Doomsday Excruciator enters the battlefield, it triggers, exiling all but the bottom six cards of each library face down.
Activate a creature you control by tapping it, causing an opponent to mill cards equal to the creature's toughness.
Repeat step 3 as desired and/or able.
Notes
If an opponent has zero cards in their library as they begin their turn, they will lose the game during their draw step due to attempting to draw from an empty library. Depending on how many creatures you have available, it is possible to cause multiple or all opponents to lose the game in this fashion.