realistic scenario) and the 95th percentile (your best realistic scenario) require many more samples to stabilize. This is because extreme outcomes are rare by definition. You need a larger sample just to see enough of them for a reliable estimate.
If you care about tail risk (and you should, given sequence-of-returns risk and fat-tail distributions), then you need more iterations than someone who only looks at the success rate headline.
The Fat-Tail Factor
The distribution you use for returns also affects how many iterations you need.
Under a normal distribution, extreme returns are rare, so the tails converge reasonably fast. Under a Student's t-distribution or other fat-tailed model, extreme returns are more common but also more variable in magnitude. The tails are "thicker" and take longer to converge.
So if you use a fat-tailed distribution, more iterations help even more.
Speed vs Accuracy Tradeoffs
More iterations take more compute time. On a modern browser, the difference between 1,000 and 50,000 iterations might be the difference between half a second and a few seconds. Not a big deal for a desktop user, but it matters for mobile devices or for simulators that run on older hardware.
Some calculators default to low iteration counts to keep the interface snappy. This is an understandable design choice, but it comes at the cost of reliability. A fast answer that bounces around by 5 percentage points every time you run it is worse than a slower answer you can trust.
A sensible middle ground is a fast run for exploring "what if" questions and a larger run when you want a precise answer. Retirement Lab runs 1,000 futures on the free plan and 50,000 on Pro, and shows the margin of error under every result.
How to Tell If Your Simulator Uses Enough
There is a simple test: run the same scenario a few times without changing anything and look at the spread. With 1,000 futures, a result can move by about 2 points either way; with 50,000, by a few tenths. If it jumps around more than that, the tool runs too few iterations - treat its result as a rough direction, not a precise number.
What Matters More Than Iteration Count
Iteration count is necessary but not sufficient for a good simulation. A calculator running 50,000 iterations with bad assumptions will give you a very precise wrong answer.
The inputs matter more:
Return assumptions. Are the expected returns and volatilities reasonable? Are they based on historical data, forward-looking estimates, or arbitrary defaults? Garbage in, garbage out, no matter how many times you repeat it.
Distribution choice. Running 50,000 iterations with a normal distribution is better than 500, but it may still understate how often extreme years happen. The distribution shape matters as much as the sample size.
Spending strategy. A fixed withdrawal assumption ignores how real people behave. If your calculator does not let you model flexible spending, the iteration count is solving the wrong problem.
Correlation structure. If asset returns are modeled as independent, the simulation overstates diversification benefits. Cholesky-correlated returns give a more realistic picture, but only if the correlation matrix itself is reasonable.
High iteration count makes a good model precise. It does not make a bad model good.
Now try it with your own numbers
An example plan is filled in - change anything, then open it in the free simulator.
Opens the free simulator with these numbers filled in - check them and run it. Nothing is stored unless you create an account and save.