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MTG Arena’s Opening Hand Algorithm and Smoothing – Some Real Outcomes

sphinx-of-foresight-art

Introduction

According to a research paper published by Cornell University, Magic is the most complex game ever known. In fact, the authors argue, it’s so complex that you could even use the game to emulate a Turing Machine. A Turing Machine is a mathematical model capable of simulating complex computer algorithms. This is a pretty big deal, or at least so my friend with a math PhD tells me. For us Magic players though, this complexity is very old news. We’re accustomed to expanding our understanding to include new rules, keeping in mind obscure old ones (quick, explain Banding in 30 seconds or less!), and endless errata. One recent example is Ajani’s Pridemate. Until 2019 Pridemate’s +1/+1 ability was optional, then the card changed and it became automatic. We adjust, we build, then we readjust when the next set drops (or sooner with Banned and Restricted announcements). Increasing complexity has been the story of the last 25+ years in a nutshell.

What players are not used to is having these processes happen behind the scenes. While MTGO has been digitally shuffling and coin flipping for almost two decades, Arena has introduced something new which seems to be creating some confusion. I’m speaking of course of Hand Smoothing (or just Smoothing) in best-of-one (BO1).

In this article I’ll provide some background about Smoothing and explain what it means as best I can with the information available from Wizards. Then I’ll demonstrate Smoothing’s effect with some data from Arena and give some examples of how to apply the information in practice.

BO1 matches are the most popular format on Arena. It’s a quick format that WotC has positioned prominently in the game GUI. As a result, understanding how Smoothing impacts gameplay is as important as understanding the cards, knowing when to mulligan, or adjusting to being on the play or draw.

To say Smoothing is misunderstood or controversial may be understating the case. It is never mentioned within the game, so many Arena players are completely unaware it exists. Some players are skeptical of its existence or effect. A small but occasionally vocal section of the population lament that it’s out to get them. The wise players not only know that Smoothing is real, they also build their BO1 decks in a fashion that exploits it. What makes the best Magic players the best is that they understand and exploit the rules better than their opponents.

What is Smoothing?

What is Smoothing though? In a typical game of Magic, you draw a random hand of seven cards from the top of your deck; this may be the oldest rule in Magic. In paper Magic we do this with physical decks but in MTGO, this is done digitally using a random number generator. Arena works the same way as MTGO, with a random number generator creating a random hand for you. However, starting in October of 2018 (not long after the launch of the open beta period), Smoothing was introduced to BO1 matches.

Smoothing was first announced on the Arena forums (https://forums.mtgarena.com/forums/threads/347) with the gist of it being:

This post resulted in a lot of guessing, questioning and hypothesizing. And a lot of math. Eventually, a follow-up was posted in May of 2019 (https://forums.mtgarena.com/forums/threads/26319?page=1). This followup said that most of the hypothesizing was wrong; a few highlights include putting emphasis on WotC’s use of “leans toward”. What that distinction means is anyone’s guess, as Wizards seems set on not divulging any more than they already have.

So we have no official explanation on the details of what this means. The basic understanding of what it is believed to mean is that if the average land count in an opening draw for your deck is 3 lands, and it pulls one hand with 4 lands and one with 3, the game will “lean towards” showing you, the player, only the hand with 3 lands. All of this happens in the background with no visibility to the player. That right there is where people start to get a little off the rails about Smoothing.

An invisible mulligan where we don’t get any input? Is this real? Is it out to get me? We can throw statistical calculations around all day (though I won’t in this case), but what’s the real impact?

The Experiment

opening-hand
Three lands are exactly what we wanted here…

I was pretty confident from my own experience playing paper Magic versus playing BO1 that Smoothing was real and what its effect probably was. A big indicator is that in paper Magic no-land hands happen pretty regularly. You draw, you grumble, then you mulligan and move on with your life. Since MTGO and Arena use random number generators to simulate that experience, no-land draws should be similarly common in Arena BO1, but in my time playing Arena I can only recall coming across such a hand once and it really stood out at the time. For a no-land hand to happen with Smoothing, both hands drawn by the algorithm would have to be no-land, a very unusual occurrence, so my anecdotal experience fits the understanding. But anecdotes aren’t evidence, they’re just stories about an experience.

To address these questions about Smoothing more concretely, I decided to collect some data. Others have run the numbers to give percentages and odds. With the veil WotC has pulled across Smoothing, I wanted to collect what the real outcomes look like. I took a 24 land deck and used it in Play, Standard Play and Ranked Play formats to see what my land counts were over a large number of hands. While we have no reason to believe that Smoothing is different for Ranked versus Play, they could be. As a control, I did the same thing with a paper deck for the sake of comparison.

