PokéBase - Pokémon Q&A
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Both me and my opponent have gotten the same lead Pokemon before (Sandaconda, Volcarona, etc.), and it seems more common than I would have initially believed.

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I'd assume it would just be 1/# of Pokémon available squared.
Thats partially true but you gave to take into consideration the fact that theres 6 slots it can fall into
I don't think the number 6 matters here because there's only one lead Pokemon on each team. If 2 people each flip a coin n times, the chance of getting the same result on the first flip is 1/2, which is true if n = 6, 5, 4, or any integer greater than 0. I don't know how many Pokemon can be leads or whether each Pokemon has the same chance of being a lead, so you'll probably get a better answer if you ask here: https://www.smogon.com/forums/threads/ask-simple-questions-here-read-original-post-before-posting.3520646/
I agree with sumwun, and I'm pretty sure that all Pokemon can be leads. So just every fully evolved Pokemon in Swsh plus Dusclops and Porygon-2. Although I think there are other mechanics in play for what Pokemon you get, as you always seem to get a legendary
It should probably be 1 by total number of mons ag to zu.

1 Answer

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Best answer

TL;DR, the chance of both players leading with the same Pokemon in Gen 8 randbats is a 1/381 chance. This counts alternate forms as the same Pokemon, so Raichu vs Alolan Raichu would count as having the same lead. If you're not satisfied with that, I can try my hand at calculating the probability of just the same Pokemon, same form (although I wouldn't look forward to doing it).

Long answer: First, I looked through the file of Gen 8 Randbat sets and did a quick ctrl+f search to find how many Pokemon had moves assigned to them (since, presumably, Pokemon with no moves assigned to them can't be selected in randbats). But before coming here, I asked on Smogon Forums to make sure the RNG wasn't skewed in any way, and turns out, it is, kind of. Showdown is programmed to weigh each Pokemon evenly when choosing for randbats, but what it counts as "each Pokemon" are separate Pokedex numbers. So, for example, Arceus' 18 forms doesn't make it 18x more likely than any other Pokemon; The chance that you get any Arceus form is just as likely as a Pokemon like Dragonite, but the chance that you get Arceus-Dark, specifically, is 18x less likely, to compensate.
The file that I originally looked through has movesets listed for every form available, so I built a simple program to comb through and only count each valid Pokemon once per form, trimming the number from 460 down to 381. Then we can just take this number outright as our answer; we don't need to square it to account for both players because it doesn't matter what the first player's Pokemon is, the second player just needs to roll the same number.

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Perfect, thanks!