Wizard difficulty last saved game, thinking time default (5000+), infinite duels vs a deck with nothing but lands in it I keep giving things to either in hand or to the battlefield in debug mode.

Inidividual Circle of Protection cards (apart from CoP: Artifacts, but including Greater Realm of Preservation) seem to fare ok. I tried each one in turn vs 5 simultaneous attackers (one of each color) and they prevented damage from the right source. None of them tried to prevent damage from cards with devoid or colorless artifacts (didn't try colored artifacts, )

But!

Once I put multiple different circle of protection on the battlefield and tried attacking with a mix of monsters, the AI started exhibiting odd behavior. Could be due to some desync or not, but I feel like I have to report it. Mainly:

a) It had plenty of leftover mana and nothing in hand to save the mana for, but it would not pay for all possible targets, often letting one or two "through" for no apparent reason.
b) It would target sources it allready prevented damage from, showing up as 0 damage sources. Often instead of actual sources, sometimes in addition to what's needed to prevent all the damage. I suppose it should be discouraged from preventing sources of 0 damage or something?
c) I attacked with about 10 creatures of various colors (all colors, some overflow in one color, an artifact and a devoid guy) but I changed their color to red before combat with Dwarven Song. The CoP did target the colored Eldrazi and Artifact properly, but it really messed up with multiple activations on the same target on the whole.

I hope this means something to you / you can make some sense of it, if anything needs further testing I'll gladly do it. It could be that desync thing, sure, but it might be something related to damage prevention in particular. Or at least preventable in this case from that angle.