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What are the odds of having all of the Pokemon's trainer ID to match with the number in the lottery in Lumoise city and winning a Master Ball?

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Sigh, I'll answer this.
However, there are a few things I need to confirm first, so wait for a bit
Take your time:)

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Right this question isn't too hard actually. I just overcomplicated things...

>The highest possible ID number in any game is 65535.

Yeah that's the amount of possible IDs.
.: The total probability?
1/65535
= 0.00001525902%

Basically, the games cannot generate a number higher than that for the ID
Bulbapedia


Now why is it 65535 specifically?
>65535 occurs frequently in the field of computing because it is the highest number which can be represented by an unsigned 16-bit binary number.

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