How many Monte Carlo iterations does a bid need?

More runs reduce noise, not uncertainty

A Monte Carlo result is itself an estimate. Run the same project model twice with different random seeds and you will get slightly different percentiles. The question is not "what is the right number of iterations?" but "how much does the answer wobble at this run count, and does that wobble matter for the decision?"

A test you can reproduce

Take an illustrative three-task project priced at $800 per person-day, with Beta-PERT (λ = 4) ranges of 4 / 6 / 9, 15 / 22.5 / 40 and 6 / 9 / 15 days. A 2,000,000-run reference simulation puts P50 cost at about $31,597, P80 at about $35,320 and P95 at about $38,796.

Now repeat the simulation 200 times with different seeds at each run count. The table shows how far apart about 95% of those repeated estimates fall around the true value (1.96 standard deviations, assuming the repeated estimates are roughly bell-shaped).

Two patterns matter. First, the error shrinks with the square root of the run count: four times as many runs roughly halves the wobble. Going from 10,000 to 50,000 runs buys far less than going from 500 to 2,000. Second, the tail wobbles more than the middle: P95 is consistently noisier than P50 because fewer samples sit out there.

Probabilities near zero need more runs

The same effect hits probability of loss. For this project, the share of simulated outcomes above a $40,000 cost is about 2.6%. Estimated from 500 runs, that figure typically lands within about ±1.4 percentage points of the true value, which is more than half the number itself. At 2,000 runs the band is about ±0.7 points; at 10,000, about ±0.3 points. A small probability is a count of rare events, so it needs a larger sample than a median does.

Compare the wobble with your input uncertainty

At 10,000 runs the P80 estimate moves by roughly ±$115. Now change one input: raise the pessimistic value of the 15 / 22.5 / 40-day task from 40 to 50 days. The reference P80 jumps from about $35,316 to about $37,648, a $2,332 change, twenty times the sampling wobble. Your assumptions are almost always a bigger source of error than your iteration count. Spend the effort on the ranges, the dependencies and the explicit risks, then pick a run count that keeps the sampling error small next to that.

A practical rule

• Exploring a range of options: a few thousand runs are enough to compare shapes and see which task drives the tail.
• Quoting from P50 to P90: use at least 10,000 runs so the percentile you quote is stable to a fraction of a percent of cost.
• Judging a small loss probability or a high percentile: use the largest depth available, then repeat once with a different seed. If the two runs disagree enough to change the decision, run longer.
• Sharing a result: keep the seed fixed so a colleague reproduces exactly the same numbers.

Read how the sampling works in the methodology, and see why a single three-point number is not enough in PERT versus Monte Carlo. To price from a percentile, use the minimum bid price calculator.