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I have an idea to calculate a birthday Pokémon.
- First, take your year of birth and substract 1900. (Yeah, it's like taking last 2 digits, but if you were born after 2000 you get 100, 101, 102, etc instead)
Example: Mine is 1986, so I get 86.
- Multiply by 365,25. If you weren't born in a leap year you'll get a decimal number; take only the entire part. (truncate, never round up)
Example: 1986x365,25 31411,5. I'll use only 31411.
- Add the day of the year you were born.
Example: Dec 17 is the 351th day. 31762
(You can notice at this point that essentially you're getting the days passed between 1/1/1900 and your own birthday)
- Take the modulo 649. You can use Windows calc in scientific mode for that. (if you don't understand what's "modulo function", it's the same as substracting 649 until you get a lower number)
Example: 31762 Mod 649 (= 31762-649-649-649-649...)= 610. I got Axew. (Oh, I liked the result)
Ah, if you get 0, it's 649.
The likelihood of getting a certain Pokémon is the same for any Pokémon and any person, since it's a 1-pokémon-per-day cycle.
If you want to get a regional Dex number, change 649 for 151, 202, 210, etc. depending of the region.
EDIT:
If you're calculating from Unova Dex, take 156 instead of 155, and if you get 0 it's 0 (Victini). Otherwise, treat zero the same as I said before.