What are the odds of five losing trades in a row?

If each trade has a 50% chance of losing and trades are independent, the chance that five particular trades all lose is 0.5 x 0.5 x 0.5 x 0.5 x 0.5, or 3.125%. Over 100 trades, the chance of at least one such streak somewhere is about 81%.

What is the law of large numbers in trading?

It says that the average result of many independent trades gets closer to the true expected result as the number of trades grows. It does not apply to small samples, which is why a win rate from a dozen trades can be far from the truth.

Probability basics for trading

Probability basics for trading: independent events, the real odds of a losing streak, the law of large numbers, and why small samples mislead.

Part of the Statistics for Investors and Traders track on Agenticks. About 10 minutes, written for a intermediate reader.

Read first: Risk and return, the basic tradeoff.

Last reviewed 2026-11-08.

Key takeaways

Probability is a number from 0 to 1 that says how likely something is, and a win rate is only a probability if it is real and stable.
For independent events, multiply the probabilities: five losses in a row at a 50% win rate is 0.5 to the fifth power, or 3.125%.
A streak that is rare in any five particular trades is close to certain somewhere in a few hundred trades.
The law of large numbers needs large numbers. Small samples routinely show win rates far from the true rate.
Linked trades, such as several positions hit by the same sell-off, make long streaks more likely than the coin-flip math says.

Probability is a number between 0 and 1 (or 0% and 100%) that says how likely something is to happen. A fair coin landing heads has a probability of 0.5, or 50%. A strategy with a 55% win rate has, if that rate is real and stays the same, a probability of 0.55 of winning any single trade. That sentence has two big ifs in it, and most of this lesson is about them. Traders use probability all the time without calling it that: how often a setup works, how likely a losing run is, how much to trust a result from 30 trades. Getting the basics right protects you from two opposite mistakes. One is panicking at a perfectly normal losing streak. The other is falling for a lucky one.

Multiply when events are independent

Two events are independent when one happening does not change the chance of the other. For independent events, the chance that both happen is the two probabilities multiplied together. Two coin flips both landing heads: 0.5 x 0.5 = 0.25, or 25%.

Apply that rule to a run of trades. If each trade is a 50/50 chance and one trade does not affect the next, the chance that the next five trades all lose is 0.5 multiplied by itself five times. Each extra loss in the streak halves the chance again.

Worked example: five losses in a row at a 50% win rate

Assume every trade has a 50% chance of losing and the trades are independent. Round, illustrative numbers.

Chance one trade loses	0.5 (50%)
Two losses in a row (0.5 x 0.5)	0.25 (25%)
Three in a row (0.25 x 0.5)	0.125 (12.5%)
Four in a row (0.125 x 0.5)	0.0625 (6.25%)
Five in a row (0.0625 x 0.5)	0.03125 (3.125%)
Five in a row at a 40% win rate (0.6 x 0.6 x 0.6 x 0.6 x 0.6)	0.07776 (7.776%)
Chance the next five trades all lose, 50% win rate	3.125%, about 1 in 32

Illustrative probabilities for independent trades, not a forecast for any strategy.

3.125% sounds rare, and it is rare for any five particular trades. But nobody takes only five trades. You take hundreds, and a streak can start at almost any of them. Counting every possible starting point, the chance of seeing at least one run of five or more losses somewhere in 100 independent 50/50 trades is about 81%. Over 200 trades it is about 97%. At a 40% win rate, a five-loss run inside 100 trades shows up about 98% of the time. So a streak that is unlikely in any given week is close to certain over a year of trading. A plan that cannot survive five losses in a row has not done this arithmetic yet.

A strategy wins 50% of the time and its trades are independent. What is the chance its next three trades all lose? 12.5% 0.5 x 0.5 x 0.5 = 0.125, which is 12.5%, or 1 in 8.

