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By: stsung, Ren Stefanek
Sep 13 2016 12:00pm
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Deckbuilding is a tricky process and building mana bases is something that should not be overlooked. Without efficient mana bases we won't be able to reliably cast our spells on time and this can cause us to lose many games. That is the reason why I always wondered why many players simply neglect building a proper mana base. Often someone sends me a decklist for review. The first thing I usually notice is the lack of mana base. Sometimes there is a note like '24 land' but the actual lands are not listed. It always seemed strange to me. When I open my six booster packs at a sealed deck event the first thing I usually look at are lands. I look at them to see what color combinations I can play and what color I could possibly splash. The mana base is something that makes our decks work. If the mana base cannot provide the right amount and color of mana we need when we need, the deck will struggle no matter how many powerful cards it contains. A good mana base means that our deck will be more consistent and consistency is something we want to achieve.

From time to time I encounter a player who bought all the spells he needed but for some reason does not have the right mana base. If anyone comes to me and asks what cards he or she should buy first I always reply: 'mana base'. But no matter how often I say this some players just buy fetch lands (and dual lands) as the last cards. Once I asked my Modern Junk playing opponent why he did not run Verdant Catacombs and Marsh Flats in his deck. He told me that the cards are too expensive and that the deck works fine even with Wooded Foothills, Windswept Heath and Flooded Strand. After trying to imagine myself playing Liliana of the Veil or finding a basic Swamp with these lands I asked him how many matches per tournament he actually loses because he can't fetch for a black source (basic or not) or because he lost too much life because he had to shock himself. He told me that he usually loses 1 or 2 matches per 4 rounds. Since he was aware of his losses I asked him if this seems 'fine' for him and suggested that he at least plays Bloodstained Mire/Polluted Delta or changes his deck so his mana base can support the cards he plays. A week later he came to me asking for 4 Verdant Catacombs.

Never cheat on lands. Don't play less land nor substitution that does not actually work as substitution. There are different ways how to build a mana base and even if you don't have the budget for the ideal one you can come up with a different one that will still work even though less efficiently. Fetch lands are very powerful cards that fetch the lands we need and if they cannot do that it can be better not to play them. We can always optimize but without considering both spells and lands we won't achieve good results.

Unfortunately (or fortunately) a game of Magic is also a game of variance and we need to accept this fact. Sometimes even with proper mana base we will get mana or color screwed or mana flooded but that is simply the effect of variance.

In my early days of Magic I did not really need to care much about mana base. I usually just needed to figure out how many Islands and mana rocks I need in my deck. After I stopped playing mono blue though I started playing multicolored decks rather than other mono colored decks and I had to figure out how the mana base should look like. By some accident I came across guidelines from a certain player named George Baxter and I use his method still today. It was his method that allowed me to find ideal mana bases for my multicolored decks and resulted in me winning many tournaments. What I describe below is the way how I approach building a mana base that is based on Baxter's ideas described in Mastering Magic Cards: An Introduction to the Art of Masterful Deck Construction.

In order to build a good mana base we need to have enough land and enough colored sources.

Land count

All of us have some kind of land count associated with certain decks. For example a Standard Blitz/Swarm deck might want to play 18-19 lands, an aggro deck could do fine with 20-21 lands, aggro-control/midrange might do fine with 23-24, control with 26 and heavy control with 27-28 lands. These are starting land counts for Standard 60 card decks. In Standard the mana base does not usually allow for cutting lands and is usually more mana hungry than other formats. In Legacy a control deck can easily run 21-22 lands and I will explain why later.

In order to figure out what the right land count is we need to know what is a crucial turn for our deck. For example if you are playing a control deck and you need to be sure to play Wrath of God on turn 4 you should make sure to play enough land to be able to have 4 consecutive land drops. The percentage of drawing the last land on the crucial turn should be somewhere between 70-80 percent (I usually used 71-75 as the percentage I needed).

