PokéBase - Pokémon Q&A
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(Asking cuz me suk at maths)

If I get 4 encounters (on average), each being Double encounters (basically 8 mons per every 100 steps), how many steps will it take for me to see 8192 mons?

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8192 * 100/8 = 102,400 steps.

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Aliright, thanks.
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If this is about managing your Repel supply, what you can do is settle into a corner where there are trees to (let's say) the north and west, then alternate pressing Up and Left repeatedly to bump into those walls. This lets you keep rolling for random encounters (limited to those that are high enough level to go through Repel, if any) but doesn't consume any steps so the Repel won't run out.

Overworld Sweet Scent is another way to get encounters without consuming steps, but the encounters you get that way will not respect your Repels.

The method of running into walls could also be used to churn through more encounters in Great Marsh without worrying about the step limit there, but those aren't double battles.

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Thanks, but this isn't about repels. I've trapped myself in Wayward cave (no, it was Bronzer, but we'll just ignore that here), and I didn't bring a sweet scent user with me. I don't want to leave, since I've teamed up with Mira for the double encounters (shiny hunting), and all my team is high leveled, so repels aren't doing much for me anyway. Sorry, but thanks for the advice, I'll be sure to use it in the future.
If you want to leave Wayward Cave without losing access to Mira's double battles forever, you might be able to start by knocking out Mira's Kadabra right away, then repeatedly switch between all your Pokemon with the hope of letting the wilds wear them down so you black out. Once you get down to the last Pokemon, you can waste turns by using a Paralyze Heal or something, without risking an attack that might KO them. This won't work if your team is so high-leveled that the wilds are unable to wear them all out before they run out of PP and faint to their own Struggle recoil (because of the forced full-party heal at the end of every battle), but it's worth a shot.
My team is in the 40's :/