Cracking the London Mulligan

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There are few decisions in Magic quite as stressful as choosing a deck before an important event.

A poor choice can kill your tournament before you even begin. This is magnified further for a Mythic Championship where all the pressure is on and you only get a few chances per year. After you’ve spent potentially hundreds of hours preparing, practicing and travelling long distances to compete — you want to make the best choice.

Here we are at Mythic Championship London — my first Modern Pro Tour, first non-US event and most importantly my first MC with full Platinum benefits! This event also features three important changes affecting preparation. The first is that this is a “pre-release” Draft format, the set will only be released a couple of days before the event and therefore all preparation at that time will need to focus on Limited. For most events I focus on Limited first, switch to Constructed, then just play a few tune-up Drafts the day before the event. At this event, my plan is to try and wrap-up constructed testing before the full spoiler has been released. The second is that decklists will be public after round four to account for coverage displaying lists.

The third twist, and the focus of this article, is the brand new mulligan rule. For those unaware the rule being tested works as follows:

When a player mulligans they will draw seven cards, then after they have decided to keep they place X cards on the bottom of their library where X is the number of times they’ve mulliganed. The first consideration is how this affects a mulligan to six. In this case we can think about it as a player getting to see the card they would have scry’d BEFORE they choose to mulligan again and they may choose something other than the seventh card as the card the wish to put on the bottom. This is a subtle, but important effect. Where the rule gets more interesting is when a player mulligans to five or even four cards. When this happens they should still have a reasonably solid shot to have a playable, albeit severely hindered, hand.

What does this mean in general?

  1. A hand after a mulligan will now on average be stronger than it was under the Vancouver mulligan.
  2. If the average mulligan is stronger, then it follows that a player should be pickier about the hands they choose to keep and likely mulligan more often.
  3. Conversely, given that after a single mulligan the player is now working with more information (they’ve seen the full seven cards) they should both be more confident in their decision and with the ability to choose the card to bottom they should on average keep MORE often.

The impact on Modern

In lower power or more casual formats such as Limited, Standard or even even Commander mulligan decisions can boil down to simply having a good mix of lands and spells. Players aren’t usually mulliganing to find specific interactions. They simply want to be able “play Magic”. I believe that for these formats the new mulligan rule is fantastic. I don’t expect it to be very exploitable, and should reduce newer players frustration while also preventing major tournaments being decided before the first land has been played.

However, all of that gets thrown out the window when discussing higher power eternal formats. This rule is clearly broken when considering Vintage, if the rule is to be used there I’d expect a restriction of Bazaar of Baghdad. I’ve seen calculations done claiming that finding bazaar is above a 99% probability, up from ~95%.

However Vintage is played by a very small percentage of the Magic community, what Wizards and the competitive Magic player base at large cares more about is whether this rule can work for the Modern format. While finding specific cards, and sets of cards, is important only a tiny percentage of draws of the current top decks can win before turn four. The larger Magic community has also begun discussing a variety of fringe combo decks that have reasonable shots at winning by turn three with the hope (or fear) that the mulligan rule will improve their consistency enough to compete.

Stress testing the mulligan

Now how do we go about testing its impact?

Even at its most extreme it will only matter by a few percentage points. However, those points are exactly what elite competitors strive for. During one of our Team Face to Face meetings early into our testing process we had a discussion about how we’d test this rule. The suggestion was raised that we needed to just begin playing as many games as possible to try and suss out its impact. I balked at this suggestion. There were simply too many variables at play and the effect could only occur on the somewhat infrequent mulligans to five or six. In addition there would be a correlation effect while it is still unclear how aggressively or not we should be mulliganing with each deck. Mulligan decisions are already quite difficult and may be the most important part of playing many of Modern’s varied archetypes. It would likely take hundreds of games to even begin to understand its impact on a single deck if all you’re doing is playing games.

Luckily for me, and I suppose also you my dear reader, Allen Wu wrote an article last year discussing mulliganing under the current mulligan system and also shared the code he used to generate the data. I used his simulation for Eldrazi Tron mulliganing as a starting point and developed algorithms for mulligan decisions with Tron, Amulet Titan, Burn and Golgari Rock. The basic idea behind the simulation is that a hand is randomly generated, its “strength” is recorded and we move onto the next hand. For more detail about how it works I recommend Allen’s article, or you can check out my own code here.

