Gambler's fallacy is believing that P(X_n+1 | sum of X_1, X_2, X_3, ... X_n /n < some "small" number (i.e. unlucky)) > P(X)
What ijuakos is saying that P(sum of X_1, ... X_n / n = 0) is very very low, in fact it is 0.0000265614.
If you have a one-sided hypothesis test where H_0: p = 0.1 and H_A: p < 0.1, you will unequivocally reject the null (unless you're working in particle physics).
https://www.wolframalpha.com/input?i...+and+p+%3D+0.1
Please don't talk about statistics as a layman, thank you, it's incredibly embarrassing.
Although what ijuakos is saying is largely irrelevant to the conversation, it is really sad to see the failure of American education in action when people spout their mouth about "gambler's fallacy" or "correlation =/= causation" without knowing elementary probability theory that they teach in middle school in actual good countries.