What are the odds off a Pokemon (zubat) to attack 8 times in a row whilst paralyzed?

Question

I was playing Pokemon x and I always notice how when I get paralyzed I cant use any moves but when I paralyze another Pokemon its like they arent paralyzed to begin with, so I wanted to see how many moves a wild Pokemon could use before their move failed from paralasys and when it was paralysed it took 8 moves before wiping out my entire team and if I had more Pokemon it probably would have hit more. And its not a one time occurance I usually see Pokemon hit 5 moves in a row while being paralyzed. if someone could answer that than ty.

Comments

25% chance per turn that you’d be immobilized from paralysis.

For the chance of you hitting that 8 times in a row, I believe that’s 0.25^8, which is 0.0015%.

I’m not good at math though, so comment instead of answer

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That's the chance of not attacking 8 times in a row.

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I misread it as “what are the odds of it not attacking”. Oops

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The odds of it being able to attack while paralyzed is 75% chance per turn.

The formula for it to attack for all 8 turns should be .75^8 which equals to about a 10% chance of happening.

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PokemonDB moment: OP thinks they're super unlucky but then the chance is literally 10%

Also, to be pedantic: 10% is the chance of it attacking at least eight times in a row. That is contrasted with the chance of it attacking exactly eight times in a row then failing, which is geometrically distributed and closer to 2.5% (although the 10% scenario is probably more relevant to this question).

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I think this happens in almost every turn-based game with randomness, not just Pokemon.

Answer 1

Now it's time for everybody's favourite subject, math!

For a Pokemon to be able to attack while paralysed equates to a 75% chance of it happening. So, if this were to happen eight times, we'll need to multiply 75% (which is 0.75 in decimal form) by itself eight times.

0.75^8 = 0.75 x 0.75 x 0.75 x 0.75 x 0.75 x 0.75 x 0.75 x 0.75 = ~0.1001
Therefore, your chances of this happening is 10% or thereabouts.

Source and math