It has been too long since we did some math. I do some form of Magic math nearly every day but rarely do I find something worth taking a deep dive on. However, with the London mulligan in place and Leylines reprinted it is the perfect time. Today I will discuss Leylines and the various probabilities involved with them; opening hand chance, viability of mulling into them, etc.
WotC clearly has struggled with the design of Leylines over the years. We now have eleven of them to choose from and the majority of them are quite awful. The distribution of them has been very odd as well. We have three in red, three in green, two in blue, two in white, and a single black one. The far and away best are Leyline of the Void and Leyline of Sanctity. These heavily disrupt archetypes; graveyard strategies and burn most obviously. In some Modern matchups, they are nearly a game-win if they go unremoved. Beyond these, the others have proven over time to be unplayable. The jury is still out on Abundance and Combustion but they are not looking promising. I do not mean to criticize WotC though. These cards are extremely difficult to design. How do you design a card that is playable at four mana and not broken at zero mana? Well, you just don’t.
The Mana Cost
We need to stop pretending that the mana cost of Leylines is relevant to their playability in a deck. When Hogaak surged everyone ran for their Leylines and less experienced players said “we cannot even cast it”. That is not relevant and it never has been. WotC is not capable of designing a card that is playable at either zero or four mana. It would be either broken or unplayable. The outcome is that these cards are good at zero mana and the mana cost is irrelevant. Leyline of the Void is a double-costed Rest in Peace that lacks an ETB; making it even more irrelevant on Turn 4. Leyline of Sanctity on Turn 4 is far too slow against Burn and will not protect you from early targeted discard. I understand that a hardcast Leyline could possibly come up but it almost never does. When you judge the playability of a Leyline, look at it as a card that does not have a mana cost; such as Lotus Bloom. Leylines are extremely good in your opening hand and nearly do not have text if and when you draw them.
Odds of Opening With a Leyline
We all know that the recent switch to the London mulligan benefits Leylines. WotC recognized this as well; the simultaneous reprinting of the Leylines was not a coincidence. Under Vancouver rules, your odds of seeing a Leyline became less favorable with each mulligan. However, the London rules have you scoop up a fresh seven cards each time. Mulligans are less painful, due to the card selection, so it is more realistic to take a low mull in order to find a Leyline. The mulligans themselves are also more likely to return a Leyline with each iteration. As explained in previous Mathed Up entries, the difference between mulligan rules becomes more apparent as you move from seven to six to five and so on. So now that the London rules are here to stay, we can take a serious look at the resulting probabilities. A common strategy is to near-indiscriminately mulligan up to two times in order to find a Leyline so we will work with that. After all, if you were to mulligan three times and then put a Leyline into play, you are trying to win with a three card hand. We will keep things simple and only look at the odds of the hand having a Leyline. The viability of the remaining four, five, or six cards varies by archetype. The old wisdom for Leylines is “run four or run zero” so let us start there.
Opening Hand: 39.95%
First Mulligan: 39.95%
Second Mulligan: 39.95%
Overall Fail Rate: 21.65%
Overall Success Rate: 78.35%
Back-to-Back Fail Rate: 4.68%
Back-to-Back Success Rate: 61.39%
So if you are willing to mulligan indiscriminately up to two times to find a Leyline, it will work out 78.35% of the time. Let’s say you won Game 1 against pre-ban Hogvine so you are just one win away from taking the match. You probably should employ the strategy outlined above. Sure there is a 21.65% chance that it does not work out. But you have Game 3 to try it again. Your chances of back-to-back failure are just 4.68%. However, there is the possibility that you lost Game 1 and Leyline is your only hope in Games 2 and 3. If you are that desperate, you might as well employ this strategy anyways. The chances of back-to-back success are a humble 61.39%. Of course you should keep in mind that degenerate decks like pre-ban Hogvine are very aware of these cards and know why you are mulling so low. There is a good chance that they will be doing the same thing to find their playset of Nature’s Claim and ruin your day. That deck really did need banned but I digress.
Opening Hand: 31.54%
First Mulligan: 31.54%
Second Mulligan: 31.54%
Overall Fail Rate: 32.08%
Overall Success Rate: 67.92%
Back-to-Back Fail Rate: 10.29%
Back-to-Back Success Rate: 46.13%
Folks really hate drawing Leylines and this leads them to trim one the first time it happens. Unfortunately, this jumps your fail rate from 2 out of 10 games up to 3 out of 10 games. As far as the “Win Game 1, then mull hard” strategy goes we go from 19 out of 20 successes to 9 out of 10. Despite the chance of removal, I would still go for it in this case. However, you cannot reasonably expect to drop Game 1 and take both postboard games with this strategy under this configuration. It will work out across Games 2 and 3 less than half of the time. Even the minority of times it does work, you still have to close the game before they remove the Leyline. It does not appear to be a viable strategy. However, it will reduce the odds of you drawing an unwanted Leyline as the game progresses. This is something we will cover in detail tomorrow though.
Do not fret, as we are far from done with this topic. Where do you think Bridge-less Hogvine stands? Is Leyline of the Void even up for consideration now? Please share your thoughts with us 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 to look at even lower Leyline counts, the effect on your draw step, and our conclusion. Until then my friends.