This is something we can find out using Hypergeometric Distribution. In order to find out the ideal land count we need to determine the chance of drawing 0, 1, 2, 3 land in 10 cards out of 60 card deck (10 cards simulating turn 4, since 7 cards is our turn 1 and we draw 3 additional cards). Add these up and subtract the total from 1. The probabilities are as follows.

If we look at the probabilities we will find out that 26-28 lands (in bold) is the number we are looking for. This number can be slightly different due to certain factors that I will talk about later.

Colored sources

When I have a land count in mind it is time to figure out how many colored sources I need. What I do is usually take my decklist and put it in a table. Next to it I write down colored mana needed to cast one spell. In the column next to it I add importance to each card and in the last column next to it I write down the total of colored sources. What I also need to do the calculation is number of cards in respective colors.

Assigning importance to the cards is important. It ranges from 1 to 3 with 3 being the most important. There is usually an ideal turn in which you want to cast certain cards. Based on the importance when to play certain spell I write down modifiers for the colored sources. For example if I need to cast Hymn to Tourach on turn 2 while playing Shardless BUG I would assign importance of 3. On the other hand I don't need to cast Jace, the Mind Sculptor on turn 4 and most of the time I do not need to cast it at all so the importance would be most probably 1.

Some cards require colored mana that is not in their casting cost (this applies to utility lands as well) so when writing what color the cards are I actually write down all the colored mana I need. Casting Tribal Flames in a Zoo deck requires at least 4 or 5 different basic land types to be efficient. That is the reason why the mana cost in my table would be marked as WURBG instead of just R. The same can be said about other alternative costs. For example if you play a certain card only for its flashback cost what you count is the colored part of the flashback cost (for example Unburial Rites fetched by Gifts Ungiven) requires W (or BW if you cast the card for both of its cost during the game). Force of Will does cost 3UU but often you cast it for alternative cost not 3UU so there is no need for additional blue sources because of Force of Will's cost. Lands that have activated ability costing colored mana should be listed as well.

Note: Utility lands that are put in a deck for their specific ability - for example Wasteland - rather than their mana producing ability should be counted as spells. These cards while being lands do not provide colored (or any) mana and thus can take up a spell slot rather than a land slot.

After doing this for all relevant spells I add up the importance modifier with the colored mana the spell requires and multiply all that by the number of cards. Then I take these values and divide them by the number of respective color cards exponent 0.5 (or square root).

Example. I have ten green cards in the deck and 31 colored sources. The calculation would be this: =31/(10^0.5) giving me the result of 9.803060747.

 

This will reveal the ratio of colored sources I need. From this point on I usually consider few more factors and make a list of lands I want to play. One needs to play with the deck a lot to find the ideal mana base but this system helps me create a mana base that works pretty well and only few small tweaks are needed. It's a kind of guess work but assigning the importance to colors you need and number of lands on specific turn helps to make the mana base efficient. For doing this properly you need to understand your deck and know how you want to play it. What I call 'importance' actually shows what is called the (mana) curve.

My table usually looks like this (see image below). There is one column with a list of lands that I want to play. The top row consists of colors the deck needs to play its cards. Then I just fill it in. I enter the number of how many times I want to play each land and check if the ratio checks or not (divide the ratio so you have numbers similar to 1, you will be getting usually numbers like 10/8/12 for example instead of 31/25/40 - I just took some random numbers). 1 Forest will have 1 under Green. 1 Bayou would have 1 under Green and 1 under Black. 1 Verdant Catacombs in Shardless BUG would have 1 in each of the colors since it can fetch all three relevant dual lands (Tropical Island, Bayou, Underground Sea).

In my BUG Delirium example if you want to have access to double black on turn 3 you need at least 16 black sources (70% chance of having them). If you get higher number of sources, that is fine. If you get less though it means there is a problem somewhere and you won't be consistently getting the colored mana you need. If this happens you need to reconsider your mana base and find different mix of lands that can get you to the right ratio and enough colored sources. If you get way higher numbers it means that you can even run some colorless utility lands that take up a land slot without a problem. Otherwise if you wish to play such a land you need to cut a spell slot instead. It also means that your deck can run couple of basic lands which can be relevant when mana denial is present in the format (talking about Legacy/Modern decks primarily).

