Mathed Up: How the London Mulligan Affects Modern (Part 3)

It is finally time to give our final word on the London mulligan in Modern. We have run the numbers on singular cards and we have conducted experiments with Tron. Today we will apply those same experiments to Burn and Dredge decks. We will then take all of our data together for comparison and determine what attributes make a deck benefit from the London mulligan most. Then we will give our final statement on how we perceive the London mulligan and our stance on its legality in the Modern format.

Methodology
While the response to Part 2 was overwhelmingly positive, there was some confusion among our readers about the calculations. So I would like to clear that up. These calculations are an experiment to compute the effect of the change in mulligan rules. These are not mulligan guides for specific decks. In this experiment we use the Vancouver mulligan as the control group and the London mulligan as the experiment group. We choose an archetype and put together a recipe for a passable hand. We then use multivariate probability to find the odds that this recipe fails to appear at different sample sizes. For the Vancouver mulligan the sample size is seven for the opening hand, seven with the first mulligan due to the scry, six with the second mulligan due to the scry, and so on. For the London mulligan the sample size is always seven. These fail rates at each sample size are multiplied together to calculate the odds that you can go through an opening hand and x mulligans but still fail to find a passable hand. Apart from the sample sizes, all other variables are held constant from the Vancouver mulligan to the London mulligan. This allows us to isolate the effect of the proposed change in mulligan rules. The only caveat, as mentioned in the previous parts, is that although the sample sizes are equal between a seven card hand and a six card hand, they are not truly equal because the card that you scry will not be playable on Turn 1 if you are on the play. This is a corner case but it is still an incalculable factor that is not an issue with the London mulligan. If you would like to try your hand at multivariate probability there is a calculator available here.

Burn Decks
Due to rumblings within the community we chose to focus on Tron first. After all, it is looking to assemble a specific three cards and the London mulligan lends itself to this a bit better. But we must also look at the entire opposite end of the spectrum in Burn. No Modern deck cares about card selection less than Burn as their effects are extremely redundant. The core of the deck is Lightning Bolt and several inferior variations of it. The number of cards in their hand is much more important than the contents of it. All of their spells are meant to deal direct damage. So our experiment has simplified the deck to 19 lands and 41 damaging spells. For the opening hand a passable hand contains at least two lands and at least four damaging spells. For the first mulligan a passable hand contains at least one lands and at least four damaging spells. For the second mulligan a passable hand contains at least one land and at least three damaging spells.  
Results:
Under the Vancouver rules, if you are willing to mull non-suitable hands up to two times you will be able to put together a suitable hand 98.7% of the time.
Under the London rules, if you are willing to mull non-suitable hands up to two times you will be able to put together a suitable hand 99.3% of the time.
So when we utilize identical heuristics across the Vancouver and London mulligan rules, the difference is only 0.6%. This is a difference of slightly more than 1 in 200 games. This is in line with the belief that Burn does not benefit significantly from the proposed rules change. It is difficult for them to mulligan under Vancouver rules due to a focus on card quantity and this is not alleviated by the London rules. The quality of the smaller hands will improve but Burn does not appreciate a mulligan of either variety.

Dredge Decks
We now know that there is a small but legitimate boost to Tron decks with the London mulligan and it would be logical to assume that this is true of all decks that try to assemble specific card combinations. We have found today that Burn barely benefits at all from the London mulligan; this should apply to card quantity decks in general. The final extreme to look at is the deck that mulligans more than any other: Dredge. This deck cares very little about the number of cards they have. For our experiment a passable hand just needs two lands, any Dredge card, and any enable such as Faithless Looting. Unlike Burn, Dredge is willing to mulligan a third time in this experiment and the passable hand is unaffected by sample/hand size.
Results:
Under the Vancouver rules, if you are willing to mull non-suitable hands up to three times you will be able to put together a suitable hand 98.6% of the time.
Under the London rules, if you are willing to mull non-suitable hands up to three times you will be able to put together a suitable hand 99.6% of the time.
Our experimental result is a surprise to me, but the success rate difference between the two mulligan rules is a single percent; equivalent to 1 in 100 games. This is more significant than the effect on Burn but it is not benefitted to the degree that Tron is. They may not care about card quantity like Burn does but they are unable to take advantage of card selection as well as Tron does. My expectation was that the third mulligan would have a dramatic effect but I was incorrect.

