Mathed Up: How the London Mulligan Affects Modern (Part 1)

Welcome to another week at Good Grief Games. We often begin our weeks with an Event Spotlight article so you may be surprised that we are skipping over the Mythic Championship. For once though, you do not need us to assemble the data for you. It has been parsed over already and we recommend that you take a look at Saffron Olive’s article on it here. What we have decided to cover instead is the proposed London Mulligan. This change gives players a greater degree of control but there has been significant outcry in the community about the impact this would have on the Modern format. We will begin investigating that today by taking a look at Serum Powder and the Leyline cycle.

How it Actually Works
Many players were exposed to the proposed change via word-of-mouth or a tweet that simplified the original article which is available here. This has already caused widespread misunderstandings. So let us break it down:
1. Players randomly determine turn order and each pick up seven cards.
2. The player who goes first will decide whether to mulligan, followed by their opponent.
3. When a mulligan occurs, the player will shuffle their hand away and pick up seven cards again. Then they will put x cards on the bottom of their library where x is the number of times they have mulliganed.
4. Then they may mulligan again, followed by their opponent.
The key misunderstanding that stems from this is that most players believe that they will not place anything on the bottom of their library until they have decided to not mulligan. This is not true. You will need to bottom cards with each mulligan before deciding whether you will mulligan again. Even if you know that you are not keeping the hand, you are supposed to bottom x cards before deciding and announcing your decision. This is mostly a formality as most players will announce that they will keep or mulligan before bottoming anything. In the case of an additional mulligan, they likely will just skip the bottoming process and shuffle their hand back in. This should not be a problem, so what is the issue with not knowing how it actually works? Well…

Serum Powder
Serum Powder is currently causing the greatest confusion under the new rule. If the London mulligan rule worked as most seem to think it does, which is incorrect, we would see this:
1. Player A does not like their opening hand and decides to mulligan, shuffling it away.
2. Player A draws a new seven. This one has Serum Powder but the hand is not good.
3. Player A utilizes Serum Powder to exile those seven cards and draws seven new cards.
4. This is a better hand so Player A decides to keep it.
5. Player A then must bottom one card because they mulliganed once.
It does not work this way.

You must bottom x cards before, and regardless of, your decision to mulligan or not. Serum Powder says “Any time you could mulligan”. Step 3 is not a legal time at which you could mulligan. Therefore, the actual sequence would be:
1. Player A does not like their opening hand and decides to mulligan, shuffling it away.
2. Player A draws a new seven. This one has Serum Powder but the hand is not good.
3. Player A then must bottom one card because they mulliganed once.
4. Player A utilizes Serum Powder to exile those six cards and draws six new cards.
5. This is a better hand so Player A decides to keep it; though they do not have to.

This confusion has led to bold claims such as “Serum Powder will need to be banned” and “Every deck will have to run a playset of Serum Powder”. Hopefully this information will spread as far as the uproar did and lead to a better understanding. The proposed London mulligan does improve Serum Powder. Each new hand will have seven shots at finding it and as long as you do not bottom it, you will have the option of pulling a new hand. This new hand will just have the number of cards you had after bottoming x cards though; you will not be pulling up seven as if it were an additional London mulligan. So Serum Powder is improved in the way that all cards are really; you will see them more often. The actual effect of the card itself will not be modified in any way. In particular though it has an effect in your opening hand that will now occur more often and it is not the only card designed this way.

Leylines
When the London mulligan was announced, most players minds immediately jumped to the Leylines. Unfortunately, or fortunately depending on your perspective, there are only two Leylines worth playing in Modern. Leyline of Sanctity is a potent hate card against Burn and black decks that rely on targeted discard. Leyline of the Void acts as an immediate, one-sided Rest in Peace against the graveyard decks of the format. These cards see play specifically because of the Leyline effect that puts them into play for free. They are not commonly cast as they are overcosted and their effects lose most of their potency if they do not come down early. So it is no surprise that people see the potential granted to Leylines by extra seven card hands. Some have said that these cards will be too powerful if this rule becomes widely adopted but let us calculate the actual effect.

