Probability Theory: How Many Trades Does it Take to be Successful?

If you’ve been around options trading long enough, you’ll inevitably hear phrases like, “Let the probabilities play out,” or, “Trade small, trade often.” The rationale given is often the Law of Large Numbers, meaning a sufficient number of trades is required to realize those probabilities. But exactly how many trades do you need to make? 

Trade small, Trade often: Does it work?

This research was inspired by a question from our very own Community. I was directly asked how many trades it takes for “probabilities to play out” when trading a strategy through Trade Ideas. I didn’t have a great answer at the time, but the one I gave related the answer to flipping a fair coin:

When flipping a fair coin (binomial trials with a 50% chance of landing heads or tails), to be within 1% accuracy of the 50/50 average with 95% confidence, approximately 9,603 coin flips are needed.

• 99% confidence, ~16,587 flips
• 95% confidence, ~9,603 flips 
• 90% confidence, ~6,763 flips 
• 75% confidence, ~3,308 flips
• 60% confidence, ~1,770 flips 

There are approximately 252 trading days in a year. A trader would need to enter 38 trades per day to achieve that many trades. In practice, if we’re willing to give up a little bit of confidence and accuracy to be “close enough” to the average, how many trades do we actually have to make?

The tastytrade team estimates ~1,000 occurrences. That number roughly reflects the accuracy of being within 3% of the average with 95% confidence:

• 99% confidence, ~1,843 flips
• 95% confidence, ~1,067 flips
• 90% confidence, ~751 flips
• 75% confidence, ~367 flips
• 60% confidence, ~196 flips