Monte Carlo is a tool for analysing uncertainty. It uses sampling techniques conceptually similar to election polling.
If you want to predict the outcome of an election, you could ask every single voter how they intend to vote. However, this would be an enormously lengthy and costly process if there are millions of voters. Instead, several hundred randomly selected voters are polled and the outcome of the election is extrapolated from their responses. In the same way, Monte Carlo analysis samples a large number of cost 'scenarios' and infers the most likely overall cost outcome from the results.
When you ask the question "who are you going to vote for?" in an election poll, you expect and normally get a discrete answer ("I'm going to vote for candidate X"). If you use the same techniques when attempting to analyse project cost estimates, things are a little more complicated.
Cost estimates are usually broken down into a series of line items or tasks. The estimate for each item may be expressed as a range of values. For example, an item might be expressed as $1000 plus 20% contingency, meaning that you expect it to cost somewhere in the range $1000 to $1200. For analysis purposes, this range is expressed as a probability distribution, which tells us not only where we expect the actual cost to be, but also how likely any particular cost will be.
The probability distribution shown below as an example indicates that in this case the most likely cost is expected to be $1100. Other costs are less likely, and there is no expectation of a cost less than $1000 or greater than $1200.
The mere fact that you have assigned upper and lower limits to a cost item is no guarantee that the actual cost to completion will be within these limits. A cost in which the possibility of an overrun is envisaged is known as an open-ended cost.
Monte Carlo analysis can include the possibility of cost overruns. Overrun probabilities are based on the level of confidence which you feel in a particular estimate.