Investment & Finance
Expected Value Analysis
預期值分析 · Source: 統計學 / 賭博理論 / 投資分析
Decisions with quantifiable outcomes — investments, business decisions, choices with probability and payoff structures
Core Concept
Expected value = Σ(probability of each scenario × outcome of each scenario). If EV is positive, this decision is favorable over repeated execution. The key question: how honest are your probability and outcome estimates?
✓ When to use this
For quantifiable, repeatable choices: investment allocation, insurance decisions, accepting a wager, product discount strategies. Most effective when you can reasonably estimate probabilities and payoffs.
✗ When not to use this
One-shot life decisions (marriage, having kids) do not fit pure expected value — emotion and meaning resist quantification. Extreme tail risks (bankruptcy, health collapse) need Margin of Safety on top.
Questions you will be asked
Using this framework, you will work through —
- 1.What decision are you considering?
- 2.List the main possible scenarios for this decision (at least three)
- 3.For each scenario, estimate the probability of occurring (should sum to ~100%)
- …and 3 more
Worked example
Expand to see what a filled-in run looks like
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Worked example
Expand to see what a filled-in run looks like
Situation
考慮把現金 30 萬投入一檔朋友推薦的早期 startup。
1. What decision are you considering?
把 30 萬投入這家 pre-seed startup。
2. List the main possible scenarios for this decision (at least three)
最好：5 年後估值 100 倍，30 萬變 3000 萬。最可能：撐到 A 輪後因 PMF 不足收掉，30 萬清零。最壞：6 個月內倒閉，30 萬清零。
3. For each scenario, estimate the probability of occurring (should sum to ~100%)
最好 5%、最可能 70%、最壞 25%。
4. For each scenario, estimate the actual impact on you (quantified in concrete units)
最好 +30,000,000；最可能 -300,000；最壞 -300,000。
5. Calculate the weighted expected value (probability × impact, summed across scenarios)
EV = 0.05 × 30,000,000 + 0.7 × (-300,000) + 0.25 × (-300,000) = 1,500,000 - 285,000 = +1,215,000。EV 為正。
6. EV is positive — but can you absorb the worst-case cost? Is this a decision you'll actually execute?
EV 正，但最壞情況是 100% 損失 30 萬。我能承受這筆失去嗎？可以——這是我可投資資金的 5%。執行，但只投這一筆，不再加碼。
Use it inside ChatGPT / Claude
Paste the prompt below and the AI will walk you through this framework, one question at a time.
你現在是引導使用者做「預期值分析」的決策教練。 依序問： 1) 你正在考慮的決策是什麼？ 2) 列出至少三個可能情境（最好、最可能、最壞）。 3) 對每個情境估計概率（加總 100%）。 4) 對每個情境估計具體影響（用同一單位量化）。 5) 計算加權預期值（概率 × 影響加總）。如果使用者數學弱，幫他算。 6) EV 為正——但你能承受最壞情況嗎？這是你會執行的決策嗎？ 特別提醒：EV 只在可重複下注時有意義。單次決策的最壞情況若致命，即使 EV 正也要重新評估。 互動規則： 1. 一次只問一題，等使用者回答後再進入下一題。 2. 使用者答完所有題目前，不要做總結或下結論。 3. 若答案太抽象、太籠統，請追問一次具體例子或數字後再繼續。 4. 全部答完後，輸出三段：(a) 摘要使用者的關鍵判斷；(b) 你看到的盲點或張力；(c) 一個具體下一步行動建議。 5. 不要替使用者做決定，只把判斷攤開讓他自己決定。
Related Frameworks
Investment & Finance
Margin of Safety Thinking
Any decision resting on critical assumptions — investments, ventures, major commitments — ensuring you survive when assumptions prove wrong
Investment & Finance
Opportunity Cost Framework
Resource allocation decisions — how to deploy time, money, attention; especially when you're treating "do nothing" as a free option
Psychology & Behavior
Base Rate Forecasting
Decisions requiring outcome forecasts — from startup success rates to investment returns, start by asking "how does this type of thing typically go"
FAQ
How is expected value different from asymmetric risk/reward?
Expected value computes the probability-weighted average of outcomes — whether a bet pays off over many repetitions. Asymmetric risk/reward looks at the shape of worst-vs-best, especially whether a single worst case wipes you out. A positive-EV bet that carries ruin risk gets blocked by the asymmetry lens but not by EV alone.
The probabilities and outcomes are just guesses — is this analysis trustworthy?
Its value isn't in precise numbers but in forcing your estimates into the open. A practical move: run optimistic, pessimistic, and base versions and see whether the conclusion flips. If all three point the same way, you're on solid ground; if a small tweak flips it, you're really betting on an assumption you're unsure of.
Should I always take a positive-EV bet?
Not necessarily. Ask two more things: (1) can you repeat it enough times for the "average" to actually materialize? (2) does a single worst case wipe you out? A positive-EV bet that can bankrupt you is effectively negative long-term, because you won't survive to reach the average. Positive EV is only truly takeable when it's repeatable and the downside is survivable.
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