One thing in the original post by Wizards about Smoothing that didn’t seem right is that it applies only to your opening hand draw and doesn’t apply to any Mulligans. So I mulliganed each Arena hand down to zero and tracked those numbers as well.

Finally, I decided to use a data set size of 104 hands. I settled on 104 because 7 mulligans in Arena gives you 8 hands to look at. Do that 13 times to get past 100 hands and you have a total of 104 hands. According to Hasbro’s recent Q4 earnings call, the average player spends 8 hours a week playing Arena. Based on my own experience, 6 games per hour is about average when playing a mix of deck styles. So 104 hands is about 17 hours of play, which is about 2 weeks of play for the average Arena player.

With the paper deck, I found that I averaged 2.78 lands per hand, which is about what you would expect from a 24 land deck. Then in Arena Bo3 104 hands averaged 2.70 lands, while Area Play B01 averaged 2.76 lands per hand. Finally, Ranked Play averaged 2.75 lands per hand. That’s a pretty consistent result between all four data sets considering the sample size. This was an expected outcome. Smoothing doesn’t change the average number of lands you would draw over a large sample size. The point of Smoothing is to reduce the individual hand extremes. Two hands with 3 lands a piece has the same average land count as one hand with 0 land and one hand with 6 land. The important difference in those two small groups is the difference in playability.

What will show the impact of Smoothing is how often we had any given number of lands per hand, from 0-7, and how many hands are keepable. While keepability for a given hand varies by deck type and other cards in hand, for a 24 land deck we’ll say that a keepable amount of lands per hand is in the 2-4 land range. How many of the individual hands were keepable based on number of lands then?

Paper Shuffling

With the paper deck, the distribution was about what you expect. The 6 and 7 land hands are a little bit high, but variance is part of data collection and they still accounted for less than 3% of draws. Based on our criteria, 26 of 104 hands were unkeepable.

# Lands# Starting Hands
71
62
56
419
334
225
112
05

MTG Arena Traditional Standard Play (BO3)

For Bo3 on Arena, the distribution broke out as you see below, with almost 20% of the draws having 0, 1, 5, 6, or 7 lands in the opening hand. That compares pretty close to what we got with the paper deck. That means we are considering a mulligan 20% of the time before we look at anything other than land. Even if you say that 5 lands is okay, 15% of hands are still not meeting the land draw criteria and only one third of hands are hitting the 3 land mark, which is arguably the ideal.

# Lands# Starting Hands
70
60
55
421
333
230
113
02

MTG Arena Play (BO1)

For Bo1 on Arena Play though, there was only one hand with a land count of 0, 1, 5, 6, or 7 lands. The land count was very consistent, with a whopping 60% of hands having an ‘ideal’ 3 lands. That’s almost double what we got in paper and Bo3.

# Lands# Starting Hands
70
60
50
410
360
233
11
00

MTG Arena Standard Ranked (BO1)

Arena Ranked Play was also incredibly consistent with only one hand having 0, 1, 5, 6, or 7 lands. Meanwhile 54 hands had 3 lands. The sample size is fairly small, but from these data sets it’s pretty clear that Smoothing has a real effect on opening hand consistency.

# Lands# Starting Hands
70
60
50
412
354
238
11
00

One important detail is that WotC’s second part of the Smoothing release was that it does not apply to Mulligans. This statement does not hold up under the collected data. The variation between the number of lands in the opening draw versus the Mulligans was minor. So not only is Smoothing definitely happening in Bo1, it happens every time you Mulligan.

What does this mean?

goblin-chainwhirler-art
One of the icons in Mono Red Aggro in 2019.

What does Smoothing mean for us as players? On the surface, Smoothing may seem like something designed to make things easier for weaker players. Smoothing does reduce the very un-fun aspect of getting lands with too many or too few lands to be playable. Exploiting Smoothing adds a layer of complexity to the game, and complexity always favors the good players over the weaker ones. Good players understand how this element of the game works. Once they understand it, they use it to their advantage in ways that less experienced players won’t understand.

When it comes time to build decks, whether you will play in Bo1 or Bo3 should be considered due to Smoothing. All deck types benefit to some degree with more consistent mana in the opening hand, from aggro to control. That said, some types will benefit a bit more.

In general, decks with three colors will benefit more than mono-colored decks. Compared to Bo3, they are more likely to have playable hands with a broad enough mana base to play all their spells. A strength of playing mono is that they have very stable mana bases, so the benefit there is less. Having a 60-70% chance of getting 3 or 4 lands in your opening hand and a less than 5% chance of having to mulligan due to 1, 5, 6, or 7 lands makes tri-color decks more consistent. It also makes them more comfortable mulliganing with a sub-optimal hand.