The London Mulligan in a Nutshell
Going into these experiments I was cautiously optimistic about the London mulligan in Modern. It is a great idea, more on this below, but I was concerned about the potential for abuse in non-rotating formats. I am pleased to report that these experimental results have led to my unwavering support for the change. Developing these experiments has clarified the differences between the rulesets for me. Obviously, the non-mulled hands are equivalent. But the first mulligan is barely different. Both see seven cards. The London rule may bottom any one of the seven cards. The Vancouver rule may only bottom the seventh card but it has the choice to not bottom it at all. So the London six is better but not by a ton and not always. We do not see a particularly large difference until the second mulligan and it is larger still at the third mulligan. At these points the Vancouver has a smaller sample size than the London while also lacking card selection. An impressive example is Dredge’s mull to four from the example above. Their success rate with a Vancouver four is only 42.9% but the success rate for a London four is 75%. This means that the proposed rules change would affect almost one out of three games to their benefit. During the set up this led me to believe that decks that aggressively mulligan would be most benefitted by the rule set change. But why did it not show in the total fail result? Because these decks can mull to four but they only want to do so if necessary and it will be necessary in only 2.4% of games under Vancouver rules; 1.6% under London rules. The previously mentioned one third of games affected are only the mulls to four. So we are talking about one third of these small percentages, not one third of all games played.
The experiment has shown that the card selection is more important than the sample size; Tron is the true winner. Our finding is that the new rules are more beneficial to decks assembling combos than they are to decks that mulligan aggressively. As expected, decks that do not like to mulligan, based on card quantity, have little appreciation for mulligans that improve card quality. For all decks though, the average mulligan is always worse than the average hand before it. The experiments show that this rules change does not massively improve these decks as they are currently built. Our only concern is that these decks could possibly be rebuilt significantly with the new rules in mind. Perhaps Tron runs fewer tutors and Dredge runs fewer enablers or Dredge cards. You could argue that the card selection of the London mulligan would allow them to maintain consistency with less spell slots committed. This would give them some percentage points but it will not make a mulligan a beneficial thing. It is only a choice when a hand is not good. The decks that benefit from these rules most have issues with sideboard hate such Rest in Peace or Damping Sphere. Their opponents will have greater card selection and find these cards more consistently. Of course anti-hate cards like Nature’s Claim do exist. But once a deck is built to be “less consistent” and lean on the consistency granted by the London mulligan, it becomes difficult to mulligan aggressively for a passable hand that also contains anti-hate. My perception is that some decks will improve and some will get worse but none will do so significantly. We will have to wait until April to really know. Even if I am incorrect on this matter, I still support this change after playing with it.

The Final Word
From a game design perspective, it is great and Magic should have been built around it from the beginning. I love Magic and have played for many years but the variance paired with very punishing mulligans is a clear issue. Non-games are not just an issue for salty players. To become a legitimate esport, as it is working to be, Magic has to be a game that professionals can consistently lead in.  This may be a bold claim, but in a 50/50 matchup I believe that an average seven in the hands of a mediocre player beats the average five in the hands of a professional. Under the London rules it will be less punishing to mulligan and it will be far more skill intensive. The professional player will not be stuck at five with a scry one to compensate. They will be looking at seven cards and effectively hitting their hand with a double Thoughtseize with the goal of doing the least damage. The London mulligan is great because it gives all players greater control over their game outcomes. Currently, mulligans are punishing to the point that we often have to keep loose hands and pray for a topdeck. Sometimes you just lose either way and your skill as a player is irrelevant. I am not saying that this will go away entirely. But it will happen less often because it is not nearly as detrimental to take a London mulligan. Most importantly though is the increased influence of skill. Every single mulligan will be a significant skill check and will further separate the wheat from the chaff. I consider these aspects so important to the health and growth of the game that I would accept it breaking or invalidating specific archetypes. I know it is controversial to say but I would accept a deck being banned so that the game itself can benefit from the London mulligan. Regardless, my experiments lead me to believe that this will not be necessary but we have to wait for the London Mythic Championship data to give us a better idea.

Wrap-Up
With the completion of this article, I have written over 5,000 words focused on the London mulligan in Modern. This topic has been interesting but these experiments were quite an undertaking. If you would like to join us and pitch in, it does not have to be this intense, please contact us here. I hope that this has helped to clear up the confusion and quell the panic surrounding this proposed rules change. I do believe that in time the vast majority of players will come to love it. Tomorrow marks the end of a two month period. To mark this we will give you a snapshot of the Modern format for the period past; similar to what we did for 2018. Until then my friends.

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