Methodology: To figure it out we must use hypergeometric probability to find the chance of failure. By this I mean that we will use our known information to calculate the probability that the hand will not contain the Leyline. Our setup is that we are willing to mulligan to five indiscriminately in order to find the Leyline. Our inputs will be a population of sixty cards, a success count of four, with a goal of one or more successes in our sample. The sample sizes for the Vancouver mulligan will be seven, six, and five. The sample sizes for the London mulligan will be seven, seven, and seven. For a total failure, the failure would have to occur in all three hands. Therefore, the chance of failure for each sample/hand would be multiplied together to find the odds of total failure. A hypergeometric calculator is available here so that you can follow along. Remember that you need to use one minus the result as your chance of failure. This is necessary to calculate simultaneous occurrences and find the total failure rate.

Vancouver Mulligan (Current Rules)
Chance of Failure in the opening seven: 60.1%
Chance of Failure in the six: 64.9%
Chance of Failure in the five: 69.9%
Chance of Total Failure: 27.3%
The good news is that if you are willing to go down to five cards in search of a Leyline, you will find at least one 72.7% of the time if you run four copies. My interpretation is that if you won Game 1 and have four game-winning Leylines to board in, you should be willing to indiscriminately mulligan to five in Games 2 and 3 to find it. For this to fail, you would have to reach total failure twice in a row. Therefore, this strategy will deliver you a Leyline in either Game 2 or Game 3 to take the match 92.6% of the time. Even if you did not win Game 1, your chance of finding the Leylines via this strategy in both Games 2 and 3 to take the match is 52.9%. I honestly do not recommend this option as Leylines can be answered but it is your decision.

London Mulligan (Proposed Rules)
Chance of Failure in the opening seven: 60.1%
Chance of Failure in the second seven: 60.1%
Chance of Failure in the third seven: 60.1%
Chance of Total Failure: 21.7%
The change in rules mean thats if you are willing to go down to five cards in search of a Leyline, you will find at least one 78.3% of the time if you run four copies. To put this into context, mulling to five in search of a Leyline under the old rules would work out in just over seven of ten games. If the proposed rules are adopted, mulling to five in search of a Leyline will work out in just under eight of ten games. If you were to employ this strategy twenty times under the proposed rules, it would work out for you just one more time than it would have under the current rules. Let us revisit the situation in which you won Game 1 and have four game-winning Leylines to board in. Under the Vancouver mulligan, you would be able to find it in either Game 2 or 3 to win the match 92.6% of the time. The London mulligan improves your chance of winning the match with this strategy to 95.3%. Based on these numbers alone, I would say that most players are overestimating the effect of the London mulligan on Leylines.

However, there are other factors that we must consider with this strategy. The power of the London mulligan is not just seeing seven cards with each mulligan to bank on a Serum Powder or Leyline. The key change is that you will be sculpting an ideal, smaller hand out of seven cards every time. When you mull to a Leyline, you do not truly win. You are only preventing the opponent from winning. Decks that cannot win through Leylines almost always have ways to remove them. Therefore, you need some form of pressure to end the game before your opponent can find an answer. This is where the London mulligan truly shines. A Vancouver mulligan to five that finds a Leyline is suspect at best. An example would be Bogles versus Burn. Your five card Bogles hand has a Leyline of Sanctity but you still need a land, a creature, and an aura to win before they find Destructive Revelry. Your top five cards having all of that just is not very likely. With a London mulligan though, you will instead be  sculpting that five card hand with your top seven at your disposal. It is not a massive difference but it does have an impact.

So your odds of finding a Leyline via mulligan are improved and your average post-mulligan hand will be better. Some players may argue that it is significant to the point that you should be willing to mull to four in order to find the Leyline. While I do not agree with this, I ran the numbers anyways. If you are willing to take it a step further and go down to four cards in search of a Leyline, you will find at least one 86.9% of the time if you run four copies. I do not recommend it but if you were to employ this “mull to four” strategy twenty times under the proposed rules, it would work out for you three additional times compared to the “mull to five” strategy under the current rules.

Wrap-Up
We understand that this is a lot to take in but we hope that we have broken it down enough to be easily digestible. It is hard for any of us to predict what effect a rules change this significant would have and you would need an extremely large sample size to test it. Therefore, complex math is our best option. We welcome you to join our Facebook group to discuss this further. Or if you are interested in writing an article yourself please message our Facebook page directly. While we were able to cover today’s topics with just hypergeometric probability, we need a bigger picture as games often do not come down to a single card. I have spent much of my weekend teaching myself multivariate probability to advance our understanding. We will be back tomorrow with further findings that examine the effect of the London Mulligan on a sixty card level. Until then my friends.

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