The fundamental reason why many traders lose money is actually that they don't understand one thing: mathematical expectation.

I've found that many people misunderstand the concept of expectation. Some say, "Expected value is the most likely outcome," which is completely wrong. For example, rolling a die, the expected value is 3.5, but you can’t roll a 3.5. A net lottery profit of -8 doesn’t mean you will definitely lose money on a single play—it just means that over the long run, losses are inevitable.

Here's a key misconception to clarify: "A positive expectation does not mean you will profit on a single trade." Even if you find a positive EV strategy, you can still lose several trades in a row in the short term because randomness can interfere with results. Only by repeating the process enough times can you gradually approach the expected value.

So, what exactly is the true mathematical expectation? Simply put, it’s the weighted average of all possible outcomes. For example, guessing a coin flip: winning 2 dollars on heads, losing 1 dollar on tails (each with 50% probability), the expectation is 2×0.5 + (-1)×0.5 = $0.50.

In trading, this concept becomes a formula:

Single-trade EV = (Win Rate × Average Profit) - (Loss Rate × Average Loss)

where win rate is the proportion of profitable trades, and the profit/loss ratio is how much you typically gain versus lose.

Therefore, the key to judging whether a trading strategy is good or not is whether the EV is positive or negative. A positive EV means that, in the long run, each trade can make money on average; a negative EV means you’re doomed to lose money over time—that’s what trading is about.

Many people think trading relies on luck or intuition, but in fact, they just don’t understand the logic of expectation. Finding a positive EV strategy and sticking to it is the right way. Short-term fluctuations don’t matter; the long-term trend is what really determines the outcome.