The law of large numbers says that as you repeat an independent trial more and more times, the average result gets closer and closer to its true value. Flip a fair coin ten times and you might easily see 7 heads. Flip it 1,000 times and the share of heads lands between 45% and 55% more than 99% of the time. The flip side is what matters for traders: the law offers no comfort for small numbers. With 10 flips of a fair coin, the chance of 7 or more heads (a 70% "win rate") is about 17%. With 100 flips, the chance of 70 or more heads falls to about 0.004%. Same coin, same true 50%, a completely different picture depending only on how many times you looked. People are bad at feeling this. Psychologists Amos Tversky and Daniel Kahneman found that even trained researchers expected small samples to look like the whole population, a mistake they called belief in the "law of small numbers". In trading it looks like twelve trades, nine winners, and a conclusion that the setup works 75% of the time. It might. It might also be a coin. Twelve trades cannot tell them apart, and the sample size lesson goes into how many trades a result really needs.

Small samples are loud

A fair coin shows 70% heads or better in 10 flips about 17% of the time, and in 100 flips about 0.004% of the time. The true rate never changed. Only the amount of luck in the sample did.

There is a quick way to see how much a measured win rate can wobble. For a win rate p measured over n independent trades, a rough range that holds about 95% of the time is p plus or minus 2 x square root of (p x (1 - p) / n). Take a 55% win rate from 100 trades. p x (1 - p) is 0.55 x 0.45 = 0.2475. Divide by 100 to get 0.002475, and the square root is about 0.0497, or 4.97 percentage points. Double it and the range is roughly 45% to 65%. So a strategy that "wins 55% of the time" over 100 trades could, on that evidence alone, really be a 45% strategy. Over 1,000 trades the same arithmetic gives about plus or minus 3.1 points, a range of roughly 52% to 58%. Ten times the trades buys a range about three times narrower, because the width shrinks with the square root of the number of trades.

Reasonably independent: Two flips of the same fair coin, Rolling a die today and again tomorrow, Two small trades a month apart in unrelated markets
Likely linked: Five long trades in five stocks during the same sell-off, A rushed trade taken straight after an angry loss

Real trades are not perfect coin flips. Several positions opened in the same sell-off can lose together, wild market days tend to cluster, and a frustrated trader can make the next decision worse. When losses cluster like that, long streaks become more likely than the independent math says. Treat the coin-flip numbers as a starting point, not a worst case. Probability is also the first half of a bigger idea. The expected value lesson combines probabilities with the size of each win and loss to get an average result per trade, and the variance, luck and skill lesson shows how far real results can wander from that average.

multiplying sample true

You can read the odds behind a streak

You can now multiply independent probabilities, explain why losing streaks are common over many trades, and say why a small sample proves very little.

Check your understanding

Each trade has a 50% chance of losing and the trades are independent. What is the chance the next four trades all lose?: 6.25%. Multiply four times: 0.5 x 0.5 x 0.5 x 0.5 = 0.0625, which is 6.25%.
Five particular trades have only a 3.125% chance of all losing at a 50% win rate. Why is a five-loss streak still likely somewhere in 100 trades?: A streak can start at almost any of the 100 trades, so there are many chances for one to appear. Counting every starting point, the chance of at least one run of five losses in 100 such trades is about 81%.
A setup won 9 of its first 12 trades. What does the law of large numbers let you conclude?: Very little yet, because 12 trades is too few for the win rate to settle near its true value. The law of large numbers only works with large numbers. A fair coin gives 7 or more heads in 10 flips about 17% of the time.
Which situation most clearly breaks the assumption that trades are independent?: Five long positions in related stocks, all opened during the same market sell-off. One market move can hit all five at once, so their losses tend to arrive together.

Common questions

What are the odds of five losing trades in a row?: If each trade has a 50% chance of losing and trades are independent, the chance that five particular trades all lose is 0.5 x 0.5 x 0.5 x 0.5 x 0.5, or 3.125%. Over 100 trades, the chance of at least one such streak somewhere is about 81%.
What is the law of large numbers in trading?: It says that the average result of many independent trades gets closer to the true expected result as the number of trades grows. It does not apply to small samples, which is why a win rate from a dozen trades can be far from the truth.

Terms defined in this lesson

Continue

Sources

Written and reviewed by the Agenticks Learn editorial team. How we write and check lessons.

Agenticks Learn is general education. It is not financial, investment, tax or legal advice, it does not take your situation into account, and nothing on it is a recommendation to buy, sell or hold any security or to open any account. Examples use illustrative numbers. Investing involves risk, including losing money you put in, and past performance does not predict future results. Tax rules and limits change; the official sources linked in each lesson are the final word.