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What is the catch rate of this?

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In percent, what is the catch rate of a Pokémon with an official catch rate of 3 when it has 1 HP, it's asleep or frozen, and you are using an Ultra Ball or any other ball that doubles your chances?

I think I almost have the answer

However I have a little question myself, Is there any Pokemon specifically because I actually need to know what Pokemon it is since it's HP plays a role in the calculations. Also, in what generation is this, because the calculations vary between the generations :)
lets just assume its BW and its HP is ONE.
ok, generation V, but I need the max HP of the Pokemon :/
........ why dont you give an ESTAMANT?
because it is very possible that it varies between Pokemon though I am guessing that all Pokemon at 1 HP with a status inducement will most likely have a 0.6% chance of being caught
I say ask Smogon's calculator because we don't have enough info to know the answer but it does. BYE HAVE A GREAT TIME
I forgot to mention.  It is 4th Gen, Azelf, with 135 max HP that made me think of this.

Well, here is the formula: So, when we personalize this to our dilemma, it is:

(((3 x HP Max - 2 x 1) x 3 x 2) / 3 x HP Max) x 2

Now - since you didn't give us the HP Max (a very important part of the equation) I will assume it's 150. I'll edit the answer once you give it to us, but just so you know. :3

Now the equation is:
(((3 x 150 - 2 x 1) x 3 x 2) / 3 x 150) x 2

3 x 150 (Maximum HP) = 450
2 x 1 (Current HP) = 2
450 - 2 = 448

The equation is now:
((448 x 3 x 2) / 3 x 150) x 2

448 (number from previous bracket) x 3 (Base Catch Rate) = 1,344
1,344 (number from above) x 2 (Ultra Ball) = 2,688

The equation is now:
(2,688 / (3 x 150)) x 2

3 x 150 (Max HP) = 450

The equation is now:
(2,688 / 450) x 2

2,688 / 450 (both numbers from previous equations) = 5.973333 (rounded to 6)
6 (number from above) x 2 (SLP or FRZ) = 12

So, the catch rate for the Pokemon with that criteria with the assumption of Max HP 150, the answer is 12.

Hope I helped. :)

selected
That's a lot of math...

(12?!?!?!  That's like 1.2%!  No wonder Azelf took so darn long to catch!!!)
(And Uxie was easy...)
Edit:  Ahem, please excuse my rushing while doing math.  I meant 1.6%.
Use dusk balls cause it's in a cave.
This doesn't have to do with what ball should be used, what matters is the math.
It also should be noted that the capture rate (12) is still pretty low, because Pikachu's capture rate is 190. Just saying. :3
Who else just skipped to the bottom to find the answer?

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