The Statistics of Magic the Gathering, part 2

Last time I talked about building your deck to have things to do: this time is mostly about having the right stuff to power those things.

Having the Right Mana

In talking about the mana curve last time, the focus was on having cards with the right total mana cost at the time you can cast them. The other part of this equation is making sure that you have the right kind of mana.

Land, and therefore mana, comes in five colours. There are some spells which don’t care what colour the mana used to cast them is (artifacts in particular), but most spells you cast require some component of the casting cost be in a specific one of those same five colours.

Broadly speaking, you want the proportions of your land base to match the proportions of different spell colours in your deck. For single colour decks this is quite easy, but multi-colour decks need a tiny bit of calculation as follows:

  1. count the number of mana symbols of each colour on your deck.
    • ignore cards which have no specific colours
    • count only casting costs (some cards have abilities which require mana, but they’re not relevant here)
    • some cards will have more than one of a colour, or multiple colours. Count all of these.
  2. add all the colour counts together to get your total specific mana requirement
  3. divide each colour count by the total to get the proportion of mana for each colour
  4. multiply each colour proportion by the number of land cards you plan to have in your deck to get the number of each you will need.

For example, I have an Temur deck (white/black/green) from a sealed draft I did which has the following proportions:

Red6 1/3831%5
Blue10 5/61142%7
Green5 5/6727%5

The fractional spells are ones which have more than one mana colour. For this deck these are:

  • Secret Plans costs one blue and one green
  • Snowhorn Rider costs one each of blue, red and green (plus another three colourless)

These land totals are suggestions rather than hard and fast rules. I especially find that a very small land count (if I’m splashing a colour) may need to be increased for it to be viable. Also, if the spells which need a particular colour are all late game then that count may be reduced.

Finally, there are a number of smart phone apps and web pages you can use to do the division and multiplication for you. I use MTG Mana Calculator on my Android phone, but a search for “mana calculator” will turn up lots of current results.

Fetching Mana

When I first started learning about Magic the Gathering I was very confused about these special cards called “fetch lands”. These are land cards, but they don’t yield mana. Instead, you sacrifice one of these cards, lose a point of life, and then get to search your library for a land card.

However, these cards do several things that are interesting:

  • they get you the land that you need, potentially at the exact time you need it
  • they shuffle your library (which if you’ve just been forced to put good cards to the bottom can help bring things back)
  • they increase your chances of drawing spell cards

It’s the last one that is most significant for competitive play, but how does it work?

Given a 60 card deck (and this is definitely a 60+ card deck technique – it is much less relevant in limited formats) you might have 24 land cards. Of these, let’s say eight are fetch lands. What happens when you draw one of those?

  1. your initial hand is three lands and four spells. What’s left in the deck is 21 lands and 32 spells. You have a 32/53 chance of drawing a spell – 60.38%
  2. your next draw is a fetch land. The chance of your next draw being a spell is now 32/52 – 61.54%
  3. you use the fetch land* and play out a new land card. Spell chance has now increased to 32/51 – 62.74%

So, drawing a fetch land even very early in the game can increase your spell draw chance by more than 2%. The swing is much bigger later in the game.

So that is why fetch lands cost so much, and why it was such a big deal that they were reprinted in the two latest play sets.

When To Hold And When To Fold

As I noted last time the heuristics for card type proportions in a deck are to increase the chances of an ideal initial draw: three land and four spells in a seven card hand. In most games, if you don’t get a playable draw, then you have the opportunity to take a mulligan: shuffle your hand back into your library, then take a hand of one fewer cards. So, if your first hand is bad you can mulligan down to six cards, then five if that is still bad, and so on.

But when should you consider taking a mulligan?

The basic heuristic is that if you don’t have anything in your hand that you can play then you should mulligan, but these are the likely scenarios:

  • not enough land – no land means a redraw.
    If your draw has just one or two land cards in it, then that’s likely to be a pretty easy mulligan also, although if the spells in your hand are all very cheap to cast it might still be playable. This is especially true if your deck trends very hard towards cheap cards (eg an aggro build).
  • not enough spells – if all you have is land, you need to redraw.
    If your opening hand has just one spell you should probably mulligan too, unless it’s good and cheap. Two spells… well, that’s tricky. Are they playable soon? Is one of them your win condition card? In those cases you could consider keeping, but this is where your experience will tell you what to do – experiment with different approaches in different games.
  • the wrong kind of mana – if all your drawn spells are red but you only have white mana, then you could think about a redraw because at that point there are no plays. There is a good chance you’ll draw into something you can play later, but the risk is that if your opponent has a fast deck you could be dead before the good draw happens.
  • bad mana curve – having talked about the mana curve of your deck, you also have a mana curve in your hand. Ideally, you would be looking for cards with mana costs that progress so you can play something on each turn. If all you have are huge beasties, that you can’t play until turn six, then consider a mulligan. You might also want to look at how many huge beasties you have in your deck.
  • no creatures – your hand has spells you can cast, but they are all removal spells. The obvious benefit here is that you can kill anything your opponent plays as they play it, but without creatures or direct damage spells, you can’t hurt your opponent. Probably time to mulligan.

If you six card hand is bad? Well, that’s unlucky – but generally it has to be much worse to consider mulliganing down to five. Starting with five or, even worse, four cards is a bad situation to be in, and if that happens you could have some deck design issues.

What’s Next

Once you’ve built your deck, you need to test it. Doing a couple of quick test hands on your own, drawing cards to see if the deck produces consistent results, is a good place to start and is the basic level of testing you should do for any draft. For my own purposes I also have a baseline draft deck that I play against decks I am trying out.

But play – learn how these guidelines work, and whether they work for you.

Enjoy the game!

[*] which can be done at any time, as it happens.

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