One of the most commonly asked questions by Lands players, and one of the hardest to answer, is whether to dredge Life from the Loam or take a natural draw. On the one hand, dredging shows you three cards, and any land from among them is essentially drawn if Life from the Loam resolves. It thus sees so many more cards than a natural draw. On the other hand, there is a good chunk of important cards that cannot be retrieved with Life from the Loam (Exploration, Library, and sideboarded cards are perhaps most notable here). It can feel very bad to dredge Loam and turn over the Exploration that would have cracked the game wide open. But even if it feels bad, it could still have been the right move. Let’s go through the thought process of when and how to dredge.
Typically, if you have a land you know you want to play, and don’t need a raw number of Lands, it’s ok to not dredge and take a natural draw. For example, if you feel 90% sure that your best line is to simply play out your combo pieces, you don’t need to dredge, and drawing a card would be better as it could help you draw interaction like Crop Rotation to help the combo go through or Mox Diamonds/Explorations to help you enact it more quickly.
In other cases, you already have an Exploration, or else you are more interested in finding powerful lands than in finding anything else. As an example, imagine you have a Diamond, Taiga, a Port, and a Fetchland. Here you’re probably ahead on mana already because of Diamond, but you don’t have a ton of action. You want to dredge Loam to find potential interaction or threats.
These are general rules of thumb. But one often finds oneself in situations where one is playing to specific outs that can be pretty easily counted up. In those contexts, it can be helpful to know the actual math behind the question of dredge vs draw.
To calculate the probability of hitting an out via dredging, take the number of dredgeable hits over the number of cards in your deck. Then add this number to itself three times, reducing the number of cards in your deck by one each time.
To calculate the probability of hitting an out via natural draw, simply take the number of drawable hits (this is usually dredgeable hits + some number of Crop Rotations/Gambles) over the number of cards left in your deck.
Let’s look at an example of this to see how it works. Let’s imagine a case that commonly comes up – you’re looking for Depths to go with your Stage. More specifically, let’s say you have 45 cards in your deck, with 3 copies of Depths, 4 remaining copies of Crop Rotation, and no Gambles. You have enough mana to play Loam, then play Depths, and still be able to combo, so the mana cost of Loam isn’t an issue here (though sometimes it will be, so it’s good to be aware of it).
In this case, your chance of dredging depths is 3/45 + 3/44 + 3/43, or 0.205. Your chance of naturally drawing a Depths (or Depths equivalent, since Crop Rotation is effectively a Depths here) is (3+4)/45, or 0.156. Since the chance of dredging is higher than the chance of drawing, you should take the dredge here.
If you run these kinds of scenarios often enough, you will see a pattern emerge. Because Loam sees three whole cards, it takes a lot of non-dredgeable hits to outweigh that advantage. As a general heuristic, you will want to dredge unless the number of non-dredgeable hits is greater than or equal to twice the number of dredgable hits + 1.
For example if you have 2 dredgable hits and only 4 non-dredgable ones (eg. your 4 Crop Rotations), you will want to dredge. But if you have 5 non-dredgable hits, you will want to take the draw (since 5 ≥ (2 x 2) +1).
If you consider this math in relation to deck construction, you will see that unless you have 5+ tutors left in your deck (only really possible in builds with Gamble or Entomb), you will almost always be better off dredging for a specific out unless you’re literally on one out only.
Of course, there are other factors to consider, such as your available mana or how likely the opponent is to have countermagic, so the question is never as simple as all that. Nonetheless, I hope the above can function as both a helpful heuristic and a guide to calculating your own situational probabilities.