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They probably have a bunch of synergizing cards and card draw, so they just get more of everything, mixed with some insane luck.
It's weird though, because i have no issue with it being 250 cards, that just means they are less likely to draw a specific card, it's just they somehow draw exactly what they need to counter everything. Probably because it's a control deck of some sort.
A deck with 60 cards, 12 of which have the same purpose, there's a 95% chance you have at least one of them in the first 5 turns of the game. A deck with 250 cards, and 50 filling the same purpose, that chance is still 93.6% to have in the first 5 turns.
The actual issue in question is a misalignment of expectations; you're expecting the size of the deck to have a much much larger impact on consistency than the math suggests.
I would say there are players who have figured out how to build decks and sometimes they play larger decks for the heck of it, knowing they are sacrificing some focus for flexibility and expect to win through any poor draws. And the rest copy their idea without understanding how it works and then end up facing some midlevel boss like myself and wonder why it didn't work.
I'm working off the assumption that if you've just started playing and don't know much, when you hear "bring a 60 card deck" you're going to put 60 cards in it. Making a 250 card deck doesn't necessarily imply a lot of skill, like you said, but if you're making that decision I figure it implies you're putting a more-than-default amount of thought in already. Your plan may not work but you do have a plan (even if it is copying what you saw someone else do) which is more than some players can say.
I'm not talking about mana.
As i SPECIFICALLY SAID, your odds of drawing a specific card goes down, since you can only have 4 of any one card. 4 of the same card in a 60 card deck is a higher percentage than 4 cards in a 250 card deck.
Yes, you can put cards with duplicate affects, so that's probably why said decks can reliably draw, say, an "exile target card". BUT most cards, for example creature cards, that are worthwhile (aka are a win condition) are unique, and it's best when you have a specific other card that synergizes well.
The odds of drawing both of said cards for a 2 card combo that goes well, is only 8 in 250, so less than 4% of the deck. I'm not sure what the statistics on drawing that is, but it would have to be really low.
Also, what affect has 50 cards that do the same affect? Except for Historic, i don't think there are THAT many cards with essentially the same affect. I could say, maybe 12, IE 3 different cards with similar affects is plausible, for things like "counter target spell" or "kill creature" or "exile creature"... but 50? that is like 13 different cards, 4 of each, with the exact same affect.... again, unless it's historic, i don't see how that is even possible for even things like "counter target spell" or something like that.
The thing is, we don't have infinite cards to work with, there is a set limit of cards, 4 per card, and only a few different cards with similar enough affects, and again, creatures specifically usually have very unique affects with some exceptions. Because cards go out of rotation, even these exceptions are likely not within the standard/alchemy rotation
You seem to be forgetting here, that there isn't an infinite amount of cards, or cards with a similar enough affect. Aside from lands.
As my main deck is a Mill one, I hate those oversized decks. That said, I too find it really annoying how they seem to always get perfect draws.
There are almost zero cards ever printed that are truly irreplaceable in a deck, in a generic sense. And the ones that are actually irreplaceable are so niche that a 60 card deck can't afford to put them in to begin with.
You can only have 4 of one card, and except for instants that generally have 4-5 different cards doing the same thing (but still not enough to have 50 cards that do the exact same thing) and creatures tend to have unique abilities.
Unless you are in Historic, there is only a certain amount of cards in rotation.
We're talking about deck size (that's an e you degenerates). Are you saying the game is rigged to make 250-card decks win?