In order to be able to do this you need to know which lands are legal and which can possibly be played and what their upsides or downsides are. There are lands that produce colorless mana, one type of mana, 2 (or 3) types of mana or and 5 types of mana. Utility lands usually have a cost and it is up to you to decide if that cost is too much for your deck or not. For example Horizon Canopy gives access to white and green mana and for tapping, sacrificing the card you can draw a card. Fast aggressive decks won't usually care that much about the life loss because they need to win fast. 'Cycling' the land can help them a lot though so the price is reasonable. Playing more copies of Horizon Canopy though might hurt too much and can result in a lost game (the cost is too high). The same can be said about Barbarian Ring. Usually aggressive red decks don't need to worry about losing 1 life per turn. Dealing two damage in midgame can mean a win though so the price is reasonable. In five-color you can have access to cards like Gemstone Mine. Some decks will operate better on this kind of lands if they need specific colored mana fast and don't need much of it (combo decks). But other decks will operate better on fetchlands and shocklands. All of this needs to be considered.

Variables

So what are the factors I mentioned earlier? There are factors that can change the number of lands in your deck. For example if you play acceleration spells like Birds of Paradise or Rampant Growth. These cards usually lower the land count by 0.2 - 0.25 per such a card (depending on how fragile the card is. For example Birds of Paradise is more fragile than Rampant Growth - it dies to removal).

A deck running cantrips can also play less land. Some cards allow us to see more cards from our decks and thus give us the possibility to find land cards more easily. In that case we can also usually cut a land per 4 cantrips.

The same way as I look at the importance of having the colors I need on turn X I also look when I need untapped lands. This is something many of us will subconsciously understand to some extent. Fast aggressive decks should not play CIPT lands since these will just make the deck lose tempo. Control decks though can have a certain amount of CIPT lands but not too many (four Celestial Colonnades is nice, but if you have other CIPT lands 4 might not be the right number). Especially if such a land can become a win condition. The thing to consider though is this. If I want to play my Supreme Verdict on turn 4 I need white producing lands to come untapped. That is the reason why my Solar Flare wasn't really running too many Seachrome Coast but rather Glacial Fortress. I always needed blue so there wasn't a problem this land would come tapped into play. Seachrome Coast on the other hand would always come into play tapped on turn 4. Since this deck also ran Liliana of the Veil and wanted to play it on turn 3 it needed black sources to come untapped. For that reason I played Darkslick Shores so I would have higher probability of getting BB on turn 3 to play Liliana of the Veil. For this same reason aggressive GR decks played 4 Copperline Gorge in addition to few shocklands. This allowed these decks to have their sources untapped during the crucial turns when they need access to both colors and mana while saving life. The number of comes into play tapped lands is also something to ponder about. Playing too many CIPT lands can make you lose tempo since you need to virtually invest 1 mana for them so finding the balance between CIPT and CIP lands is crucial (this also requires us to sequence our lands correctly - see my article Show and Tell: Lands).

The choice of specific lands and their count can also depend on mana denial present in the format. Either be it Blood Moon making our dual lands worthless Mountains or Wasteland/Strip Mine destroying just one but needed land (in terms of color). In these cases running some basics so we can fetch them help. The number of basics should correspond the mana our crucial cards need. For example (Modern) Jund needs Liliana of the Veil in order to function properly. This deck will most likely play 2 Swamp but will only need 1 Forest since there is no important card requiring GG. Note that running basics can make the land count higher since it makes the mana base less efficient in terms of color (and also speed). Some decks though require too efficient mana base that they cannot run basic lands (Legacy 4c Delver for example).

If you don't want to create a workaround by playing Legacy 42Lands.dec, just do your homework and count your mana sources properly. Who knows, maybe that 4th Mutavault in a Merfolk deck is overkill!

