There are two types of Zombie Discount cards in the game, and they each have different effects.

Economic Breakthrough
Grants a discount bonus for every gate destroyed. The further you advance in the mine, the higher the discount becomes.

The effect is not active in the first zone of the mine because no gates have been cleared there yet.

Cost Reduction
This card can be found during certain events and grants a fixed bonus upon upgrading.

Its effect is always active and does not depend on the number of cleared gates.