Old Guillotine

The Old Guillotine is an item in Risk of Rain 2.

The holder will instantly kill any Elite enemy that falls below 13% (+13% per stack) of its maximum health.

Math
The threshold at which it will activate is determined by the formula: $$f(x) = \bigg(1 - \frac{1}{0.13x + 1} \bigg) = \bigg( \frac{0.13x + 1}{0.13x + 1} - \frac{1}{0.13x + 1} \bigg) = \frac{0.13x}{0.13x + 1}$$

where x is the amount

Version History

 * PC Patch v1.1.1.2
 * Bug Fixes
 * Fixed Old Guillotine’s behavior for enemies with shields or barrier
 * Early Access Content Update 5
 * Major Content
 * Added New Item Lore Entry: Old Guillotine
 * Gameplay Changes
 * Execute Threshold: ~20% (+20% per stack) ⇒ 13% (+13% per stack) Developer Notes: Since we’ve re-tuned the health of elites across the board, the Guillotine should be appropriately re-tuned as well.
 * Early Access Artifacts Content Update
 * Bug Fixes
 * 🌧 Fix ‘Old Guillotine’ item not checking if the victim body is immune to executes (no more instantly killing yourself with Old Guillotine,, and /)
 * Early Access Hidden Realms Content Update
 * Bug Fixes
 * Fix Guillotine sound not playing over the network
 * Early Access 'Skills 2.0' Content Update
 * Gameplay Changes
 * 🌧︎Tier: 1 ⇒ 2
 * Update Logbook entry to properly reflect its stacking behavior
 * In the Logbook, it said it scaled the execute threshold by 20%(+5% per stack), but it ACTUALLY stacked by 20% (+20% per stack). Instead of reducing the threshold down to 5%, we decided to keep the current behavior and upgrade it to tier 2 instead.
 * Early Access Scorched Acres Content Update
 * Major Content and Changes
 * Added New Item:

Trivia

 * The Old Guillotine may be a reference to The Ol' Lopper from Risk of Rain 1. Both items are "old," have a strong execution motif, and give the player an extreme benefit against low-health enemies: the Lopper causes the player to land guaranteed critical strikes against weakened enemies, while the Guillotine will instantly kill those enemies if they are Elite.
 * 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.