Choices, Games & Branching Paths

Probability, Risk & Uncertainty

Established idea
Formal theory
Working interpretation

Most choices that matter come with uncertain results and missing information. I want to reason with probabilities without pretending that everything I value can be turned into a number.

Which uncertainties can I put numbers on, and what matters beyond the numbers?

The idea

Probability measures how likely something is. Risk adds what is at stake. Uncertainty, in the economist Frank Knight's older sense, is the harder case where I cannot even say how likely things are. Most real choices mix all three.

An example

In my Queueing & Staffing Lab, requests arrive at random. A team that is busy only 80% of the time can still leave many people waiting too long, because random bursts pile up faster than the team can clear them (Why Lines Grow When Timing Varies). The Queueing Simulation Lab plays out each customer one at a time and can repeat the run 20 times, so the spread of results is visible, not just the average. That spread is the risk an average hides.

What I think (and don't know)

I want to use numbers where they are earned, from data or careful reasoning, and to say plainly when a number is only a guess. Changing those guesses as evidence arrives (Adjusting My Confidence as Evidence Arrives) is part of the discipline. But some things I value, such as trust or love, do not fit on a scale, and forcing them onto one can distort the choice (Love Is Not Something to Maximize).

Where it connects

These probabilities describe my uncertainty about choices and events. They are a different kind of thing from the probabilities in quantum physics, which come from a rule built into the theory, called the Born rule (The Rule Behind Quantum Probabilities, What Quantum Physics Says About Possibility). Mixing them up muddles both. Rough estimates like these are what I attach to the chance points of a decision tree (Mapping the Futures a Choice Opens).

What this does not establish

The probabilities I give to personal choices are estimates of my own uncertainty. They are not quantum probabilities, and quantum theory does not give odds for which life path I will take.

Questions I'm still exploring

When does putting a number on a choice help, and when does it give false confidence?
How should I decide when I cannot even list all the possible outcomes?
What do I lose when a choice is reduced to one average number?

Sources and further reading

Stanford Encyclopedia of Philosophy, "Interpretations of Probability"
Frank H. Knight, Risk, Uncertainty and Profit (Houghton Mifflin, 1921)

Working interpretation: drafted from my notes and interests for review. It is not a direct quotation, and I may still change it.

In short

Probability is a way to put a number on how likely something is. Risk adds the question of what is at stake if things go badly. Some uncertainty can be measured from data, like how often customers arrive at a counter. Some cannot, like how a new job will feel in five years. The economist Frank Knight drew this line in 1921, calling the first kind risk and the second true uncertainty.

Why this matters to me

My labs keep showing me that averages hide what matters. A help desk busy only 80% of the time can still keep people waiting far too long, because requests arrive at random. I want the same honesty in personal choices: use numbers where they are real, admit when they are guesses, and remember that some of what I value cannot be scored at all.

Connections

What Quantum Physics Says About PossibilityAnalogy

Both deal with possibility and chance, but they need separate models: quantum chances come from the theory's own mathematics, while everyday risk is about decisions made with incomplete knowledge.

Adjusting My Confidence as Evidence ArrivesMethod

Adjusting confidence as evidence arrives gives one precise way to reason about choices made under risk and uncertainty.

The Rule Behind Quantum ProbabilitiesContrast

My uncertainty about a decision must be kept separate from the rule quantum physics uses to predict the odds of measurement results.

Why Lines Grow When Timing VariesUncertainty

Waiting lines show how randomness and uncertainty turn into real costs: longer waits, missed targets and greater risk.

Life as an Evolving GamePart of

Chance runs through every turn of the game, so reasoning about probability, risk and uncertainty is part of playing it well.