Does Trinisphere affect spells that already have a converted mana cost of three or more?

Trinisphere reads: 'As long as Trinisphere is untapped, each spell that would cost less than three mana to cast costs three mana to cast.' The key word is would cost less than three. If a spell's total cost (after applying all other increases and reductions) is already three or more mana, Trinisphere does nothing to it.

The process for determining a spell's total cost is laid out in CR 601.2f and CR 601.2h. You start with the mana cost or alternative cost, apply cost increases, then apply cost reductions. Only after all of that do you check whether Trinisphere needs to set a floor of three mana (CR 702.67a). It is effectively a minimum, not an additional tax.

One nuance: the 'three mana' minimum means at least three mana of any type must be paid. Trinisphere can force a spell to cost more than its printed cost, but it never reduces a cost that is already high enough.

Concrete example: Your opponent casts Counterspell, which has a converted mana cost (mana value) of 2. With Trinisphere untapped, they must pay at least {1}{U}{U} — three mana total — rather than just {U}{U}. But if they cast Wrath of God (mana value 4, cost {2}{W}{W}), Trinisphere does not change that cost at all; they still pay {2}{W}{W}.

Citations: CR 601.2f and 601.2h govern total cost calculation; CR 702.67a defines Trinisphere's effect as a cost floor applied after all other modifications.