Before I write what will be a series of articles (hopefully to be put into book form at some later date), I just want to say that I love the game of Magic the Gathering. I have enjoyed many hours of it with friends and have come to enjoy card-based games more because of my exposure to it. I also want to share the caveat that I am not an expert Magic player by any means, however because of my background in analytics and stats, I have been able to apply specific principles that I know to the game to help me build decks that are competitive with my friends. I also believe these principles will be useful to anyone who wants to build their own Magic decks so they can play leisurely with their friends (and win some games).
Please rid your mind of the notion that there must be a set number of cards of each type
Other than the standard rule of not having 4 of the same card within your 60 card Magic deck, there really is no rule to how many cards you have of each type. That said, it is important to keep in mind that you want your deck to work ‘for you’ and the ‘way you want’ within the confines and laws of probability that your deck will be built around. And to calculate the probability of anything that you put into your deck, it is always x/60, with x being a generic number representing how many cards you have of a certain type or ability.
I like the idea of having at least 2 lands in your starting hand
The starting hand of 7 cards is very important. Further, it’s useful to think of your starting hand as a ‘sample’ from the ‘population’ of 60 cards that you are drawing from. Since the game focuses on having enough Mana to cast spells, I like the idea of having at least 2 lands in your starting hand. That would come out to be 2/7 cards in your first hand, which when applied to your deck strictly would be 17/60 (7x=60 which is 8.57, 8.57 *2=17, 8.57*7=60, thus 17/60). Keep in mind though, when you are going from a larger sample of 60 to 7, the chances of drawing at least 2/7 (or 29% chance) goes down, so I add a few more cards to this to make my chances greater (say 3-5 more cards). So, in my example, at the minimum I recommend 20 lands, at the maximum 22 lands.
The Weighted Average Casting Cost tells you how ‘fast’ and ‘powerful’ your deck is
I honestly think they should publish the weighted average casting cost with each deck you buy. Why? Because it can tell you how fast and powerful your deck is. A deck can be fast (meaning you can cast lots of low mana cost creatures and they can come out quickly), but not very powerful (because there typically is a positive correlation with casting cost and how powerful the cards are that you have). And when I say ‘powerful’, I mean how much damage or benefit they can deal. Further, a deck can be slow, in that it will take more time to build up mana in order to cast the cards within it. The cards you have may be powerful, but if it takes a long time to play them, you risk dying before you get there. This is why personally I like to keep my weighted average casting cost around 2-3. Below two means you’re betting on less powerful cards to win and above 3 means you are betting on more powerful cards to win, however it will take more rounds for your deck to get moving. 2-3 is about average. I will calculate the Weighted Average cost with a sample in the next sections.
For our purposes, let’s use a pre-purchased Magic deck as an example of how many cards of each type can be in a deck
I have enjoyed purchasing pre-built decks from Magic the Gathering. I think they are, for the most part, well built. And I expect, they are built by experts who know the game well. So for this article, I decided to purchase the Yanling Planeswalker Deck, just so it can be used as an example. Keep in mind though that you can totally create our own custom built deck however you want, realizing that you are at the mercy still of the laws of probability and chance as you play.
After opening this deck, I observe the following (at a high level):
There are:
25 lands, translating to the chance of having almost 2.87 cards (so 2-3 cards) in your starting hand (the math for that is 25/60=0.417, then 0.417*7=2.87.
27 creatures, translating to the chance of having almost 3.15 creatures in your starting hand (same math, except its 27/60).
4 instants, though I did notice that there are 10 creatures that have ‘Flash’ which makes it also an instant. Keep in mind that this would effect the probability of drawing an instant (making it 14/60 instead), but does not effect the probability of drawing a creature (27/60, which is different).
3 sorceries
With either the 3 or 4 cards (or even combining them to make it 7/60), there is a chance of drawing <1 card of either type in your opening hand. And that chance is small because of the smaller sample of 7 cards. So I have a greater chance of drawing only creatures and lands in my opening hand.
And finally, 1 planeswalker
Calculating the Weighted Average Casting Cost for this set of cards
The Weight is calculated as the # Cards/60 for each Casting Cost type
The Weighted Average Cost is the Casting Cost * the Weight for each Casting Cost
Once you get the Weighted Average Cost for each Casting Cost, you sum this together. For my population, the answer is 2.13.
Understanding what can be affected in gameplay first, before I run out the probabilities for abilities across cards
Before I go into calculating the probabilities of abilities across cards, I want to step back and talk about the aspects of the game that can be affected by the cards you have. This will provide a framework, in my mind, of understanding how the deck you build (and the probabilities of abilities across cards) will play out. And it will make it easier for someone to customize their decks and get their deck to do what they want.
