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Example:

first turn
Surf did 50% of the foe's health.

second turn
Surf did 49% of the foe's health.

Why does damage differ when using the same move every time?

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Because the Damage formula has a random factor in it

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That is the damage formula
enter image description here
>rand is a random number from 0.85 to 1.00.

So basically, the bit which says random will vary anywhere between 0.85 to 1 which causes the changes in damage that you see.

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I bet he's asking why the random thingy is there, just sayin' xD
Yeah, then the answer is "Because Gamefreak wanted it to be!!"
Also to add a random factor in the game. *ANOTHER random factor.
It would make more seance without random thingy.
Obviously GF wanted you to think that ur gonna win, and them dis you by doing this