The London Mulligan – Legacy Edition!

Hello everyone! I know it’s been a bit since I’ve written an article, but such is the life of a student. The biggest development for Legacy over the past few weeks was the introduction of a new mulligan rule. The new rule, called the London Mulligan as it will be tested at the Mythic Championship in London, changes mulliganing in a big way.

Unlike the Vancouver mulligan, where you draw one less card for each successive mulligan, the London mulligan allows you to redraw a full seven! That’s right, seven! When you are done mulliganing, you return X cards from your hand to the bottom of your library, where X is the number of mulligans you took.

The power of the London mulligan is both in drawing seven cards and sculpting the hand you decide to keep. There is also the small fact that you’ve placed known cards on the bottom of your library, effectively increasing your chances of drawing cards you may want on future turns – barring any deck shuffling effects.

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Many folks have focused on the mathematics of drawing to an out card, such as Leyline of the Void, and combo pieces such as Tron. However, I haven’t seen any looking at the effect of the mulligans on the next three draw steps. In other words, how do the mulligans differ when drawing 3 more cards?

Inspired by Emma Handy’s article on the impact of the London Mulligan on Legacy, I decided to test two decks: B/R Reanimator and Dredge (Tron has already been extensively examined). I built a deck simulator in Python that produced 100,000 random hands from the selected deck. Each hand was inspected for the elements of the ‘perfect’ hand. If the hand held the perfect hand, it was assigned as a success.

This method was straightforward for the standard, opening seven cards. However, mulligans were a little trickier. Vancouver mulligans were handled normally, draw 7 – X cards, where X is the mulligan you are taking. As before, if the hand was ‘perfect’ it was assigned as a success. If not, then the simulation scryed 1 and drew 3 cards. If the new hand was ‘perfect’ it was assigned as a redraw success.

The London mulligan drew 7 each time. If a card was a part of the ‘perfect’ hand, it was labeled ‘keep’; otherwise, it was labeled as ‘pitch.’ Once the cards were sorted into ‘keep’ or ‘pitch’ piles, the simulation looked to see how many cards it could keep (7 – X, just like rules). If the ‘keep’ pile was smaller, it randomly added cards from the ‘pitch’ pile until it reached the 7 – X limit. If the ‘keep’ pile was larger, it removed cards with the highest frequency, i.e. most repeats, first, if no one was ahead, it randomly removed cards, until it was 7 – X in size. Finally, if the ‘keep’ pile was exactly 7 – X in size, it was kept, and if it was size 0 – no keeps – then 7 – X cards were randomly pulled from the ‘pitch’ pile.

As with the Vancouver mulligan, if the original draw held the ‘perfect’ hand, then it was assigned as a success. Otherwise, it went through the method described above and then drew 3 more cards. If the new hand held the perfect cards, then it was assigned as a redraw success.

Using Emma’s article as a start, here were the perfect hands for the two decks. Reanimator: any 1 fetch/black land source, 1 Chancellor of the Annex, 1 Faithless Looting, 1 Reanimate. Dredge: 1 Faithless Looting, 1 Lion’s Eye Diamond, and any 1 dredger.

Reanimator (First Draw)
Hand Vancouver London Increase % Increase
7
6
5
4
3.32
5.07
5.78
5.95
3.32
6.53
9.64
12.65
0.00
1.46
3.86
6.70
0.00
22.86
66.82
112.50
Reanimator (Successive Draws)
Draw Vancouver London Increase % Increase
0
1
2
3
3.32
6.3
10.8
13.7
3.33
8.00
15.40
22.10
0.00
1.70
4.60
8.40
0.00
26.06
41.99
61.55

Unsurprisingly, drawing the perfect hand in Reanimator has a very low success rate (around 3 percent) but each mulligan does increase the likelihood of drawing into it. The increase in odds is significant between the old and new mulligan rules. I used: ((London % – Vancouver %) / Vancouver %) to yield the percentage increase when using the new London mulligan while a straight increase was simply the absolute value of (old – new).

