It is better to think about this question in terms of cylinder pressure instead of calculated compression ratio.
Calculated compression ratio is simply the volume ratio between a full cylinder and a fully compressed cylinder.
Cylinder pressure is the cranking pressure (in psi) that the cylinder sees during a compression check. The cam profile and cylinder "leak-down" has a big influance on this number. This is why big cam profiles are combined with higher compression ratios, the cam "bleed-off" is off-set by the higher C/R to yield a desired cylinder pressure.
Here is my opinion on cranking cylinder pressure readings and the fuel you need to use:
Anything under 100 psi = rebuild the engine.
100 to 140 psi use 87 octane
140 to 170 psi use Premium (92 octane)
170 to 200 psi use Race gas (100+ octane)
200 to 240 psi use Super Race Gas (114)
240+ alcohol
Finding the true cranking cylinder pressure for a new combination is difficult to do, you really have to build the engine and check it.
That is why it is nice to find a "proven" combination of parts which is already known to produce the proper cylinder pressure for you application.
DD