PokéBase - Pokémon Q&A
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Alright, this will be answered using MATH estimation. Remember you need at least 200 friendship to do this. First, to solve how long it takes to run 1000 steps:

About three minutes running in a circle. Hold your left stick right and your right stick left.

1000 steps = 5 laps around the mesagoza typing circle. It takes like 2 minutes.

Source1

Alright, so about 2-3 minutes to run 1000 steps. Now how rare is it to get a Partner Mark?

Partner Mark: 1 in 100 every 10,000 steps

Source2

So you have a 1 in 100 chance to get this mark every 10,000 steps, or 20-30 minutes.
So the chances are you should get the mark after doing this 100 times.
100•(20-30 minutes)

You should get the mark in about 2,000-3,000 minutes(or 33.33-50 hours) if you continue to run the entire time. Hope this helped!

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wow that's insane, can I automate this?
I’m not for sure. There may be a place you can infinitely run at in S/V.
You can connect a Gamecube controller or other third party controllers with turbo buttons/controls to have it done automated