Probability for Traders

Trading is decision making under uncertainty. No setup works every time, no forecast is certain and every trade has a range of possible outcomes. Probability gives you a way to think clearly about that uncertainty: how likely an outcome is, how outcomes combine and how to judge whether a strategy has an edge. You do not need advanced mathematics to benefit; a handful of core ideas will change how you size positions, interpret results and react to streaks.

What probability measures#

A probability is a number between 0 and 1 (or 0% and 100%) describing how likely an event is. A probability of 0.6 means that if you could repeat the situation many times, the event would happen about 60% of the time.

The core rules#

P(not A) = 1 - P(A)
P(A or B) = P(A) + P(B) - P(A and B)
P(A and B) = P(A) × P(B)   (if A and B are independent)
P(A and B) = P(A) × P(B | A)   (in general)

P(B | A) is the probability of B given that A has happened. See Conditional Probability.

Independent and dependent events#

• Independent: one outcome does not change the probability of the other, such as two coin flips.
• Dependent: one outcome changes the probability of the other, such as the chance of a stop loss being hit after a major news event.

Many trading mistakes come from treating dependent events as independent (assuming separate positions are unrelated when they share the same risk) or independent events as dependent (believing a win is "due" after losses). See Gambler's Fallacy and Correlation Management.

Probability and streaks#

Odds and implied probability#

Betting markets and prediction markets express probabilities as odds or prices. A prediction market share at 30 cents implies about a 30% chance. Decimal odds of 4.0 imply 1 / 4.0 = 25%. Converting between formats lets you compare your estimates with the market's. See Reading Odds as Probabilities.

Probability distributions#

Rather than single outcomes, traders often think about the full range of possible results: a probability distribution. Returns, for example, are spread around an average with some chance of large gains and losses. Understanding the shape, including fat tails, is essential for risk. See Probability Distributions Explained and Fat Tails.

Probability and edge#

A trading edge means the probabilities and payoffs, combined, favour you over many trades. A strategy can win less than half the time and still be profitable if winners are much larger than losers. Expected value brings probability and payoff together. See Expected Value.

Common probability mistakes#

Frequently asked questions#

Why is probability important in trading?#

Because every trade has uncertain outcomes; probability helps estimate how likely different results are, size positions and judge whether a strategy has an edge.

What is the difference between independent and dependent events?#

Independent events do not affect each other's probabilities; dependent events do.

Can a strategy that wins less than 50% of the time be profitable?#

Yes, if its average win is large enough compared with its average loss, so that expected value is positive.

Next, combine probability with payoffs in Expected Value.