Win streak distribution: what normal luck looks like

[Shadow Trader]

How long should a streak of consecutive winners be expected to run? Most people guess too short, and the same goes for losing streaks.

A coin flip gives an intuition. In 100 flips of a fair coin, the longest run of heads is typically around six or seven. Increase the sample to 1,000 flips, and a run of ten is unsurprising.

A strategy with a 60% win rate produces winning streaks of 10 or more over a few thousand trades. A 40% strategy produces losing streaks of the same length. These runs have no mystical meaning. They're just what randomness looks like when it's given enough room.

Understanding that helps in two ways. A long winning run isn't proof of genius. A long losing run isn't proof of failure.

A quick simulation in a spreadsheet, using the strategy's real win rate, shows the expected longest streaks across, say, 500 trades.

For a feel of the numbers, imagine a 55% win rate over 300 trades. The longest winning streak is likely around 8 to 10, and the longest losing streak around 6 to 8. Seeing those numbers in advance makes the real thing less alarming when it arrives.

Streaks also tempt superstition. After five wins, some traders feel "due" a loss and reduce size. After five losses, some feel "due" a win and increase it. Independent trades don't work that way, though if results show real serial dependence, with wins following wins more than chance predicts, that's worth investigating as a sign of regime sensitivity.

How long has the longest personal losing streak been, and how did it compare with what a simulation would suggest?