Tag: magic

Testing Magic

So, you’ve built a deck (perhaps following some of the previous statistical guidance). How do you know if it’s any good?

This post is about testing to see if the deck you’ve built behaves consistently, and whether it’s actually competitive. It’s basically expanding on the closing points I glossed over in the second Magical statistics post.

Draw Testing

The first thing to do is to shuffle and draw a hand to see if you got the land proportions right.

  1. shuffle
  2. draw seven cards
  3. is the hand playable? If not, then mulligan: back to step 1, but draw one fewer cards this time.
  4. If you have a playable hand, then play it – put down a land for your first turn, then draw and play another land and a spell, and so on. Imagine how your opponent would respond; imagine the results from your actions.

The goal here is to get a playable hand in the first draw or the first mulligan, and then to continue to have land to cast spells and things to do each turn. If it regularly takes more than one mulligan to get to a playable state (and winning from an opening five card hard is way more difficult), or if you are regularly left with nothing to do on a turn, then you should look at the reasons for the unplayability and adjust things in the deck:

  • too much land, not enough land, or the wrong colour mix: look again at the number of land cards. If this is too hard to get right, then maybe that five colour deck is just not going to work out.
  • too many expensive spells: look again at the mana curve for your deck.
  • not enough creatures: look again at the mix of creatures to non-creature spells

Pilot Testing

Once you have a deck that consistently makes playable hands and draw sequences, you should try playing it against other decks.

If you’re building a limited deck at a draft event of some kind, that testing will be done against other players and the decks they build in the course of the event.

However, if you’re building at home for later play, then you’ll want to play the deck against another baseline deck or two to see how it fares.

  1. clear a space large enough to layout two board positions close to each other.
  2. roll to see whether left or right goes first.
  3. lay out the cards as you would normally, but if they’re side by side then I would recommend mirroring the two.
  4. play each hand in turn. Stick to the normal phases of play* on each turn. This isn’t just good practice, it will also help you to not forget anything – the phases are a checklist for each player’s turn.
  5. keep notes of how the test hand performs.
  6. make adjustments if appropriate or possible.
  7. test again.
  8. and again. Normal matches are best of three, so you want to run each iteration of a deck against the baseline at least three times.

Tips:

  • use all the paraphernalia you would use in a normal game: life dice, tokens, and counters – the more authentic you can make it, the more thorough the test is.
  • try to play each hand based only on what that player can see. Try to ignore the knowledge you have of the other player’s hand.
  • if you have trouble separating the two in your mind, try putting the different board positions on opposite sides of a table so that you have to get up and move to the other side in order to play the other hand when the turn changes. This physical change can reset things and help with mental separation.
  • if there’s an instant response which one player would likely make, leave a marker visible which will remind you to glance at the other hand at the proper time.
  • don’t be afraid to go back and fix something if you made a mistake playing one hand because you forgot something the other player would have done, but only do this retconning for situations where there is a response the defensive player would have made based on the information at hand rather than because you’re rooting for one side or the other.
  • be honest, and be brutal. Your opponents won’t cut you any slack because it’s a new deck, so don’t soft-pedal your baseline deck to give the other deck a chance.

Or, of course, get a friend to play against you instead.

Different Tests for Different Contexts

So far, I’ve only really played limited formats with (what should usually be) 40 card decks. In that context, I have kept my first limited deck intact as a baseline deck: it plays fairly consistently, it has multiple win conditions, and it has actually won quite frequently during my play tests**. What I’ve been testing are different clan decks*** drawn from a sealed pool.

If you’re playing a constructed format (whatever the deck size) you should consider pulling together archetypal builds for test purposes. These are the kinds of decks you will encounter at competitive events, so if you new deck can’t beat them then you need to rethink.

… and by “pull together” I don’t necessarily mean buy all the cards for those builds, but rather find a deck list and print out proxy copies of the cards. Unless, of course, you like those decks and want to start playing with them.

For the Modern format, Red Deck Wins or Mono Blue Tron seem representative. If you’re playing Standard then this budget Mono Red deck will be a good test bed. Those are all Tolarian Community College videos because I find the Professor’s presentations easy to understand.

Good luck with your decks, and may the statistics be supportive of your plan.

[*] untap, upkeep, draw, main, combat, second main, end of turn, cleanup.

[**] originally it was a 60 card deck which consisted of all my relevant picks from the booster draft, but that was a mistake. Trimming it to 40 made it good. If that’s not a metaphor for the value of editing, then I don’t know what is.

[***] these being the clans of Tarkir, the current play set as of this writing.

