Old Guillotine

Old Guillotine is a new item in Risk of Rain 2.

It allows Elite enemies to be executed when damaged at or below 13% health. Note that in similar fashion to Artificer's default utility skill and alternate secondary skill, enemies are only executed by this threshold when they are damaged when they reach the threshold; not the moment they reach it. This means that if an Elite monster has 100 health and takes 88.5 or more damage while the player has this item, it will not die until it takes another instance of damage from the same player. Old Guillotine can only trigger on health, not shields, therefore Overloading Elites have a minimum damage requirement of 50% before they die.

Although the health threshold is increased by +13% each stack, this is not linear, and additional Guillotines will provide a slightly smaller amount. This means that Elites cannot be executed at 100% health, as extra stacks of the item will eventually fall off.

Math
The threshold at which it will activate is determined by the formula

Trivia

 * The Old Guillotine is currently the only item to have undergone a rarity change. It was originally added as a Common item before later being changed into an Uncommon item.