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Let's just say a Clefable uses Metronome and ends up with Brick Break. What are the odds, or like the percentage, of using Metronome again right after and ending up with Brick Break again?

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1/381924
Calculation: When you use /nms maxgen8 command for seeing the total no. of moves, it shows 844 moves. Counting unselectable moves from Metronome it's 63 (source), along with 18 from Z-moves for each type, and another 19 from Max moves from each type, signature z-moves: 17, G-Max moves: 34 and moves deleted from Gen 8: 75. These moves can't be selected from Metronome. Total no.: 226. Now: 844-226=618, so 618 moves can be chosen randomly from metronome, or 1/618 is the chance of a move from Metronome. Chance of getting it twice would be 1/618 square, = 1/381924
Hope this helps!

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What if its nat dex and they aren't deleted?
We do consider Gen 8 since it's the most common. Nat Dex isn't that common compared to Gen 8.
Nat Dex isn't official too. Nat Dex is in unofficial ladder, and also, it's the asker mistake to not specify the generation and format.
I asked for a percentage, but whatever
You also asked for odds, which can be expressed as a fraction. The percent chance this will happen is ~0.000262%
wow, ok thank you Hellfire Burrito. I mean taco
hehe funny i laughed