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

Estimate win probability from a large, clean backtest sample
Compute EV — only trade positive-EV setups
Trade often enough for EV to materialize
Update probabilities as new data arrives
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.