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Conduit of Ruin's last ability can't reduce the amount of colored mana you pay for a spell. It reduces only the generic component of that mana cost.

Conduit of Ruin's last ability doesn't change the mana cost or mana value of any spell. It changes only the total cost you actually pay.

Conduit of Ruin's last ability will look at the entire turn, even if Conduit of Ruin wasn't on the battlefield for some of it. Notably, if you cast Conduit of Ruin in a turn, then no other creature spell you cast that turn can be your first.

If the first creature spell you cast in a turn has converge, you can't ignore the cost reduction of Conduit of Ruin's last ability in order to spend more colors of mana.

If the first creature spell you cast in a turn has {X} in its mana cost, you choose the value of X before calculating the spell's total cost. For example, if the first creature spell you cast in a turn has a mana cost of {X}{G}, you could choose 2 as the value of X and pay {G} to cast the spell.

If there are additional costs to cast a spell, or if the cost to cast a spell is increased by an effect, apply those increases before applying cost reductions.

If you control more than one Conduit of Ruin, the last ability of each of them applies only to the first creature spell you cast each turn, not to different spells; the first creature spell you cast each turn will cost {4} less.

The cost reduction can apply to alternative costs (such as dash costs).

The first creature spell you cast each turn doesn't necessarily have to be the first spell you cast. You could cast a sorcery spell and then cast a creature spell that would get the discount.