When looking at drawing your next 3, we see that the London mulligan rule also increases the likelihood of drawing your desired cards. This means more consistency for decks searching for combos, or answers – something we will talk about in a second. Now let’s look at Dredge.

Dredge (First Draw)
Hand Vancouver London Increase % Increase
7
6
5
4
10.53
16.73
20.27
21.78
10.53
19.96
28.39
35.93
0.00
3.23
8.12
14.15
0.00
19.28
40.05
64.94
Dredge (Successive Draws)
Draw Vancouver London Increase % Increase
0
1
2
3
10.53
11.80
21.00
27.70
10.53
13.0
24.2
34.0
0.00
1.20
3.20
6.30
0.00
9.90
15.36
22.74

Dredge fairs better when it comes to mulliganing, so that’s not a surprising result. We are also looking for fewer cards to combo off of, so increased rates of drawing the perfect hand are also unsurprising. Again, large increases in drawing occur at the second and third mulligans. For drawing three, we see smaller increases in drawing the ‘perfect’ hand.

Overall, we see a significant increase in not only hitting the desired hands for the London mulligan but an increase in the likelihood of drawing desired cards over the next three hands. But what does this all really mean?

The new rule means decks, all decks, will be more resilient, in theory leading to fewer ‘non-games.’ However, one of the drawbacks to ‘glass cannon’ decks was consistency issues. We are now increasing the likelihood that these decks will find their devastating starts more consistently which, ironically, leads to ‘non-games.’ Better have the FoW…

Here are a few other things about the rule – which will be implemented regardless of results in the Mythic Championship coming up…

One, for Standard and Limited, this probably isn’t too much of a concern. Mulligan away to find those fat bombs people! For Vintage, Legacy, and Modern, this is going to be a problem. Now, WotC could really care less about Vintage and Legacy, those formats don’t make them a lot of money. However, Modern keeps players, specifically newer players, involved in Magic longer; providing more cash flow into WotC’s coffers. Begin messing with the format too much – like a lot of bans because of the new rule – then it could hurt the format and, by extension, cash flow. I think bans will have to happen if this rule comes online as decks become more consistent.

Two, we will see an increase in mulligans. For Magic Online and Arena, mulligans are pretty painless and quick. In real life, shuffling cards takes time, and is pretty boring to watch. The new rule effectively allows your first two mulligans to almost equal keeping your original seven. There really isn’t any disincentive to pitching ‘medium hands’ when a mull to 6 or 5 doesn’t hurt like it used to… heck, even a mull to 4 isn’t looking too bad for certain decks. This means more folks may begin tuning out to ‘real’ Magic as it becomes a shuffle-fest. Remember when I said this helps combo and ‘finding answers’? Think about how many mulligans may occur as folks try to out-smart each other looking for answers.

Three, WotC decided this mulligan rule was too good before, why the change of heart? Tin foil hat me says WotC envisions an eventual change to paperless Magic, converting completely to Arena which is way ‘sexier’ than paper cards and helps Magic become the e-sport WotC wants it to be. The rule is fine for lower powered formats, like Standard and Limited, so as far as Arena is considered, it isn’t an issue.

Finally, this rule favors the pros. Pros are good because they can play the slight edges better than the rest of us. It’s what makes them great, and makes us watch them and how they find those obscure lines of play for ultimate payoffs. Giving them a rule that effectively allows them to sculpt opening hands and, well, it’s going to be entertaining to see them break this rule.

Overall, I’m not a fan. The math says it’s going to change how the game is played. It’s going to help push paper Magic out in favor of the slick MTG Arena animations and e-sport viability. It will help Standard and Limited, which will sell more cards. So, I guess, WotC wins on those two counts. Now, if they make it illegal for Vintage, Legacy and Modern, then I think you have something. If they keep it for Modern, well, enjoy your dumpster fire.

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