Flat based and tangent ogive bullets (aka old style) are more tolerant to twist rates.
The new style, high BC bullets typically require a much faster twist to both stabilize and to achieve the listed BCs.
Berger have a stability calculator that can tell you if your bullet/twist/velocity combination will work or nor.
In regards to 308 and 165gr bullets, I'd say you'd be fine 1:11 is pretty standard for 308 and 165gr I pretty lightweight. If you were talking 175gr+ then you might run into issues but 150-170gr is pretty much the normal range for 308win.
There is a trend towards higher twist rates these days as heavy for caliber bullets, high bc are now the norm.
Cartridges like 243, 260, 284win all used to come in slower twists for the lightweight bullets of the 60s and 70s, but now 1:8 is pretty much the standard twist for almost everything it would seem.
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