Delta and probability question

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Quote from kalikahuna:

you know...I've been using TOS's probability formula (1sigma=stock price*volatility*(SQRT(Days to expiration/365))) and it is different than if one used the delta as a measure of probability.

The difference is your formula does not take into account skew or expected returns. If interest rates get back into the 15%-ish range (or you're in for a very long time), the difference will be important.

But, like you said, neither measure is terribly accurate ("accurate" meaning the error of the prediction versus observed results is small).