More than the number you were hoping for, and that is the answer nobody likes.
You often read that about thirty trades would do. That is an order of magnitude borrowed from statistics textbooks, and it is already optimistic here: it assumes independent draws of the same nature, which a run of trades almost never is. Markets change regime, the strategy evolves, and the trader of October is not the trader of March.
Two concrete markers, more useful than a threshold.
THE FIRST: on a small sample, the range in which the true rate sits is wide. A displayed win rate around one half over thirty trades remains compatible with a true rate markedly lower as well as markedly higher. That is not a flaw in the measurement, it is the measurement itself having nothing yet to decide with.
THE SECOND, and this is the one that counts: a win rate says nothing on its own. A strategy that wins four times out of ten can be excellent, and one that wins eight times out of ten can ruin an account. It is the pair of win rate and average win/loss ratio that decides, never one of the two.
What we look at instead, while volume builds: STABILITY. Does the rate measured over the last fifty trades resemble the one over the fifty before? A value that barely moves as the sample grows is a value that is starting to mean something. A value that jumps with every new batch is not a measurement yet, it is still noise.
And a losing streak is not evidence. On an ordinary win rate, runs of several consecutive losses are expected, regularly, without anything being broken.