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Step 02

Probabilistic Thinking and expected value

Level: beginner

Learning objectives

  • Understand the nature of probability and expected value thinking in investment thinking.
  • Know how to distinguish well-founded decisions from emotional decisions.
  • Apply a practical principle to reduce mistakes when investing.
  • Identify behavioral risks that often skew investment decisions.

Why it matters

Thinking determines the quality of long-term results

Investing is about making decisions under conditions of uncertainty, so good results come from probability and process rather than absolute certainty. If the thinking is wrong, investors can use the right tools but still make poor decisions.

It helps reduce noise from the market

expected value is a weighted average of possible outcomes. A good decision can be lost on a single occasion, and a poor decision can still succeed by luck. What needs to be evaluated is the distribution of outcomes across multiple decisions. When you have a clear frame of mind, you are less susceptible to news, short-term prices or crowd emotions.

It protects learning capital

In the early stages, the important goal is to survive, learn the right lessons, and not let one big mistake ruin long-term accumulation.

Core lesson

The essence of the lesson

Investing is about making decisions under conditions of uncertainty, so good results come from probability and process rather than absolute certainty.

New investors often look for formulas to choose assets before building their thinking system. This is dangerous because the same information can lead to very different decisions depending on how risks, probabilities, time horizons and capacity limits are understood. The right mindset does not make the market easier, but it helps you respond with more discipline.

Analytical framework to use

expected value is a weighted average of possible outcomes. A good decision can be lost on a single occasion, and a poor decision can still succeed by luck. What needs to be evaluated is the distribution of outcomes across multiple decisions.

A good investment decision must answer four questions: what do you expect to happen, why is that expectation reasonable, if it is wrong, what is the downside, and is this decision consistent with your personal financial goals? If one of the four answers is missing, the decision is still weak.

How to put it into practice

Before every decision, write at least three scenarios: good, baseline, and bad; assign approximate probabilities and estimate the impact on capital.

It's important to write down your assumptions before taking action. It forces you to turn feelings into testable arguments. Later, whether the result is profit or loss, you still know where you were right, where you were wrong, and what part of the process needs to be improved.

Risks to avoid

Evaluating a decision only by the final outcome without considering the initial probability.

An investment mistake usually does not appear as an obviously wrong decision. It often comes in the form of a reason that sounds reasonable but is unproven. Therefore, always have a checklist, position-size limit and review schedule so that your decision does not depend entirely on emotions at the time of purchase.

Key terms

expected value

The expected value is calculated by multiplying each outcome by the corresponding probability and then adding it together.

Distribute results

The set of possible outcomes with their relative probabilities.

Resulting

The mistake of evaluating the quality of a decision based solely on results that have already occurred.

Classification

According to the decision-making basis

Decisions can be based on data, analysis, rules or emotions. Investors need to know which group they are in before increasing their capital scale.

According to time frame

A decision that is right for a 10-year goal may be wrong for a 6-month goal. The time frame determines the level of volatility that can be tolerated and the evaluation criteria.

According to the level of risk control

Good decisions always have loss limits, reasonable weights and review conditions. If downside is not controlled, expected returns can easily become an illusion.

Real-world examples

Illustrative situation

Application in investment decisions

An investment that has a 60 percent probability of a 20 percent gain and a 40 percent probability of a 10 percent loss has a positive expected value, but can still lose money over a specific period.

When thinking is wrong

Behavioral risks

Evaluating a decision only by the final outcome without considering the initial probability. When this happens repeatedly, investors are more likely to increase risk just when discipline is weakest.

Common mistakes

Looking only at short-term results

A profitable decision is not always a good decision, and a losing decision is not always a bad one. Evaluate both the process and the initial probabilities.

Not writing assumptions before buying

Without a written buy thesis, it becomes hard to know when the thesis is wrong and easy to rewrite the narrative after prices move.

Increasing position size without understanding the risks

Evaluating a decision only by the final outcome without considering the initial probability. Position size should increase only after the process has been tested, not after a few favorable outcomes.

Practical application

Checklist before making a decision

  1. Write down your goals, time frame, and maximum amount at risk.
  2. Before every decision, write at least three scenarios: good, baseline, and bad; assign approximate probabilities and estimate the impact on capital.
  3. List three risks of making your argument wrong.
  4. Determine the maximum proportion and conditions for review or sale.
  5. Record the decision in a diary to reassess in 30-90 days.

Exercises

Exercise 1 - reflection

Describe a recent investment decision you made and evaluate it from the perspective of probability and expected value thinking.

Exercise 2 - case_study

An investment that has a 60 percent probability of a 20 percent gain and a 40 percent probability of a 10 percent loss has a positive expected value, but can still lose money over a specific period. Identify the decision basis, the main risks, and the downside controls.

Exercise 3 - action_plan

Write a checklist of 5 questions to avoid this mistake in your next investment decision.

Key takeaways

  • Investing is about making decisions under conditions of uncertainty, so good results come from probability and process rather than absolute certainty.
  • expected value is a weighted average of possible outcomes. A good decision can be lost on a single occasion, and a poor decision can still succeed by luck. What needs to be evaluated is the distribution of outcomes across multiple decisions.
  • Principle of practice: Before every decision, write at least three scenarios: good, baseline and bad; assign approximate probabilities and estimate the impact on capital.
  • Mistake to avoid: judging a decision only by the final outcome without considering the initial probability.
  • Good thinking does not eliminate risk, but helps it to be understood, limited and systematically reviewed.