Now, double-Stout Shield doesn't completely stack. However, you get a 60% chance to block 20 of the damage that gets through the first 60% chance, meaning your net block chance is 84% to block 20 damage.
There's been some controversy about the usefulness of double-stout shield on Axe as early items. I did the math, and here's the result:
Summary of Double-Stout on Axe:Yes, double-stout IS actually quite effective for damage mitigation.
It's only once attack damage passes 60 per hit that the RoP + single shield option overtakes the double-Stout choice. Thus, for almost all camps and neutrals (except Rosh), you actually mitigate more damage by using two Stout shields.