Let's talk about something every trader must understand—mathematical expectation. Many people lose money simply because they don't grasp this concept.

First, the most straightforward explanation: trading is really about having a long-term positive EV. What does that mean? It means that on average, each trade makes money, and the more you repeat this, the more you earn over time. Conversely, if your trading strategy has a negative expectation value, no matter how hard you try, it’s doomed to lose money in the long run.

Mathematical expectation, simply put, is the weighted average of all possible outcomes. Here's a simple example: flipping a coin, winning 2 dollars if heads, losing 1 dollar if tails (each with a 50% probability). The expected value is 2×0.5 plus (-1)×0.5, which equals 0.5. That’s a positive EV. If you win 1 dollar on heads and lose 1 dollar on tails, the expected value is 0, meaning it's completely fair.

Applied to trading, the formula is: expected value per trade = (Probability of profit × Average profit) - (Probability of loss × Average loss). The key numbers are—how high is your win rate, and how much do you make when you win versus how much you lose when you lose.

But there's a trap many people fall into. Expected value ≠ most likely outcome. The expected value of rolling a die is 3.5, but you can’t roll a 3.5; the actual result is always an integer from 1 to 6. The expected net gain from buying a lottery ticket might be negative, but that doesn’t mean you will definitely lose money—there’s still a tiny chance of winning. Similarly, even if your strategy has a positive expectation, you can still lose in the short term because randomness can amplify short-term fluctuations.

That’s why I emphasize the importance of long-term positive EV. You can’t tell much from a single trade, but if you stick to a strategy with a positive expectation and repeat it enough times, the results will approach the expectation value infinitely. That’s the power of probability. Conversely, no matter how lucky you are in the short term, it won’t save a strategy with a negative EV.

So, the core of trading isn’t about guessing how much you can make on the next trade, but about finding a logic with a long-term positive EV and executing it with discipline. That’s the mindset of a winner.