The Pulse method for deciding under uncertainty

Decision Tree & Expected Value شجرة القرار والقيمة المتوقعة

Five stages that take you from a fuzzy question to a choice you can defend: map the options, weight each outcome by its likelihood, see the size of the risk, then learn exactly what would flip the decision.

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Stage 1/5

Frame the decision

Write the choice as one clear question and pick the yardstick before any numbers: net value (benefits minus costs, higher wins) or total cost (lower wins). Every option is measured on the same yardstick and over the same time horizon.

Decision question

Yardstick Net value higher is better Total cost lower is better

Display currency Display only; amounts are not converted.

Stage 2/5

Map options and outcomes

Add 2–4 options you could genuinely act on (waiting counts if it is real). Under each, name 2–4 outcomes that make a material difference, and leave out detail that would not change the choice.

Stage 3/5

Quantify probabilities and values

Give each outcome a value on your yardstick and a probability. One option's outcomes cover everything that could happen, so they total 100%. Lean on past data or similar projects where you can, and note where each estimate came from.

Timing: values here are not discounted. If one option's cash arrives later (a pilot that delays full launch by a year, say), enter each outcome as its net present value (NPV) so the comparison stays fair.

Stage 4/5

Compute EMV and risk spread

Expected monetary value weights each outcome by its probability. It is a long-run average, not a forecast of this one decision, so read it next to how widely the outcomes spread.

EMV = Σ (p × value) σ = √Σ p (value − EMV)²

Risk profile per option

Expected value is blind to risk appetite: two options with the same EMV can differ sharply in how bad things could get. Standard deviation (σ) measures how far outcomes scatter around the EMV.

Stage 5/5

Test and decide

Before you commit, find the assumption that would flip the choice and how far it has to move. If a small shift is enough, invest in better information first; if not, decide and move on.

Sensitivity: the break-even point

Move the probability of The option's other outcomes rescale in proportion so the total stays 100%.

What if it were

How far can each probability move before the choice flips?

Advanced: expected value of perfect information (EVPI)

What this tool does not do

It treats probabilities as known and independent; the answer is only as good as your estimates.
It does not discount: enter net present values (NPV) when the timing of cash differs.
It models one decision with one layer of chance, without follow-on decisions.
Expected value suits repeatable or affordable bets; for a one-off bet with a severe downside, give the worst case and your risk appetite more weight.

An educational tool, not financial advice. Your numbers are saved in your browser only; nothing is sent to a server and no data is collected.