If you add ink to your inkwell and play one card every turn, going first you'll naturally run out of cards on turn six
The full texts of these abilities are "At the beginning of the monarch's end step, that player draws a card" and "Whenever a creature deals combat damage to the monarch, its controller becomes the monarch." If the triggered ability that causes the monarch to draw a card goes on the stack and a different player becomes the monarch before that ability resolves, the first player will still draw the card
Shi Tian came up with the concept of using enablers (Faithless Looting, Insolent Neonate and Tormenting Voice) alongside dredge cards (Stinkweed Imp and Golgari Grave-Troll) to essentially mill our deck, which will reward us with free creatures in the form of Bloodghast, Narcomoeba and Prized Amalgam
It still has a place (mostly driven by nostalgia, probably) in dredge decks like Jarad, Golgari Lich Lord, and you absolutely have to run it on principle in Saffi Eriksdotter and Hans Eriksson decks