How Many Monte Carlo Simulations Are Enough?

“How many Monte Carlo simulations are enough?” is usually asked as if there is a sacred integer — 1,000, 5,000, 10,000 — and as if the person who picked the biggest number won. There is not a sacred integer. There is a standard error, a runtime budget, and a decision you are trying to make. This page is the arithmetic behind the 1,000-path default in the product and the 5,000-path tables in the longer studies. It is not a claim that 1,000 is “the right” Monte Carlo sample size for every paper ever written.

The useful question is smaller. How tight does the success-rate print need to be before you will change a contribution, a retirement age, or a withdrawal rule? Once you name that tightness, the path count falls out of a formula. Everything after that is taste, and taste is a poor reason to wait 40 seconds for a number that will not move a decision.

How many Monte Carlo simulations are enough?

Enough for what? If you are deciding between two plans that print 78% and 91%, you do not need a third decimal place. The gap is larger than the sampling noise at a few hundred paths. If you are deciding between 89% and 91%, or publishing a table that ranks policies to one decimal, you do. How many Monte Carlo simulations are enough is a question about the decision, not about the dignity of a large n.

Killion’s answer for an interactive plan is 1,000 seeded paths. That is enough to see the shape of a household — median, tails, a success rate with a roughly one-point error — in a time a person will wait. The answer for a published research table on this site is usually 5,000, because a table invites comparison and comparison invites false precision. The answer for a journal article that wants a standard error well under half a point can be 10,000. None of those integers is a law of markets. They are budgets.

A success rate is a binomial proportion

Each simulated lifetime either makes it to the horizon with money left, or it does not. If the true (unknown) success probability is p and you run n independent paths, the number of successes is a binomial count. The estimated success rate is just successes over n. The success rate standard error of that estimate is sqrt(p(1−p)/n). The formula is oldest-hat statistics. It is also the one most retirement tools never print next to the big percentage.

The error is largest when p is near 50% and smallest when p is near 0 or 1. An 85% plan and a 15% plan have the same sampling error; a coin-flip plan has more. That is why a 99% print can look more “precise” than an 80% print even at the same n — the formula gives it less room to wiggle. It is also why you should not treat a 99% on 100 paths as a settled fact. A couple of unlucky seeds move it.

What the success rate standard error actually says

At p = 85%, the closed form gives:

• n = 100 → about 3.6 percentage points
• n = 1,000 → about 1.1 percentage points
• n = 5,000 → about 0.5 percentage points
• n = 10,000 → about 0.4 percentage points

Read the chart from left to right. The first jump, 100 to 1,000, cuts the error by a factor of about three. The next jump, 1,000 to 10,000, cuts it by another factor of three — and costs you ten times the runtime. That is the usual square-root law: to halve the error you quadruple the paths. The dashed 1-point line is a useful reference for household decisions. Most people will not change a savings rate because a plan printed 86% instead of 87%. They will change it because a plan printed 70% instead of 90%.

A 95% confidence interval is roughly plus or minus two standard errors. At 1,000 paths and an 85% print, that interval is about 85% ± 2.3 points — call it 83 to 87. At 100 paths it is 85% ± 7, which is wide enough to hide a bad plan inside a good-looking round number. At 5,000 paths it is 85% ± 1. That last tightening is what a published table is paying for. It is not what a person clicking “run” on a Tuesday is paying for.

Monte Carlo sample size versus the decision

Monte Carlo sample size should match the smallest difference you intend to act on. If two withdrawal rules differ by 12 points, 500 paths already separate them. If they differ by 2 points, you want a few thousand, and you should also ask whether 2 points is a real difference in the household or a difference in the random number generator. Seeded engines help: the same seed, the same plan, the same n should reprint the same rate. Changing the seed and watching the rate jump by more than the formula is a bug, not a reason to buy more paths.

There is a second, quieter cost. A huge n on a bad model is a confident wrong number. Independent annual draws that ignore clustered crashes will converge, beautifully, on an optimistic success rate. The error bars will be tiny. The lie will be precise. The overstatement piece is the other half of this page: more retirement simulation paths will not fix a gentle market or an obedient household. They will only make the overstatement harder to argue with.

Retirement simulation paths we actually run

The product and the public demo use 1,000 seeded paths. The 4% study used 5,000. The free-calculator band uses 1,000. The August age-and-horizon table on this site used 200, which is why that table is reported in whole percents and discussed as a slope, not as a ranking of 55.5 against 56.0. The methodology page is the engine; this page is the sample size.

We seed the generator so a published figure can be regenerated. We do not seed it so that a household can shop for a flattering seed. The seed is a scientific instrument, like a lab notebook date. If you change the plan — a different savings rate, a different retirement age — you should keep the seed and change the inputs. If the success rate barely moves, the plan did not change in a way the engine can see. If it jumps by more than a couple of standard errors, it did.

What more paths will not fix

They will not add 1929 to a model that cannot cluster. They will not add taxes to an engine that ignores them. They will not add a spouse, a pension, or a healthcare shock. They will not turn a rigid 4% into a flexible 4%. They will not make a 50-year retirement as easy as a 30-year one. Those are modeling choices, documented on the methodology page and in the Monte Carlo explainer. Sample size is the last knob, not the first.

Runtime is the other half of “enough.” A 1,000-path household run is something a person will wait for. A 10,000-path run of the same plan is something they will walk away from, and then they will not see the range at all. The product default is a compromise with attention, not a claim that the 1,001st path is worthless. Studies on this site that need a tighter table pay the extra time once, offline, and publish the result. Interactive tools should not make every click wait for a journal-article standard error.

Independence is an assumption in the formula, too. The 1,000 product paths are distinct draws from the regime engine, not 1,000 copies of one life. If you somehow ran the same seed 1,000 times you would have n = 1 and a beautiful, useless 0% error. Seeded and independent are not opposites: one seed starts the stream, then each path consumes a different slice of it. That is why reprinting a study works, and why shopping for a flattering seed does not.

So how many Monte Carlo simulations are enough? Enough that the error is smaller than the decision, and not so many that you confuse a tight interval with a true model. For Killion that is 1,000 paths when you are planning and 5,000 when we are publishing a comparison table. If your question is finer than that, say so — and then say what you will do if the extra precision lands on the other side of the line.

Notes on the figures. The line chart is the closed-form binomial standard error SE = sqrt(p(1−p)/n) at p = 0.85, plotted against n = 100, 200, 500, 1,000, 2,000, 5,000 and 10,000 on a logarithmic x-axis. The dashed line is a 1-percentage-point reference, not a fitted curve. No Monte Carlo was run to draw this figure; the arithmetic is exact. Product and demo defaults (1,000 paths) and research defaults (5,000 paths) are stated in the methodology notes and in the relevant study articles. This article is educational analysis, not investment advice, and does not recommend any security or strategy.