Every financial model I have built started life as a single, confident version of the future. You fill in the assumptions, the totals turn green, the net present value comes out positive, and somewhere between the third tab and the investor deck the forecast quietly promotes itself from “a guess I made on a Tuesday” to “the plan”. The model has only ever seen one future, and it is remarkably sure about it.
The problem is not that the number is wrong. The problem is that it is alone. A base case answers exactly one question — what happens if every assumption lands more or less where I put it? — and then stops. It says nothing about how often things land somewhere else, which, in the experience of anyone who has actually run a business, is most of the time. A forecast built this way is a hypothesis with the experiment quietly removed.
Founders are usually told the fix is to “do a sensitivity analysis” or to “add an optimistic and a pessimistic column”, and both help a little. But three columns still describe three futures, hand-picked by the person least likely to imagine the one that hurts. To see the actual shape of the risk you have signed up for, you need more futures than you can be bothered to type. Which brings me, slightly improbably, to a card game.
A convalescent, a deck of cards, and a casino
In 1946 the mathematician Stanislaw Ulam was recovering from a serious illness and, by his own account, passing the time playing Canfield solitaire — the variety where your odds of winning are genuinely dismal. Being a mathematician, he wanted to know precisely how dismal. He started down the combinatorial route, trying to calculate the probability of a winnable layout, and rapidly discovered that the exact maths was a nightmare. So he had a lazy and rather brilliant idea: instead of computing the odds, why not simply lay the cards out a hundred times and count how often he won?
That instinct — when the exact calculation is intractable, simulate it instead — turned out to matter a good deal more than solitaire. Ulam realised the same trick could estimate how neutrons scatter through material, a problem nobody could solve on paper. He took it to John von Neumann, they ran it on the early computers at Los Alamos, and a colleague, Nicholas Metropolis, supplied a suitably discreet code name, borrowed from an uncle of Ulam’s who used to borrow money to gamble at the Monte Carlo casino. The method that now sits behind risk analysis in finance, engineering and climate science began with a man too unwell to do the sum and too curious to leave it alone.
The lesson survives the journey from physics to finance intact. A startup model is exactly the sort of system Ulam was describing: a handful of uncertain inputs — acquisition cost, conversion, churn, price, hiring pace — that interact in ways too tangled to hold in your head. You cannot intuit what happens to month-30 cash when CAC drifts up while churn drifts up at the same time, because the two effects compound rather than politely add. So you do the modern equivalent of dealing the cards. Instead of one churn figure you give the model a plausible range; you do the same for the other drivers; and you let the computer run the entire model thousands of times, drawing a different combination on each run.
What comes back is a shape, not a number
What the simulation returns is not a single answer but a distribution — a picture of how the outcome behaves across all those futures. The first time I ran this on one of my own plans, the result was educational in the way that being slightly humiliated is educational. The base case showed a net present value of around €420,000, which had made me feel quite clever. The simulation showed that roughly a third of the runs came out negative. Same model, same arithmetic; the only thing I had added was a bit of honesty about the inputs. A positive base-case NPV had been concealing a plan that failed once in every three attempts, almost always in the runs where acquisition cost and churn went the wrong way together.
Payback, incidentally, told an even more flattering and even more useless story. An average payback period is silent about the futures in which you run out of cash before you ever reach it, and those are precisely the futures that end the company. A point estimate, however carefully calculated, cannot warn you about a risk it has been designed not to contain.
What the heavy users already know
None of this is a startup novelty. Monte Carlo simulation has been standard equipment for decades in exactly the places where a wrong number is expensive. Banks use it to estimate value at risk and to model the probability of default across loan portfolios; insurers use it for capital adequacy; project-finance teams use it to price the risk of cost overruns on infrastructure that takes a decade to repay. Financial advisers use the same technique on the other end of the wealth spectrum, simulating thousands of market paths to estimate whether a household’s savings will outlast its retirement. The method has been quietly built into the spreadsheet risk add-ins that finance and engineering departments have run for years.
The clearest lesson comes from the oil and gas industry, which has been forced to be honest about uncertainty for longer than most. When a company estimates how much sits in a reservoir, it does not report a number; it reports three. The P90 is the conservative figure, with a 90% chance of being met or beaten; the P50 is the midpoint; the P10 is the optimistic case. In one worked example from a Stanford teaching report, the gap between the conservative and optimistic estimates for a single field came to roughly 82% — a spread wide enough to separate a sound investment from a write-off, and entirely invisible if you quote only the middle figure.
The same industry also supplies the warning that matters most here. A long-standing caution in the petroleum literature is that the P90 of your reserves does not translate into the P90 of your net present value, because the two distributions do not align — and that opaque, black-box models are exactly where this kind of error hides. A simulation inherits the trustworthiness of the model beneath it. Run an unauditable model a million times and you have a million unauditable answers.
