Does running in the grass, or caves in the generation 3 games (RSE, FRLG) make it more likely to encounter wild Pokemon?

Question

ANOTHER ZUBAT?!

Comments

Not a full answer, but https://sha.wn.zone/p/pokemon-encounter-rate

Answer 1

Running doesn't affect the encounter rate, at least not in Emerald. Apparently later games change this.

Source

Comments

More specifically, running doesn't affect encounter chance per step. However, you'll take steps faster, so it often takes less time to find a wild Pokemon.