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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:

ColourSpellsMana%ageLand
Red6 1/3831%5
Blue10 5/61142%7
Green5 5/6727%5
Total:232610017

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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The Statistics of Magic the Gathering, part 1

There are lots of cool things about playing Magic the Gathering: putting together a board state where you deliver six points of unblockable damage every turn; pulling off a nifty inversion of control that forces an opponent’s most valuable creature to block your tiny little death touch attacker; or fighting your way back from a huge deficit to claim victory over a formerly smug foe.

Oh, it can be an awfully satisfying game.

But that is playing the game with the cards you find in your hand. Designing decks is where you try to make sure that the right cards end up in your hand when you need them, and a great deal of the basic techniques of deck design are based on statistical principles.

These notes are aimed at relatively inexperienced deck builders with questions about why some of the guidelines for deck construction exist. I would be lying if I did not say that I am also writing these down here for my own reference.

Having Mana

Casting spells costs mana, and to get mana you have to have land on the table. Ideally, you want to be playing down one land card every turn for the first few turns at least.

Standard deck-building guidelines are that you should have 16-17 land cards in a 40 card deck, and 22-24 land in a 60 card deck. In each case this proportion is about 40%.

The reasoning for this is simple: on your first draw you will take seven cards to make your opening hand. This hand wants to have 3-4 spells and the rest land, just so you can have things to do early in the game. Three out of seven cards being land is a little more than 40%, so to have a fair chance of drawing the desirable amount of land you need that proportion of land in your deck.

The Bend of the Mana Curve

Above I mentioned “having things to do”. This is what the mana curve is about.

Having land is great, but not very useful if you have no spells to cast. On average, with 40% land in the deck providing the mana, the other 60% should be spell cards which use that mana. So, you would expect to draw a spell every other turn or so*.

The trick is to make it so that you stand a fair chance of having spells to cast when you have the mana to cast them. Since you can put down one land card per turn you would expect to have one mana on the first turn, two on the second, and so on. Hence, you would hope to have a one mana cost card to play on the first, a two mana cost card to play on the second, etc (“mana cost” here is the total amount of mana to cast a spell, regardless of colour – this is often termed Converted Mana Cost or CMC).

This is where the mana curve comes. The mana curve for your deck is the number of cards playable at each mana cost. In particular, you want to have cards in your deck which will allow you to play early spells if they come up, but to raise your chances of having a strong card you can actually cast on the third or fourth turn**.

Let’s take a 40 card deck, the standard size for a draft deck, and consider a reasonable distribution of card casting costs. For this deck size the total spell card count of is likely to be around 23 while the number of creatures is going to be about 18, distributed thus:

  • 1 mana – 1-2 cards
  • 2 mana – 2-3 cards
  • 3 mana – 3-4 cards
  • 4 mana – 4-5 cards
  • 5 mana – 2-3 cards
  • 6+ mana – 1-2 cards

So if 40% of your cards are creatures, and more than half of those are going to be castable on turn 4 (assuming your land draws behave themselves), then the chances are very strong that that you’ll have things to do in the first few turns. Similarly, there are only a handful of cards that are very expensive because otherwise you run the risk of getting stuck with too much uncastable stuff in your hand.

When to Break The Mana Curve

The most common build for a deck has this kind of skewed bell curve distribution where there are a lot of medium weight spells and not much on the high or low end, but some build strategies will lead you to make different choices:

  • aggro – this is a fast deck where the goal is throw out lots of little guys fast that can attack your opponent early before any of his creatures are even our to defend. In that case, you’d end up with a lot of low end cards that can be cast in the early turns, but you never ramp up to larger stuff.
  • tribal – in these strategies, there are lots of creatures of a similar type. Elves, for example, or goblins – perhaps even squirrels. In this case the goal is to have creatures and other spells which have synergies, such as effects like “all warriors gain first strike” or “all slivers have flying”.
  • control – the goal with these kinds of decks is to delay the game until you can play a big creature which stomps your opponent. Here the creature base is going to skew big, but there would be a lot of smaller spells for removal and countering.

These strategies are all valid, but usually in a constructed deck rather than a draft simply because of the limited pool of cards available to you.

That’s the first part of this series on the statistics of Magic the Gathering. The second part will be along next week.

[*] the law of averages doesn’t exist, but regression to the mean does.

[**] third or fourth turn is important because many decks don’t really start being aggressive until this point.

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Gathering Magic

Recently, I’ve been learning about Magic the Gathering.

