How many attacks to knock out the opposing Pokémon

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The multiplier goes on first and the reduction comes off afterwards, which is the order that costs people games. Nothing here is tied to one game: any fight where damage is multiplied and then reduced works out the same way.

Results

Damage each attack really lands
Attacks it takes
Damage thrown away on the last one
More damage needed to save an attack
Damage you could add that changes nothing
Attacks per point the knockout is worth

The damage each number of attacks needs

AttacksLeast damage that does itMost damage before it stops matteringDamage in that band that buys nothing

That last column is the reason most damage increases are worth nothing. Attacks come in whole numbers, so between one threshold and the next every extra point lands on a target that was already going down in the same number of hits.

And the wasted band gets wider the faster you already are, not narrower. Going from four attacks to three is a small step; the band where three attacks stays three is wider than the one before it, and the band where two stays two is wider still. The closer you are to ending it in one, the more of your damage is decoration.

It also explains why hitting a weakness does not simply halve the work. It moves you along the same staircase, and where you land decides everything: sometimes it saves three attacks, sometimes one, and sometimes none at all because you were already at the bottom step.

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Why does more damage so often change nothing?

Because attacks come in whole numbers. Between one threshold and the next, every extra point of damage lands on a target that was already going down in the same number of hits.

Against three hundred and thirty health, with no weakness or resistance in play, anything from a hundred and ten to a hundred and sixty-four damage takes exactly three attacks. Fifty-four points of damage buy nothing.

Does that get better as my damage goes up?

It gets worse, which is the part that surprises people. The band where the count does not move gets wider the faster you already are, so the closer you are to ending it in one hit, the more of your damage is decoration.

With three hundred and thirty health, thirty resistance and a doubling weakness, the bands run like this.

AttacksLeast damage that does itMost before it stops matteringDamage that buys nothing
4576912
3709727
29817981
Does hitting a weakness halve the work?

Not as such. It moves you along the same staircase, and where you land decides everything: the same doubling can save three attacks, or one, or none at all if you were already at the bottom step.

That is why the page reports the count rather than the multiplier: the multiplier is an input, and the count is the answer.

Which order are the two applied in?

The multiplier goes on first and the reduction comes off afterwards, which is the order the page uses and the one that costs people games when they get it backwards.

Doing it the other way round makes a resisted attack look weaker than it is against a weakness, and stronger than it is without one.