4 Comments

Lots of numbers heavy advice. by Paul Leicht at Tue, 09/13/2016 - 14:31
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Lots of numbers heavy advice. Lots to chew on. Interesting article, thanks. :)

Thx for reading and the by stsung at Wed, 09/14/2016 - 05:12
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Thx for reading and the comment. I actually tried to avoid maths as much as I could. Magic is a game of variance and such has to be accepted. This variance is something we can influence to some extent. Deckbuilding is one of the ways how to do that. To achieve the best results we need to assess how much a certain situation is probable and use this knowledge to our advantage both while deckbuilding and playing. Those that are good at understanding how probability works, and understand zero-sum and non-zero sum games will be able to meet what people call 'luck' with more success.

Even though I have degree in Fine Arts I was always digital and analytical person. What I do not see in numbers I do not really understand much, or I do, but I cannot interpret it. That is the reason why I was reluctant to write this article. This is how I approach Magic. It is a topic I never really talked about with other players. Game theory and probability is what I see. But I do not know how common this approach is. To me it seems to be the only one. On the other hand I realized that not all players see a great decision tree while playing but rather decide based on intuition. I decide based on free information, hidden information and probabilities involved and whether my opponent is wont to bluff or not etc. I analyse. But my flatmate who happens to be also a Magic player plays intuitively. I couldn't understand how such a person can play a game that is rigorously mathematical well without actually using maths to assess the game. But I can clearly see that he can play well and understands the game. I can also see that he does not understand the struggles I face when playing with a deck. So it is possible that you are in the same camp as my flatmate. There's nothing wrong with that. Knowing this I tried to avoid maths as much as possible.

I learned this when trying to play Shops. My flatmate usually plays some kind of MUD staxx deck while I'm more of the blue player and would never touch Shops. We switched decks and we were both quite lost. I ended up with Shops deck in my hands having no clue what the deck can do. But I saw the cards in my hand and I knew what the cards do. But what is the right play now, what is the right strategy? I wondered about several scenarios trying to figure out if playing Lodestone Golem first is better than playing Thorn of Amethyst and then playing the Golem. This is an easy decision and scenario considering it is turn 1 but what I saw where too many possibilities that could lead to different situations even though all I had available and thought about was my seven cards. I knew what the game looks like from the blue deck's perspective and decided based on that at first. We both came to the conclusion what the optimal play is at certain point in a game but we arrived to that conclusion in a very different fashion.

I am not in the same camp as by Paul Leicht at Wed, 09/14/2016 - 15:24
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I am not in the same camp as your room mate. I am somewhere in between. I use both math and intuition. Perhaps not the heavily analyzed math you refer to but it is definitely in there.

Interesting you bring up shops as that is a very easy to grok deck for me. Well at least some versions of it. The problem is it tends towards an aggro strategy which I usually abhor. Though I like the prison aspects, it is generally not that much fun imho to play against so I never bring those kind of decks to casual play (because not fun and super efficient. I don't mind bringing slow to develop prisons because they are hard to play.) Not that there are a lot of Vintage players, playing casually these days.

In my humble opinion, not while playing but just brewing and relaxing is the best time to crack open the insides of how things work and really apply the hard math so I approve of your choice though I am no fan of Baxter (purely from an opposition to some his shadier text.) Figuring out exactly what mana is required and how to deliver it seems like the perfect place for a by the numbers approach.

My own problems with magic arise from being an entirely impatient person.

I still have my copy of that by Procrastination at Wed, 09/14/2016 - 09:07
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I still have my copy of that book! So many old notebooks were filled with deck lists using that pocket structure. It completely changed how the players in my high school built decks (60 cards main, not 80+) and was clearly a "level up" point for us as players.

I discussed how I plan out mana bases in my Brain in a Jar article. It starts out in a similar fashion, but you add in some additional steps that provide more data to pull from. I was curious how others went about it, so this article was a useful read!

Don't worry about whether an article seems too math heavy our not. Like you said, different folks approach Magic in different ways. If you are inspired to write it, then your passion for the subject might "sell it" even to folks that normally don't think about the math aspects of the game. If a single player stops to consider this article and then goes on to improve their game, I would call that a win.