# Mathed Up: Leylines in Modern (Part 2)

I have tried to keep it brief but today’s entry is even longer than yesterday’s. But between the two you should have everything you need to accurately assess Leylines in Modern. Today we will cover the remaining opening hand probabilities, your odds of drawing them as the game goes on, and deckbuilding considerations. If anything is unclear, please let us know and we will try to elaborate further.

Odds of Opening With a Leyline
As expected, a persistent response to yesterday’s article was “What about 1-2 Leylines?” It is not a common choice but it is a valid question. The resulting probabilities are what you see below. It is interesting to see that even with only two Leylines, you are narrowly favored to find one by indiscriminately mulling up to two times in order to find one. Though your odds of succeeding with this strategy in both Game 2 and Game 3 are quite poor. So why even consider this strategy in deckbuilding?

Two Leylines
Opening Hand: 22.15%
First Mulligan: 22.15%
Second Mulligan: 22.15%
Overall Fail Rate: 47.18%
Overall Success Rate: 52.82%
Back-to-Back Fail Rate: 22.26%
Back-to-Back Success Rate: 27.89%

One Leyline
Opening Hand: 11.67%
First Mulligan: 11.67%
Second Mulligan: 11.67%
Overall Fail Rate: 68.92%
Overall Success Rate: 31.08%
Back-to-Back Fail Rate: 47.49%
Back-to-Back Success Rate: 9.66%

Odds of Drawing Late Leylines
Players are tempted to run fewer than three or four Leylines because they absolutely hate drawing them. I cannot say I blame them. As explained yesterday, it is opening hand or bust. You play these cards to beat linear decks and Turn 4 is way, way too late. On a related note, why do they all cost four mana? I have no clue.

Anyways, I have calculated the probabilities of drawing a Leyline as the game progresses. “One Draw” means that Leyline was on top of your deck right away. “Two Draws” means that there was at least one Leyline within the top two cards of your library. And so on. These probabilities are based on a population size of 53; a 60 card deck with an opening hand pulled out. However, a post-mull population would be 52 or fewer cards if the card you bottomed is not a Leyline. Furthermore, a fetchland will reshuffle the population and remove a card from it. The point is that in an actual game, it can become very complex. But these odds give you an approximate idea.

Four Leylines
One Draw: 7.55%
Two Draws: 14.65%
Three Draws: 21.35%
Four Draws: 27.64%
Five Draws: 33.55%

These odds are pretty troubling at first glance. If there are four Leylines in the population, you will end up drawing one by your fifth draw step in one out of every three games. You could view this as mulling one third of a card every post-board game. However, the good news is that the population and your deck are not exactly the same thing. The population is the 53 cards that remain in your deck after you have kept your hand. If you cared enough to run a full set of Leylines and boarded them in, why did you keep a seven card hand without one? If you did this, your hand is probably the nut draw and you do not really care what you draw from here. So the probabilities for four Leylines are not relevant very often.

Three Leylines
One Draw: 5.66%
Two Draws: 11.10%
Three Draws: 16.33%
Four Draws: 21.35%
Five Draws: 26.17%

This is where it is really at. As above, you probably should not look at this as “My sideboard has three Leylines.” Because if you run them and you boarded them in, you should try to mull to them; there should not be three in the population. These odds are relevant for the players that run four Leylines. They will keep a hand with one and there will be three left in the population that they would rather not draw. The result is that across four draw steps, they draw into one in about 1 out of 5 games. If it goes five draw steps, that jumps to about 1 out of 4 games. That can be frustrating, but is not as common as I would have assumed.

Two Leylines
One Draw: 3.77%
Two Draws: 7.48%
Three Draws: 11.10%
Four Draws: 14.66%
Five Draws: 18.14%

One Leyline
One Draw: 1.89%
Two Draws: 3.78%
Three Draws: 5.66%
Four Draws: 7.55%
Five Draws: 9.43%

Deckbuilding Considerations
You should look beyond the probabilities when deciding whether or not to run Leylines in your sideboard. The first consideration is cards drawn as outlined above. Different decks draw differing numbers of cards over the course of a typical game. For example, a UW Control deck is not capable of ending the game quickly whether the opponent is Leyline locked or not. They will draw several cards and therefore be more likely than a Humans deck to draw an unwanted Leyline before they can end the game. Along these lines, cantripping effects in general make Leylines worse. You draw more cards, you draw more Leylines. It really is that simple; those that can bottom an unwanted Leyline can be situationally helpful though.

On the opposite end of the spectrum, drawing Leylines is less of a problem if your deck pitches cards for value. Cards like Liliana of the Veil hurt less to use because you do not care about the card that you are discarding. Faithless Looting, as if we needed more reasons to use it, allows you to cycle a drawn Leyline into something useful. Cards like Collective Brutality virtually print some text onto an inert Leyline. Most of these effects do not actually net value by binning a Leyline. They just make the card disadvantage irrelevant. Decks that mostly ignore card advantage utilize Leylines most effectively.

Leylines are at their best in decks that can comfortably mulligan low. Obviously, you need to mulligan into one for them to be effective. On top of this, the Leyline is never really a card in your hand; it does not further your gameplan. When you mulligan twice and then put a Leyline into play, you are now playing a four card hand. If you are playing a critical mass deck, such as Burn, you will struggle to win post-mulligan. The more comfortable a deck is post-mull, the more effectively it will be able to utilize Leylines. It also worth noting that Serum Powder decks, by virtue of more mulligans, are able to leverage Leylines more effectively as their odds of finding them are improved.

Conclusion
So this was a lot to take in. Lots of numbers. Lots of factors to consider. So I will try to briefly break it down:

-The London mull makes Leylines much better; better odds in each mull and mulls hurt less.

-The casting cost of a Leyline is irrelevant; it is opening hand or bust.

-Running more Leylines is good because they will be in your opening hand more often.

-Running more Leylines is bad because you will draw into them more often.

-Leylines are best in decks that can win with few cards in hand.

-Leylines are best in decks that can win quickly and lack draw effects.

-Leylines are best in decks that bin cards; think Faithless Looting.

With all of this in mind, you should run four Leylines if you run any at all. You can get away with three but you should probably consider an alternative with a similar effect. The key exception is Dredge. It can mull into oblivion in order to dig up a Leyline. This deck can consistently end the game on Turn 4 with a four-card hand. They also commonly do not draw a card after Turn 2; opting to dredge instead. So their odds of drawing into an unwanted Leyline are minimized. Even if they do draw into one during that short window, they run multiple discard effects that will allow them to bin the Leyline. Or they just go about their gameplan discarding dredge cards and going off undeterred; in reality, their graveyard is their hand. So Dredge can get away with fewer Leylines but even they should aim to max out on them.

Wrap-Up
I think that should cover everything you need to know about Leylines. Leyline of the Void is not as desirable as it was a week ago, but you ought to grab a set while they are cheap. Graveyard decks take over Modern every couple years. Do you have your eyes on any of the other Leylines in Modern? How do you think the Hogvine deck fares in Bridge-less Modern? Please share your thoughts in our discussion group. Or if you would like to take a swing at writing content for the site you can contact us directly here. We will be back tomorrow with another article for you to enjoy. Until then my friends.