What a Monte Carlo simulation is
The phrase on every venue page, explained — including what it does not do.
Running the same night thousands of times
A Monte Carlo simulation answers a question about something uncertain by doing it over and over with the luck redrawn each time. Instead of asking "how many people are in the room at half past ten", which has no single answer, you simulate the whole evening — every arrival, every drink ordered, every person deciding to leave — and then you do it again, and again, with different luck. One run tells you almost nothing. Thousands of runs tell you the shape: what a normal night looks like, what a quiet one looks like, and how far the busy ones go.
That is the whole idea. There is no clever formula underneath it. The method is patience — you let chance play out enough times that the pattern stops moving.
Los Alamos, and a card game
The method is named after the casino, and the name was a joke that stuck. In 1946 the mathematician Stanislaw Ulam was recovering from an illness and playing solitaire, and he wondered what the chances were of a game coming out. He found the combinatorics hopeless and realised it would be far easier to lay out a hundred hands and simply count how many worked.
He took the idea to John von Neumann, and at Los Alamos they turned it on a much harder problem: how neutrons travel through shielding, scattering and being absorbed, where the arithmetic is likewise intractable and the luck of each collision is the whole story. It needed a code name. Nicholas Metropolis proposed Monte Carlo, after the casino in Monaco where Ulam's uncle borrowed money to gamble. The name outlived the secrecy.
What made it practical then is what makes it ordinary now: a machine that will do the same thing a great many times without getting bored. Their machine filled a room. The sweep behind this site ran on a laptop.
Where else the method is used
This section is about the method, not about us. These are places Monte Carlo simulation is standard practice; none of them has anything to do with this site, and none of them has checked our work.
- Physics, where it started: how particles scatter through matter.
- Weather forecasting, where the same forecast is run many times from slightly different starting conditions — the reason a forecast is given as a percentage chance of rain rather than a yes or a no.
- Finance and insurance, for pricing and for asking how bad a bad year gets.
- Engineering and logistics, for queues, for failure rates, and for how long a thing lasts before it breaks.
- Drug trials and epidemiology, for how an effect might play out across populations that are not identical.
Why it suits a Friday night
A bar's evening is made of chance. Nobody arrives on a schedule. A group of six turns up at nine and a couple turns up at nine as well, and whether the bar copes depends on which happened and in what order. Somebody takes twenty minutes over a drink and somebody else takes five. Every one of those is a coin coming down differently, and they compound: a queue that forms early is still there an hour later, and one that never forms never costs anything.
That compounding is why a single average night is the wrong thing to compute. Averaging the arrivals first and then simulating gives you a smooth evening nobody ever has, and it hides the queue entirely — because the queue comes from the clumping, and averaging is precisely the operation that removes clumping. So the room is simulated with the clumping left in, thousands of times over, and the answer is reported as a range across those nights rather than as one number pretending to be certain.
On this site that is 2,400 simulated nights for every figure published, read from the engine's own constant rather than written into this sentence.
What it does not do
This is the part worth reading twice. Monte Carlo handles the randomness IN the inputs. It does not make the inputs right.
The simulation assumes a pattern of when people arrive, how long they stay, and what they spend. Those assumptions are ours. If the spend per head is wrong, every one of the thousands of nights is wrong in the same direction and by the same amount — and the range does not widen to warn you, because every night in it was built on the same wrong number. A band from this method says how much the answer moves when the LUCK changes. It says nothing at all about whether the assumptions were any good.
Which is why every page carrying one of these figures also states what it assumed, and why none of them is presented as this venue's takings. They are our simulation of a room, and we have never seen the books.