Among archetypes, Smoothing probably most benefits aggro decks. Many aggro decks run lighter on land. Smoothing facilitates that by giving players a better chance at a playable hand when running lighter on land. The consequence is being able to fit more threats into the deck mix.

Combo decks can also benefit a great deal from hand smoothing. Many combo decks, such as the current cat decks or even Reclamation decks, lean towards having at least one part of their main combos in their opening hand. Smoothing doesn’t effect that directly, but it does enable taking a mulligan with more confidence so the player can take another shot at finding that key card.

Ramp decks have a mixed bag with Smoothing. While Ramp likes having more consistent land in the opening hand, part of their strength is being more consistent due to their ramp effects. Ramp builders may want to build with fewer ramp effects when working in Bo1, and keep in mind that opponents won’t have the consistency problems they do in Bo3. Testing with Smoothing in mind is critical to find the right mix.

One specific deck that has benefitted a lot is Mono Red Aggro, also called RDW (red deck wins). RDW is one of the strongest decks in the meta in general right now, including strong deck selection at Worlds. RDW often runs light on lands, with only 20 lands in many best of 3 builds this is the deck’s biggest weakness. Having that weakness all but eliminated takes the deck up a notch. Personally, I took this a step further in my use of RDW earlier this season. I dropped down to 18 lands and replaced the two cut lands with low casting cost spells. While this would be foolish in Bo3, the deck had a 65% win rate in Bo1. The far more consistent mana base is huge in the high rate of RDW in Bo1.

Control decks probably get the short end of the stick on Smoothing. While all decks enjoy having more stable mana, classic Control may benefit less. Smoothing isn’t bad for Control, but it makes other archetypes consistent enough that Control has fewer openings in the Bo1 format.

It shouldn’t be a surprise that the decks mentioned are what we see a lot of in Bo1. Ramp, three color decks, and especially RDW make up a huge slice of the Bo1 metagame. Control is still present, but definitely seems less strong than in Bo3. How much of this is conscious and how much is incidental is difficult to say.

Conclusion

In conclusion, Smoothing is real in Best of One. Perhaps more important, Smoothing applies to mulligans, contrary to the statements by WotC. That doesn’t mean the improbable won’t happen. Crazy hands will always happen, but it will happen less often than in Bo3. Smoothing stabilizes your mana base and gives you a better chance at a playable mulligan if you don’t love your first draw. The question for each Bo1 player is: Now that you know Smoothing is real, how are you going to take advantage of it?

The impact of Smoothing on Best of One is not something that can be covered completely in one article. This is just one in a series of articles by MTGAZone covering the unique aspects of Bo1, from deck design and metagame analysis to Hand Smoothing and mulligans. As our understanding of the effects of Smoothing expands we’ll publish more pieces on tuning each archetype to best operate in Bo1. As always MTGAZone is committed to providing readers with the best information possible to master the format.

Red5ive

Red5ive

Brendan Dillon is an old school mono-artifact dude with a penchant for overthinking the little things.

22 Responses

  1. Paweł Piątkiewicz says:

    Great article. Very informative. I’m really looking forward to more Bo1 content. Really appreciate what you’re doing.

  2. Pedro Gonçalo Roque Correia says:

    Really good article…
    As a MTG player for decades i have to say that this smoothing thing ruins the game….
    But that is just my opinion…
    You cannot state that the average number of lands being the same or almost the same is enough to proof all is right…

    One simple example..
    Gilded Goose green cards with only one mana cost…

    Due to this mechanism. and i already complained several times about it… It is almost impossible and extremely rare to have it in my opening hand… And i have 4 times the card in a 60 cards deck.

    Although the full deck does not depend on this cards, it is a very important source of extra mana and extra life…
    If the engine is already putting you this handicap it removes the pleasure of the random behavior by playing the game…

    In my opinion it does not improve the game..
    Just brings additional frustration.

    • GlosuuLang GlosuuLang says:

      Just play Bo3 and forget about smoothing

    • Red5ive Red5ive says:

      In general, whether we like it or not, it’s here and we need to account for it. My own feelings are pretty mixed. I understand it as a business choice, but I don’t approve of it not being mentioned at all in-game. Players need to understand the difference in formats.
      That said, I’m curious about your Gilded Goose comment. Can you tell me a little more of what you have experienced?

    • Blazz says:

      “It is almost impossible and extremely rare to have it in my opening hand”
      Then why when I play, my opponent ALWAYS HAS GILDED GOOSE in their starting hand if they are playing it?

      Why when I play it, it’s frequently in my starting hand???

