Baloth Cage Trap — ruling 1

You may ignore a Trap’s alternative cost condition and simply cast it for its normal mana cost. This is true even if its alternative cost condition has been met.

Baloth Cage Trap — ruling 2

Casting a Trap by paying its alternative cost doesn’t change its mana cost or mana value. The only difference is the cost you actually pay.

Baloth Cage Trap — ruling 3

Effects that increase or reduce the cost to cast a Trap will apply to whichever cost you chose to pay.

Baloth Cage Trap : règles, fonctionnement et interactions (MTG)

Baloth Cage Trap is one of those cards players keep asking about. Here is, in plain words, what its official text says, the rulings published by Wizards of the Coast, and the combos players actually run.

Official card text

If an opponent had an artifact enter the battlefield under their control this turn, you may pay rather than pay this spell's mana cost. Create a 4/4 green Beast creature token.

How it works : Baloth Cage Trap

Original English text — Wizards of the Coast / Scryfall

#1October 1, 2009· Wizards of the Coast
You may ignore a Trap’s alternative cost condition and simply cast it for its normal mana cost. This is true even if its alternative cost condition has been met.
No other card is named in this ruling.
#2October 1, 2009· Wizards of the Coast
Casting a Trap by paying its alternative cost doesn’t change its mana cost or mana value. The only difference is the cost you actually pay.
No other card is named in this ruling.
#3October 1, 2009· Wizards of the Coast
Effects that increase or reduce the cost to cast a Trap will apply to whichever cost you chose to pay.
No other card is named in this ruling.