Calculate probability that my chances are 50/50, despite limited but favorable data

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Let's say you're trading forex, and you set a random trade, setting the stoploss and take profit exactly the same. Theoretically, in an infinite number of tries, your chances of success are 50/50 (ignore spread).

Now, you have a strategy whereby, after 500 tries, you've managed a 67% success rate. Assuming market conditions remain the same, how can you calculate the chances that your 67% success rate will return to 50/50 after 1000 tries? 10,000?

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You need a required amount of failures and thus success to get back to $50$ percent overall.

$$\frac{335+x}{1000}=\frac{1}{2}$$

Solve for $x$

$$335+x=500$$

$$x=500-335=165$$

So you need exactly $165$ success in the next 500. This here isn't gamblers fallacy and is perfectly valid to ask what is the probability of getting $165$ success out of $500$ trials.

To figure this, use the binomial distribution.

$$P=\binom{500}{165}(0.5^{165})(0.5^{335})$$

$$=\binom{500}{165}(0.5^{500})$$

Wolframalpha tells me that is about $5.95 \times 10^{-15}$ or very unlikely.