PokéBase - Pokémon Q&A
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So, if a Fossil was facing a Pokémon faster than it, but its partner used Fake Out on the Pokémon, would they still get the 2x boost? Or does it count as “moving” when they “Flinch and can’t move” and therefore Bolt Beak and Fishious Rend don’t get the multiplier? Just curious.

Thanks in advance!

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Best answer

No

The Pokemon will not get the boost from Fisheous Rend/Bolt Beak
Here is the replay:
https://replay.pokemonshowdown.com/gen8doublesou-1174565272-kp0ymilwl4oafilusrlse1vssm5vsrrpw

So, in the replay, Incineroar uses Fake Out, causing Emolga to flinch and leaves it 81% HP. Dracovish, holding an Iron Ball for this, uses Fisheous Rend on Emolga, causing Emolga to have 21% HP.

Let's see what the calcs have to say:
For the calcs, Emolga is at 81% HP.
The calculations for Dracovish using Fisheous Rend when Speed EVs aren't inveseted:

252+ Atk Dracovish Fisheous Rend (85 BP) vs. /0 HP/ 0 Def Emolga: 180-213(71.7 - 84.8%) -- 31.3% chance to OHKO
Possible damage amounts: (180, 183, 184, 186, 189, 190, 193, 195, 198, 199, 201, 204, 205, 208, 210, 213)

Calcs for when Dracovish has Speed EVs invested:

252+ Atk Dracovish Fisheous Rend (170 BP) vs. 0 HP/ 0 Def Emolga: 358 - 423 (142.6 - 168.5%) -- gauranteed OHKO
Possible Damage Amounts: (358, 363, 367, 372, 375, 379, 384, 388, 393, 397, 400, 405, 409, 414, 418, 423)

To sum it up:
If Dracovish got the boost, its Fisheous Rend would've OHKOed Emolga, but it didn't. Dracovish could've OHKOed it without the boost, but the chance is 31.3%, so don't rely on that chance. So no, if a partner Pokemon uses Fake Out on a Pokemon faster than the Fossil Pokemon, it will not receive the Fisheous Rend/Bolt Beak boost.

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Thanks for the detailed answer!
Your welcome. Glad I could help!
I always thought it did. Today I learned.