My goal for these simulations was not as much about exact accuracy as much as determining how much of an improvement could be seen with fairly aggressive mulliganing strategies. For each of these decks I developed a few “buckets” which I decided roughly measured the hand’s strength. A hand could potentially fall into multiple buckets, but I only recorded it under the hand I’ve deemed to be the most powerful. My assumption was that any hand fitting into these buckets should be a keep by even the most aggressive mulligan strategy. This does not mean a player should mulligan as much as these numbers suggest, but the goal is that any hand outside of these buckets are at least close to being a mulligan. A player could mulligan this often if they wanted to look for a deck’s best draws. I was focusing on hands that essentially had everything they needed to function without needing to draw anything, but I’ll focus on the specifics for each deck.

First I calculated the probability of each hand classification with 4-7 cards using the current mulligan system. Next I consider how likely a player would find a keepable hand by their second mulligan. I consider the Paris mulligan instead of the Vancouver rules system (no scry) as all of my hand strength metrics are only considering the hand in view. Next I consider the same cards with the London mulligan where I make the assumption that a hand that has mulliganed once or twice will have the same strength probability as a seven. This is assuming that most decks need at most five specific cards to have their most powerful draws. Of course these hands will be less redundant, but this should adequately consider the consistency an “unfair” deck would hope to gain. For each deck I’ve simulated 500,000 hands for a total of two million hand simulations. For reference, this took roughly half an hour to run the full simulation on my machine.

Karn Tron


Mulliganing with Tron is all about setting up your mana. The rest of the deck is either your payoffs or cantrip artifacts. While I have never been a Tron player myself, my understanding regarding mulliganing with the deck is that the focus should be on establishing Tron and you should cross your fingers on drawing your threats after that. When I’m specifying whether the player has Tron I’m including Expedition Map and Sylvan Scrying if the hand also contains the green mana to cast it.

  • The Nutz: aka Turn 3 Karn GG: This hand contains all the pieces to play a karn on T3
  • Tron + Payoff: This hand contains Tron and either Wurmcoil or Walking Ballista
  • Tron No Payoff: This hand contains Turn 3 Tron but has no payoff
  • Keepable: At least 2 lands and 2 cantrips and no more than 3 payoffs

For Tron I’ve added an extra metric which includes the likelihood of finding Tron if a player decided to use these very aggressive mulligan tactics. As you can see having turn-three Tron in your hand with seven cards is only a 20 per cent probability and the overall keep rate is actually below 50 per cent. While I believe the consensus is that Tron should mulligan frequently, I’m sure it’s actually nowhere near this low. With this very aggressive tactic we see that the London mulligan would increase the likelihood of turn-three Tron from 28 up to 41 per cent and that they could be finding a keepable hand from 69 up to 86 per cent. To me this makes it very clear that at least in the case of Tron players should begin mulliganing even more aggressively then they had previously been doing.

Amulet


This was far and away the most challenging deck to create mulligan rules for. It took the vast majority of my development time attempting to come up with these formulas. Luckily my team mate and Amulet aficionado Edgar Magalhaes was willing to lend a hand going over a few dozen hands with me sanity testing my mulligan classifier. He also told me from tracking his Magic Online matches he found he mulliganed a little over 30 per cent of his hands. Therefore it’s a good sanity check seeing our simulation mulliganing just shy of 40 per cent of its hands as the goal was to mulligan very aggressively.

  • The Nutz: This has it all, likely going to win or deterministically win by T3
  • Stir Into Nutz: This is missing something to win quickly, but it has a Ancient Stirrings to try and find it
  • Double Amulet: This hand is missing a couple things, but has 2 Amulets and the mana to cast them. Could win on the spot after 1-2 draw steps
  • Turn 4 Titan: This hand guarantees that we can put a Titan on the stack by turn four, while this might not be quite good enough in some matchups, it’s still a solid hand
  • Keepable: This hand doesn’t necessarily do anything, but it should be keepable and has many live draws

Golgari Rock


Rock is on the other end of the spectrum compared to the decks I’ve looked at so far. You’re generally just looking for mana, a piece of interaction and a threat. In many matchups you’re also fine just overloading on one or the other. Your hands are much flatter, the power between your best and worst keeps are pretty similar. You aren’t looking for anything specific, you’re just looking to “play Magic”. I’ve decided to employ a fairly aggressive mulligan strategy where I want at least two lands and both black and green sources of mana. This misses some hands that are likely good keeps such as: Swamp, Field of Ruin, Dark Confidant, Thoughtseize. But specific hands like this can be somewhat hard to check for, so I’ll instead leave a note here that I’d assume these percentages are likely a bit higher especially for the “moderate keep” bucket.

