Under uncertainty a gut call quietly drops half the problem: it fixes on how likely something is, or on how big it would be, but rarely both. A decision tree puts every option, every outcome, its probability and its payoff on the table, then rolls the expected value back so you can compare like with like. Decide by EV — then sanity-check for ruin, because the highest-EV bet is still a bad bet if losing it ends the game.
Three options, each with an upside and a downside. Set the probability split and the payoff on every branch; the tool rolls the expected value back live, names the winner, and flags any option whose worst case would wipe you out. Drag things around and watch a tempting bet turn into a ruin risk.
Branch thickness grows with probability · green is a gain, coral a loss. The tinted band marks the highest-EV option; a green ring marks the disciplined pick when the two differ.
Payoffs and the ruin line share one scale — read them as $000s, or whatever your bet is denominated in. Probabilities on each branch always sum to 100%.
A pros-and-cons list stacks reasons but weighs neither their odds nor their size. EV is stricter: it forces a probability and a payoff onto every branch and collapses them to one comparable number. But EV isn't the only rule for deciding under uncertainty — and it's the wrong one when a single loss is fatal.
| Decision rule | The question it asks | It picks the option that… | Reach for it when | Blind spot |
|---|---|---|---|---|
| Expected value (max-EV) |
"What's the average if I could run this many times?" | maximises Σ(probability × payoff) | the bet is repeatable and no single loss can sink you | ignores variance — can march you into a ruinous tail |
| Minimax (worst-case) |
"How bad is the worst that can happen?" | makes the worst outcome as good as possible | the downside is fatal or irreversible; survival comes first | leaves money on the table; too timid when losses are survivable |
| Maximax (best-case) |
"How good is the best that can happen?" | makes the best outcome as good as possible | upside is uncapped, downside is cheap, and you get many shots | ignores probability and downside entirely; reckless on its own |
| EV, capped for ruin (Kelly intuition) |
"Highest average — among the bets I can survive?" | maximises EV subject to a ruin constraint | almost always: real decisions with a real, bounded downside | needs an honest ruin line — set it wrong and it misleads |
Applied to your tree above
The ruin caveat (why not always max-EV): a bet can have a wonderful average and still be ruinous, because you don't get the average — you get one draw. Lose the draw that bankrupts you and there is no next round to regress toward the mean. The Kelly criterion makes this precise for repeated bets: even with the odds in your favour, staking too much guarantees eventual ruin, so you bet a fraction of your bankroll, not all of it. The everyday version is simpler — take the highest EV you can survive, and never bet the company on a coin flip.
Five real decisions, two options each. Pick the one your instinct prefers — then the tool does the arithmetic and shows you the expected value of both, whether either can ruin you, and the disciplined call. Watch how often the gut ducks a bet the numbers say to take — and how twice the numbers say to duck a bet anyway.
The tree earns its keep wherever the stakes are real and the odds are guessable but unignorable. A handful of recurring shapes a leader, founder or engineer will recognise — including the two cases where max-EV is exactly the wrong instinct.
The arithmetic is the easy part. The hard part is doing it honestly when the room is anchored on a hunch, naming probabilities you'd rather leave vague, and holding the line on ruin when a spreadsheet is shouting "take the bet". That's the work we do with the leaders and teams we coach — turning judgement calls into reasoning you can lay out, argue, and improve.
Talk to us about coachingGut fixes on one and forgets the other — the vivid disaster, or the tempting prize. EV is the discipline of multiplying them on every branch before you compare.
The highest average is the right call only when you can survive the worst draw. If one branch ends the game, no expected value redeems it. EV chooses; ruin vetoes.
The tree's real gift isn't the arithmetic — it's dragging your hidden assumptions into the open, where a probability can be challenged and a payoff improved.