Damage dealt to a player causes that player to lose that much life.

Rakdos can be put onto the battlefield by another spell or ability even if no opponent has lost life that turn.

Rakdos's last ability cares about the total life lost, not necessarily what an opponent's life total is compared to what it was at the beginning of the turn. For example, if an opponent loses 5 life and then gains 10 life in a turn, creature spells you cast will cost {5} less to cast.

If an opponent lost life and subsequently lost the game, Rakdos's first ability is satisfied, and its last ability counts that loss of life.

Rakdos's last ability can't reduce the colored mana requirement of a creature spell you cast.

If there are additional costs to cast a creature spell, such as a kicker cost or the commander tax, apply those increases before applying cost reductions.

Rakdos's last ability won't reduce the cost to cast Rakdos itself. It applies only to creature spells you cast once Rakdos is on the battlefield.