Probability Basics: Odds, Expectancy, and Frequency

A trader who doesn't think in probabilities thinks in hope. Hope is not a strategy.

Every trade is a bet on an uncertain outcome. The language of that uncertainty is probability. Without it, "good setup" is just a feeling; with it, you can compute whether a setup is actually worth taking.

Probability vs odds

• Probability = expected frequency of an event: P = favourable ÷ total, range 0 to 1
• Odds = ratio of winning to losing: Odds = P ÷ (1 − P)

Example: a setup wins 40% of the time.

• Probability = 0.40
• Odds = 0.40 ÷ 0.60 = 0.67, or "2 to 3 against"

Brokers quote odds; statisticians use probability. Convert between them freely.

Expected value: the only number that matters

Expected value (EV) is the weighted average outcome:

EV = (Pwin × Reward) − (Ploss × Risk)

Example: 40% win rate, $300 reward, $100 risk.

EV = (0.40 × 300) − (0.60 × 100) = 120 − 60 = +$60 per trade

Positive EV means the setup makes money over many trades. A single trade is noise; EV only asserts itself across a large sample. This is why trade frequency matters (see the next section).

Frequency and the long run

EV pays out only across enough trades. With a 40% win rate:

• 10 trades → wide variance, anything can happen
• 100 trades → results start clustering near 40%
• 1,000 trades → actual win rate ≈ 40%

This is the Law of Large Numbers in action. A positive-EV strategy needs enough at-bats to realize its edge — one trade per week may take years to distinguish skill from luck.

The gambler's fallacy

A common trap: "I've lost five in a row, so I'm due." Wrong. If each trade is independent, the next trade still has a 40% chance of winning regardless of the streak. Coins have no memory, and neither do independent market setups.

The flip side: a long losing streak can reveal that your true win rate is lower than you think — but only if the setups were genuinely identical.

Bayes: updating beliefs

Traders should think like Bayesians — updating probability as new evidence arrives:

P(A|B) = P(B|A) × P(A) ÷ P(B)

If your prior belief is "60% chance this is a bull trend" and a breakdown occurs, that evidence should lower your probability. Many traders instead freeze on their original thesis. That's how small losses become large ones.

Putting it together

1. Estimate win probability from a large, clean backtest sample
2. Compute EV — only trade positive-EV setups
3. Trade often enough for EV to materialize
4. Update probabilities as new data arrives
5. Never confuse a streak with a change in probability

Summary

Odds describe a single trade. Expectancy describes a strategy's worth. Frequency determines whether that expectancy can actually be realized. Trade like a probability thinker — not a prediction maker — and you've taken the first real step toward a durable edge.