K, so here's what GameFAQs told me. First, the number of possible ID numbers.
Granted, there are 65,535 possible lottery numbers / IDs, so your chances still aren't very good, but you may get lucky.
That's quite a few. The gravity of that many possibilities below.
>[So the odds of winning the Jubilife Lottery are **N/10^5**] where N is the number of different OT numbers you have:
The winning numbers change every day, so on average it would take (10^5)/2 days (or 136 years) to win one Master Ball without trades (and average one Master Ball every ~274 years.)
Dang. That's, like, five generations of PXs. Here's the same statistic from a different source for verification:
Now, in Platinum, you can have a maximum of 18 PC boxes that hold 30 Pokémon each. 18 x 30 = 540. You can also hold six Pokémon in your party, so the number goes up to 546 Pokémon maximum. If, by some impossible feat, you managed to get 546 Pokémon with different ID no.'s, let's see how that affects your odds.
10^5 = 100,000
N = 546
546/100,000 = 0.00546
This means your chances of getting a Master Ball, with as many possible different ID numbers, is about 0.005, or 5 in 1000, or 1/200, or 0.5%.
Of course, you likely won't get that many different IDs, so here's your chances with only Pokémon you've caught:
N = 1
1/100,000 = 0.00001
So, your chances alone are a mere 0.00001, or 1 in 10,000, or 0.001%. Good luck!
I am not a mathematician. If I erred, please inform me.