The objection is correct, and it misses the point
Here the honest objection arrives, and it deserves a proper answer. If I invent the ranges, am I not just manufacturing sophisticated nonsense — false precision with a respectable Latin name attached? If you treat the output as a prophecy, then yes. Feed a simulation distributions you pulled from the air and you get ten thousand fictional answers, delivered faster and with nicer charts. No technique can rescue assumptions you have not bothered to think about.
But that objection misreads the job. The simulation is not there to hand you a more precise number; it is there to tell you which of your assumptions actually decide your fate, and how much of the outcome range you could survive. Run it and you usually discover that two or three drivers move almost everything while the rest are noise, which tells you exactly where your scarce attention is worth spending. A Monte Carlo simulation works as a stress test rather than a fortune teller, and it earns its keep on the days it reveals that your confident plan has a fat, ugly left tail you had simply never looked at.
The critics have a second point worth holding on to. The method is weakest at the genuinely rare, regime-breaking event — the 2008-style shock that no sensible distribution would have included in the first place. It maps the risk you can imagine, which is never quite all of it. That is a reason to treat the output as a discipline rather than a guarantee, not a reason to go back to a single line of best hope.
The randomness goes in the inputs, never in the formulas
There is one condition, and it is the part most tools quietly get wrong. A simulation is only as trustworthy as the model running underneath it. If the engine doing the arithmetic is improvising — an AI, say, that produces a plausible-looking but subtly broken cash flow — then running it ten thousand times multiplies the error rather than the insight. Simulation is a layer you place on top of a calculation you can already trust, not a substitute for one. The uncertainty belongs in the inputs you are sampling; the relationships between them must hold every time. The balance sheet has to balance in all ten thousand runs, or the exercise is theatre with a progress bar.
That ordering is the reason FinModeler is built the way it is. The model is produced by a deterministic engine — the same structured assumptions always yield the same auditable statements — and the scenarios and Monte Carlo simulation run on top of that engine rather than around it. When you look at the distribution, you are looking at thousands of versions of a model whose arithmetic you can open up and inspect line by line. The AI layer then reads that output and points at the drivers carrying the risk, which is the one task AI is genuinely good at in finance: interpreting and interrogating numbers it did not invent.
It is worth saying where this is heading, because the economics are shifting fast. Simulation has always been constrained by compute, and that constraint is falling away: cheap parallel hardware and, increasingly, machine-learning surrogate models — fast approximations trained to imitate a slow model — are making it routine to run millions of scenarios where a few thousand used to be the practical ceiling. The more interesting change is at the other end of the process. Running the simulation was never the hard part; reading it was. A distribution only helps if someone notices the ugly tail and does something about it, and that interpretation — explaining in plain language which assumptions are quietly steering the outcome — is the part now being handed to AI, and the part it can do well precisely because it never has to touch the arithmetic.
None of this makes the future knowable. It does something more modest and far more useful: it trades a single brave guess for an honest map of the outcomes your own assumptions permit, including the ones you would rather leave off the slide. Ulam reached for the method because the exact answer was out of reach, which happens to be the permanent condition of anyone deciding where to put capital. Before you commit yours to the one green-celled future your model happens to favour, it is worth seeing the others.
Test the downside before you fund the upside — build your model and run the simulation on FinModeler.
FAQs
What is a Monte Carlo simulation in financial modelling?
It is a way of running your model many times, each time drawing a slightly different value for your uncertain assumptions from a plausible range. Instead of one outcome you get a distribution of outcomes, which shows how often the plan succeeds, how often it fails, and by how much.
How many runs do I actually need?
Enough that the picture stops moving when you add more. A few thousand is usually plenty for a business model; ten thousand is common. The precise count matters less than having ranges you have thought about honestly.
Is Monte Carlo better than scenario analysis?
They answer different questions and work well together. Scenario analysis tests a few hand-picked futures — base, optimistic, pessimistic. Monte Carlo samples the whole space between them, so it catches the awkward combinations you would not think to write down. Use scenarios to communicate; use simulation to find the risk.
Can I trust the result if I am guessing the inputs?
A simulation cannot fix bad assumptions, and it is not meant to. Its value is in showing you which assumptions your outcome is most sensitive to, so you know where a better estimate is worth the effort — and where it would not change the decision at all.
Sources
- Probabilistic reserves and the P90/P50/P10 framework: DNV, Terminology explained: P10, P50 and P90; Enverus, P10, P50, P90 Reserves.
- The ~82% spread between conservative and optimistic reserve estimates: M. Almajid, Oil Reserves Uncertainties, Stanford University (Physics 240 report).
- The warning that P90 reserves do not yield P90 NPV, and the risk of black-box models: Oil & Gas Journal, “Probabilistic reserves definitions, practices need further refinement”.
- Adoption across VaR, credit risk and project finance: Interactive Brokers, The Power of Monte Carlo Simulations in Finance; retirement-planning use and the rare-event critique: Analytica, Monte Carlo Modeling in Personal Finance; cross-industry use of simulation add-ins: Lumivero (@RISK).
- Future direction (GPU acceleration, hybrid AI–MC and machine-learning surrogate models): review literature on AI-assisted Monte Carlo and surrogate modelling.