If I have a whole house surge protection device wired into one of my main panels, and I attach a sub panel to that same panel, I am assuming I don't need another surge protection device for the sub panel?

 

The protection would extend to any downstream panels.

 

You wouldn't need the second surge device, but installing one would be supplemental protection just like continuing to use a surge protector strip at your computer and other electronics locations.

 

Appreciate what a protector does. It does not stop, block, or absorb destructive surges. Protectors that do that are for surges that cause no damage. Your concern is a surge, maybe hundreds of thousands of joules, that hunts for earth ground destructively via appliances.

Either connect that surge to earth BEFORE it enters a building (ie at the mains box). Or a protector is doing little useful. IOW what is the most important component in every protection system? An item that absorbs hundreds of thousands of joules.

A 'whole house' protector is not protection. It is a connecting device. To be effective, it must connect low impedance (ie 'less than 10 feet') to single point earth ground. A sub panel does not have that earth ground connection. Only the main panel has that. A protector without an earth ground does what with hundreds of thousands of joules?

How to increase protection? Not with more protectors. Protection is defined by earth ground. How to make a protector more effective? Upgrade, expand, or install the single point earth ground. Earthing and how it connects defines your protection; where joules dissipate.

Protectors are simple dumb science. 'Art' of protection is earth ground. That is where most of your attention and questions should focus. Then appliances and power strip protectors have sufficient protection.