Michael Kitces has an excellent blog on getting a grasp on what the academic terms Probability of Failure (or Success) mean to most people who have difficulty digesting the concept of probability.
Past, more academic labels, of probability of “… “success” and “failure” do little to connote the true reality – that “success” actually means an excess left over, and that failure merely means that some kind of mid-course adjustment may need to occur.”
I would say the terms Possibility of Adjusting (Spending) and Possibility of Excess (outliving your money, or passing it to your heirs) are better understood by you, the reading general public.
What Monte Carlo does is simply look at a range of possible outcomes. What my research collaborators and I have done, is develop a method to string those simulations together which allows us (and the professionals who adapt the methodology and perspective) to better measure the impact of decisions you make today (your Present Self) on you in the future (your Future Self). This is illustrated below by showing three (3) simulations strung together.
Understanding how decisions you make today affect your future is important; as described in the linked New York Times article Future Self vs. Present Self by David Leonhardt. Incorporating the ability to measure your decisions is equally, or even more, important.
Understand that there are methods to measure your exposure to outliving your money (Possibility of Excess) when times are good, and overspending (Possibility of Adjustment) when times are not so good.
An annual review is important to determine just how you are doing. A deeper discussion, for those interested, may be found at this blog.
PS. Note that the perception that risk to market sequences appears to “go away” in the picture below … the range of possible outcomes in the third year are inside the wider range of possible outcomes in the first year. However, that is an illusion! Possible outcomes continue to be uncertain in the present, when the present gets there in the future. The earlier two years are not relevant anymore when it comes to making decisions about the future again.