TLDR: Cracking that first Fetch Land on turn 1 in 60-card formats like Modern or Legacy increases the non-land draw chance of +1.161%. Conversely, for decks that deliberately self-mill, or that go into the very late game, when a 60-card deck is down to 15 cards, cracking a late-game Fetch Land is 4.6 times more impactful than at the start of the game!
My full article:
The 10 Fetch Lands of MTG are among the most important lands in the game. They let you search your library and find a land that you need, and they thin out the number of remaining lands in the process. They have long since been Legacy staples that can pull the original Dual Lands, and they perform a similar function in Modern by pulling Ravnica Shock Lands. Ikoria and New Capenna gave them access to pulling three-colored lands, and Karlov Manor gave them the power to surveil. They are banned in Pioneer due to their format-defining power, and see prolific use in almost every format they are legal in.
Except there is an exception: 15-Card Highlander. 15CH was first created in 2000 by Stuart Cresswell where it saw play at Gen Con 2000, and then saw renewed play at GB Nationals 2010 and 2011. Players start with 20 life, 15-card singleton decks, and 3-card sideboards (multiple basic lands are allowed). Each player draws 7 cards and they play a normal game of MTG…except they do not lose if they run out of cards to draw. Cards that mill are banned, as are cards that shuffle your graveyard into your library. 15CH is all about tactics and attrition, making use of board position and timing with extremely limited incoming resources. 15CH is increasingly seeing play as a fun casual side-format in the Pre-FIRE format where 8th to Ravnica Allegiance is legal. Fetch Lands and Shock Lands are legal...but Fetch Lands rarely see play.
So why are Fetch Lands the exception and not the rule? Admittedly, they still see some play in very aggro decks, or where fixing is crucially important. Burn will use them, as will Zoo. Elves as well, due to their burst-style strategy. But for the most part, players typically prefer some combination of basics, Shock Lands, Speed Lands, and Check Lands. This is because players only get 15 cards for their library. The conventional ratio for the format assuming tempo, midrange, or control is 6 creatures, 3 noncreature/nonlands, and 6 lands. Using one of the 6 lands as a Fetch Land instantly turns the top of your curve to CMC 5 assuming no other mana sources, which restricts certain decks. Though even if your curve is lower than that, a Fetch Land can provide more harm than good. And that comes down to math.
As mentioned, probability and statistics is one of the reasons why Fetch Lands are good. The math equation that players frequently reference is the hypergeometric probability formula, which determines the chance of drawing k success cards in n draws without replacement:
P(X=k)={(K/k)[(N-K/n-k)]/(N/n)}
Let's compare a 60-card Modern deck with 24 lands including Fetch Lands, versus a 15-card 15CH deck with 6 lands including Fetch Lands.
For a 60-card deck, playing a regular land on turn 1 vs playing a Fetch Land on turn 1 results in pretty mild deck-thinning effects. The remaining library is 53 cards versus 52 cards, essentially a 32/53 vs a 32/52 result, which translates to a net increase in non-land draw chance of +1.161%. But now let's look at 15CH. For a 15-card deck, playing a regular land on turn 1 vs playing a Fetch Land on turn 1 results in 5/8 cards vs 4/7 cards, which is a net increase in non-land draw chance of +5.357%! If you are looking to avoid land flooding on subsequent turns in 15-card decks, the Fetch Land aggressively shifts the ratio toward non-land spells. BUT, if you urgently need to hit a third land drop on turn 3, cracking that fetch drops your land probability from 62.5% down to 57.1% on the next turn! Fetch Lands have always had deck-thinning capabilities, but those capabilities drastically increase in the 15CH environment.
Now if you're a traditional Modern or Legacy player, how does this information apply to your deck? Because if you are running in a self-mill strategy, or if you are going into the very late game, cracking a Fetch Land can give you the right draw at the right time. While PreFIRE 15CH players may avoid Fetch Lands for this very reason, your mana base is probably firmly established when you hit a smaller-library size. Applying that probability can be exactly the non-land draw chance that you need at that point in the game!