I didn’t play Magic when it first came out because I was in a fearfully serious phase of my life – this was when I was putting all my energy into work, and when I was suppressing my urge to write. Whatever the reasons, the first time I really became aware of the game was from a passing reference in Neal Stephenson’s Cryptonomicon where one of Randy Waterhouse’s old roleplaying buddies says that he doesn’t do tabletop games any more and instead plays deck-building card games because there’s all of the combat and none of the tedious parts.

That didn’t sell the game to me, since combat is the part of tabletop RPGs that I enjoy least.

Anyway, I follow the Geek & Sundry web series Tabletop and saw this other show, Spellslingers, in the episode listings: it’s a bit like Tabletop, except that the game played is always Magic. I enjoyed watching it, however confusing it was at first.

Then my boys asked about the game, because they both have friends at school who play, and we went to get a couple of intro decks to play with at our FLGS*. It was fun, and well balanced – we’ve all won and we’ve all lost, but never so overwhelmingly that it was dispiriting.

There are also some players at the day job so I will probably go through a booster draft**. I have no intention of going much further than that with mass card acquisition because I have neither the time nor the funds, but it is a lightweight game with enough luck to give any player a fair chance but enough complexity to reward strategic thought.

Where’s the Storytelling?

I am always interested in the storytelling mechanics of a game, and one of the problems I have with Magic is that there really don’t seem to be any. It’s a combat game, pure and simple – there is a back story about planeswalkers coming into conflict and trying to stay ahead of some executioner-style figure who seeks out those who disrupt the walls between realities, but there’s really nothing in the game itself to reinforce that story. About the closest you get to in-game narrative is that some of the cards interact with each other to produce stronger effects, but basically you’re looking for tactical ways to remove your opponent’s life force in the game and the storytelling seems to be unrelated to the game mechanics themselves. There’s no requirement that decks be thematically consistent beyond using compatible forms of magic.

Having said that, the actual magic system which the game implements is quite interesting: land you control yields mana which you may harvest to cast spells. That’s a pretty strong mechanic, however isolated from the storytelling it may be (why do you control the land? how are the creatures summoned?).

Big System

Which brings me to the subject of magic systems in fantasy novels.

Most of my exposure to magic systems has been through roleplaying games. These give a structured framework for casting spells which usually have a cost in magic points or other components, and limitations like range, casting time, ritual elements, and so on. Then you roll some dice to determine whether and how successfully the spell was cast.

Magic in novels doesn’t need that level of detail (and frankly the explication of that level of detail is one reason why making fiction from the events in roleplaying campaigns tends to fall flat) but it does need some kind of systematic nature to limit the actions of spellcasters. If your protagonist can basically do anything at all with magic, then there is no constraint and no story. And the magic needs to be self-consistent also: if a character casts a shielding charm by smearing frog blood on their clothes in one scene but performs the same effect with a mere snap of their fingers later then there’s either a break in suspension of disbelief or the need for a very urgent explanation.

Magic in fantasy novels vary enormously.

  • in The Lord of the Rings it is difficult to think of a single spell that Gandalf casts, and Saruman’s great power seems to be in technology rather than sorcery. Even Sauron, arguably a being of pure magic, makes his greatest magic in artifacts rather than spells.
  • the Harry Potter books use wands and potions in equal measure, but the mechanics of magic itself are reduced to well-pronounced words and accurate hand motion***.
  • Chritsopher Paolini’s Inheritance series (Eragon and its sequels) use words of power, but they are words in a special language giving the true names of things.
  • Charles Stross’s Laundry novels use mathematics and computation as summoning spells, the mere act of executing certain algorithms weakening the walls of our reality.
  • in Michael Scott Rohan’s trilogy The Winter of the World, the MC’s magic is bound up in forging artifacts of great power, combining runes and the proper materials to make magical items.

This business of magic systems is a particular subject of interest for Brandon Sanderson as expressed repeatedly on Writing Excuses, so it’s worth trawling the archives for more.

As it happens, I effectively built a magic system for my science fiction novel last year, Shapes of Chance – the MC’s abilities were rooted in the concepts of quantum physics, but the effects needed to be proscribed so as to limit her capability. And now I am building a new magic system for this November’s story, since the one I used in its precursor is not really appropriate this time, so I need to think about what magic can do and where it comes from.

What magic systems do you enjoy in your fiction? How would you change them?

[*] Friendly Local Game Shop, in this case Other Worlds Games.

[**] getting lots of packs of cards and taking turns drawing from them, then playing with the decks that result.

[***} the question of where new spells come from is disposed of with throwaway remarks about “research wizards”, as if that is an answer.

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