One instance of two things
A probability is a statement about a future made with what is known now. It needs both: a time ahead, and information about the present. Take away the time and nothing is uncertain. Take away the information and nothing can be said.
The modern account starts with an unfinished game: how to split the stakes fairly when play stops early. Pascal and Fermat settled it in letters in 1654.1 Laplace treated probability as relative partly to what we know and partly to what we do not.2 Kolmogorov gave it the axioms it still rests on.3
Two widths, added together
The range ahead of a household has two sources of width. One is the uncertainty about the present: not knowing exactly where you stand today. The other is the future itself, which widens with every year it runs.
They behave differently. The first does not grow with time and can be narrowed now, by measurement. The second grows with time and cannot be narrowed by asking. Knight drew the same line in 1921, between risk that can be measured and uncertainty that cannot.4
What the engine does with it
The engine carries both widths. A field the household has not given enters each future as a draw from what people like them hold, so the present is a range before the future is. Each run then draws its returns year by year, and the chance is counted across a thousand runs.
A probability read off a simulation is itself an estimate, with a margin set by the number of runs. That is why a chance is always said with its count.
Sources
- Peter L. Bernstein, Against the Gods: The Remarkable Story of Risk, 1996.
- Pierre-Simon Laplace, Essai philosophique sur les probabilités, 1814.
- A. N. Kolmogorov, Grundbegriffe der Wahrscheinlichkeitsrechnung, 1933.
- Frank H. Knight, Risk, Uncertainty and Profit, 1921.