Most everything in prob/stat has confidence intervals associated with it.

The original response has merit. The event probability will continue to approach the "true" probability as n events approaches infinity.

So in order to answer your question, you have to establish your "tolerance" level.

How many events are required to get an event probability that's "close" to the outcome probability within say 5% confidence interval?

I'm not going to pull out my texts to do the calculations, but for a binomial, you can calculate the overall event probability based off the number of the sampling....

so the output would look something like 50% +/- x%, where x gets smaller as n gets larger.

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The question is a simple one. In truth, the real answer is that for a 50-50 chance all you need is only one flip since flipping a coin is a single event and there are only two possibilities. This is the only answer with a 100% confidence level. Any more flips will change the probabilities which will eventually converge to 50/50 if you are willing to explore the infinity. However, if there was an infinity out there perhaps we would not call it infinity anymore, a paradox.

The point here is successful traders don't trade statistics, they trade opportunities and expect only two outcomes. We can't have useful stats for trading since they must include variables such as fear, greed, ego, intuition, experience, and stupidity.

This is 1 excel sheet that I like very much .. It use random coin tosses to create charts
Believe it or not, you might see support/resistance, trends, and many technical formation .....
Enjoy