All hands contain minimum two lands and access to both colours of mana.

  • The Nutz: Thoughtseize (or IoK), Goyf (or Bob or Ooze) and Liliana
  • Good Keep: No more than half your hand is lands
  • Moderate Keep: No more than ⅗ of your hand is lands

Burn


Burn’s mulligan strategy is even more about quantity than quality than Golgari. I focused on just having spells with the mana to cast them. I decided to assume that I’d never keep a one lander at seven cards, but I realize that may be somewhat contentious. Burn’s “nuts” hand is also pretty clearly the weakest of the decks tested here, but as the results show it’s also much more likely.

  • The Nutz: Exactly two lands, access to white and a one-drop creature
  • Good Keep: At least two lands and at least ⅔ spells ie. 4 in 7, 3 in 6, 3 in 5
  • Moderate Keep: Already mulliganed, at least one land and one creature

Analysis

The focus so far has simply been on how likely each deck can draw its best hands and keepable hands. Now I’d like to examine what this means when considering the new mulligan rule. This will focus on the exact cards the player has in hand, not considering how likely they can draw out of it or how powerful the hand is in comparison to other hands. I assume that this will have come out from my definition for keepable hands above.

Disclaimers:

  1. I’m not considering the Vancouver mulligan’s scry rule at all. This is only for simplicity and a later investigation could potentially consider them in concert. I’ve focused on only the cards in hand from the old Paris mulligan rule and will compare that with the new London rules.
  2. I am also going to assume that a seven card hand is of equivalent power to the same hand after two mulligans where a player must choose two to put on the bottom. I believe this is reasonable as my focus is on the keep-ability and initial power of a hand more so than its win rate.
  3. My mulligan rankings mostly focused on what a player is looking for on seven cards and not considering matchups or play/draw. These likely all have significant effects, but I’ll leave these up to the reader to consider.

First I display a comparison for how much mulliganing currently affects the keep-ability of a hand. We see a somewhat predictable result showing that Amulet and Tron are less likely to see a keepable hand as they are looking for specific cards and they simply get to see less of them. Burn and Golgari show that they are much more likely to find keepable hands on five and six, but this is less that they are finding strong hands and more that they’ll keep nearly anything playable after a mulligan.

Below this paragraph is what I consider to be the “money” chart. Given my aggressive mulligan strategies this shows a rough estimate for the increase in finding a keepable hand before mulliganing to four. The delta is completely centered around the keepabilty of 5 and 6 cards hands as the only change between Paris and London. My simulation estimates that Tron should see a 17 per cent increase in keepable hands while a tiny 0.75 per cent increase in keepable hands for Burn. This is quite close to what I would have expected before running the simulation and is an excellent sanity check for if the data is sound.

Conclusion

Now how can we use this going into MC London? As discussed at the top, the first is simply deck selection. The first takeaway is pretty straightforward and one that the community has more or less figured out already: decks looking for specific cards benefit from this rule change. Tron, Amulet, Dredge, etc gain from this rule.

On the flipside a deck like Burn gains basically nothing and also isn’t very good at interacting with the decks that do. Burn is a complete non starter for me, and I expect very little of it to show up. A more interesting case is Golgari and Thoughtseize decks in general. While they don’t gain much from the change itself, Thoughtseize has long given players fear of mulliganing by forcing them to live off the top of their deck rather than what’s in their starting hand. I believe Golgari could be a good choice for this tournament and if I were to choose to play it I’d be sure to include a pile of Thoughtseizes, Inquisitions and Duresses.

Lastly this shows us that a more aggressive mulligan strategy can pay off with the new rule, especially for a deck like Tron. This is especially true with the other change for the Modern portion of the event — public decklists. Players can feel confident mulliganing to hands that interact well with their opponent. This part of the rule change can also benefit answer decks like Golgari or even Azorious Control.

I hope you’ve found this article interesting, would love to hear from you if you liked what you saw or have any questions, so if you’d like to see more please let me know!

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