    • Aaron Hahn says:

      Decades means 20+ years. Arena has existed for less than 3. Even MTGO is only 18 years old. So that’s wrong. Second, smoothing has almost no effect on drawing or not drawing any non-land card–it only brings your land count closer to the middle. And, as someone below says, it is in no way almost impossible–when I play it, I have it in hand about 40% of the time, exactly what it should should be based on states (hypergeometric calculation). The only reason smoothing would effect this is if you are playing an especially low land count (don’t know the exact number, but I would bet it’s less than 20), then you’d have a slightly lower chance to draw any given non-land card vs. paper since you’d expect slightly more lands in Arena. Why do you think smoothing effects which non-land cards you draw?

  3. Hoid says:

    Thoughts about exploiting smoothing:

    1. The algorithm seems to not differentiate between basic/non-basic lands. Maybe smoothing can be tricked by playing non-basic lands with potential board value like [Mobilized District], or which thin out the deck like [Fabled Passage].

    2. How about playing fewer lands, but instead more “valuable” ones like [Lotus Field]? Or fewer lands, but adding ramp artifacts like [Chromatic Lantern] or [Heraldic Banner]?

    3. Perhaps [Elvish Reclaimer] is better due to smoothing.

  4. Steven Stadnicki says:

    Good data, though the sample size is still a little small; it would be great to see a mathematical analysis of the presumed ‘closest to the expectation’ smoothing to show how closely the distribution of smoothed hands in practice hews to what would be expected if that is specifically what’s happening.

  5. Marc Klein says:

    The fact is that if it is truly random, knowing each hand and picking them manually is not relevant. I prefer playing with no all land or no land hands, but the rest of the shuffler issue regarding always clumping cards etc is where I have issue.

    • redblacktree says:

      Can you explain what you mean re: “always clumping cards?”

      • CdBobo says:

        The likelihood of drawing the same card is astronomically high in MTG arena. If you have 4 copies of a card, getting an opening hand with 3 of them is not uncommon in a 60 card deck, while in paper format almost never happens.

        • Chris Monaco Santana says:

          Man I’m glad I’m not the only one that noticed this. It always seems to happen when I’m screwed. I continue to draw copies of cards I already have in hand smh

  6. David says:

    “One important detail is that WotC’s second part of the Smoothing release was that it does not apply to Mulligans. This statement does not hold up under the collected data. The variation between the number of lands in the opening draw versus the Mulligans was minor. So not only is Smoothing definitely happening in Bo1, it happens every time you Mulligan.”

    I theorize that ‘mulligan smoothing’ changed when the London Mulligan was introduced in mid-2019. It’s likely that smoothing did not apply to mulligans when the Vancouver Mulligan was in effect; but when the London Mulligan was introduced, they use the same code for both opening hands and mulligans, and therefore the smoothing applies to mulligans as well, and they never thought to disclose the change in how mulligans work.

  7. Tim Richmond says:

    Smoothing has an effect on play, but nowhere near as much as the matchmaking algorithm.

    I’m not sure if you have noticed, but if you win 10 games in a row, you will be put up against impossibly perfect players with God Hands.

    • Dominic says:

      I agree with your statement. There’s also another BS that happens if a deck goes over 70% w/l ratio, you end up with no mana being drawn or only mana being drawn. Another thing that annoys me is the number of hands where you get all 4 copies of the same spell and keep drawing another series of 4.

  8. the equivalent of smoothing in paper magic would be to draw 2 7 card hands and choose which you like then shuffle the other back into your deck. Granted, arena removes the choice between the 2 hands.

    If this rule were implemented in any paper format people would absolutely hate it, as it would give certain archetypes a distinct advantage, kind of like you described in regards to RDW on BO1.

    PS – every time the ad changes on your site it shifts the page in my browser and forces me to stop typing or need to scroll to find where i was reading. it is very detrimental to the quality of your website.

  9. Beren says:

    You have done very good research. Unfortunately, however, he went the wrong way.
    The amount of mana in the starting hand is not the Arena’s problem.
    You would have noticed it if you played Arena a lot, especially Drafts (a limited format that makes the Arena software problem much more visible and unavoidable).
    But it became very evident in one of the World Championship semi-final duels (Marcio Carvalho x Seth).
    The problem is that the cards do not arrive so randomly, especially during duels. Sometimes only 1 color of terrain comes. At other times there seems to be no other cards in the deck besides lands, even though you have less land than normal.
    It is true that they do not always occur. But it occurs quite often. Standard manages to make them up a little due to the large number of options to solve them, however they still occur.
    Please watch the duel I mentioned (seth x marco, I don’t remember which battles) and you will understand better the feeling of all the people who play Arena.

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