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Fox, being a non-mathematician I've wrestled with this problem for quite some time. i.e. extrapolating sigmas into a probability of directional movement in a set time frame, as you do with flies and condors.

But there is a problem at the heart of the way volatility is calculated which makes it unsuitable for this purpose, viz, the annualized standard deviation of logarithmic daily change in price.

This is what I wrote in a blog post a while ago -

Although the standard practice is for volatility to be annualized (and sometimes extrapolated to "monthized" for we d-neutral traders), in my opinion this is a complete furphy, and a highly dangerous assumption.

This is the reason I abandoned so-called "high probability" condors in favour of  flies and low probability condors and adjust/morph as necessary.

I used to take some losses on my high prob condors, but so far have not had a loss on the low prob variety (it will come one day I'm sure). Total risk is also much lower in the low-prob variety in the event of a black swan.

I now only use volatility for pricing and largely ignore it for determining probability of price swings over time periods. It is using a ring spanner to hammer in a nail IMO.

Witness low volatility (as measured) trends that can move one helluva a long way in any number of instruments; the grinding upward move that can go 20% or so as you watch statistical volatility sliding the slippery slope to historic lows.

FWIW