Aspects of play affected (high level):
Your own creature(s) or someone else’s creature(s)
Your graveyard or someone else’s graveyard
Your draw deck or someone else’s draw deck
With a planeswalker deck, your planeswalker (or someone else’s if they also have one)
Your own spell or someone else’s spell (other than a creature)
Your land or someone else’s land
Your casting cost or someone else’s
Your hand or someone else’s hand
This is pretty much it! And, any ability(ies) you have on a given card will affect one of these aspects of gameplay.
Here are some examples from the deck I purchased:
Flying: Affects my creature
Flash: Affects my land (because I have to use a land to cast it)
Return target creature to owner’s hand (for simplicity, I will call this ability ‘Return creature’): Affects someone else’s creature
Draw cards: This affects my draw deck (makes it go down and makes cards available to my starting hand)
Search the deck for the Planeswalker and put it in your hand: Affects your hand
Understanding the probabilities of your abilities across cards and why that’s important to getting your deck to do what you want it to do
Calculating the probabilities of abilities across cards is easy. Getting your deck to do what you want and have a higher chance of that is ideal.
For our example, I will use the pre-purchased deck again. And just go ability by ability across cards. And realize there may be more than one ability on a given card, however for our purposes, we will calculate the probabilities separately (irregardless if there is more than one ability on a given card).
There are 16 creatures with Flying. That can be given a couple of probabilities. 16/60: The probability of there being a creature with Flying in the deck overall, 16/27: The probability that at least one of your total number of creatures has flying.
There are 10 creatures with Flash. That translates to 10/60: The probability of there being a creature with Flash in the deck overall, 10/27: The probability that at least one of your total number of creatures has Flash.
There are 6 cards with Return Creature. That is 6/60 overall, and for the Planeswalker it is 1/1, for creatures it is 1/27, and for Instants it is 4/4.
There are 10 cards where it affects positively my own creature’s strength and/or defense (+X/+Y) That is 10/60 overall, 10/27 for Creatures. Please note than I am combining, just for simplicity, whether is affects your own creature or someone else’s.
There is 1 card that negatively affects someone else’s creature’s strength and/or defense. That is 1/60 overall and 1/1 for the Planeswalker.
There are 3 cards that Tap another player’s creature. That is 3/60 overall and 3/27 for the creatures.
There’s are 2 cards that can put the Planeswalker into your hand. That’s 2/60 overall. 2/27 for creatures.
There are 3 cards that Tap a target creature. That is 3/60 overall. 3/27 for creatures.
There are 6 Draw Cards abilities. That is 6/60 overall and 3/27 for creatures and 3/3 for sorceries.
There are 3 cards with Casting benefit. That is 3/60 overall and 3/27 for creatures.
Get out of your mind that there is a ‘perfect’ deck and instead focus on increasing your chances of the deck doing what you want it to do
At this point, it is helpful to create a visual (kind of like a score card) of your abilities across cards. Here is this deck’s based on the probabilities I just calculated…
Weighted Average Casting Cost: 2.13
Observations – This deck is fair, it could TOTALLY be better
There are several observations I have when looking at the numbers for this deck. As follows:
- You shouldn’t have problems being able to cast most spells within the next 10 rounds. If you have 2/7 in your hand in the first round, you will have 2 mana out within the first two rounds and then have a 23/53 chance (The denominator is 53 because you are taking out the 7 in your hand) of drawing a land on the second round (so about 2.3 cards out of the next 5.3 should hopefully be a land – Note I am purposely not taking into account the margin of error).
- This deck is creature heavy. You won’t have a problem drawing creatures. And, since the weighted average casting cost is 2.13 and since your starting hand will have 2-3 mana, you will be able to cast a good number of your creatures within the first several rounds (because you should have at least 4 mana in the first 5 rounds – 2.3 within the next 5.3 after your first round).
- Although there are a good number of creatures, it’s important to note that a good percentage of them are in the 1-3 mana cost range (because your Weighted Average Casting Cost is 2.13).
- Flash is a nice ability. And in this deck, while 37% of your creatures have it, only 17% of total cards have it.
- This deck seems to want to focus on Flying, Flash, and +X/Y, but these probabilities are getting dragged down by other abilities that may or may not prove useful in supporting those (especially given their low probability scores within the deck).
- Unless the creature of the other player is a flier, the return creature ability may or may not be useful. Further, if the other player’s creature is a flier, the tap creature might be useful…but what if it isn’t? Do you really need Tap Creature, especially since you have so few cards with that ability?
- Given that you have a decent number of creatures and a good weighted average casting cost (and a good chance of drawing mana in a decent number of rounds), do you really need the ability to draw more cards?
- The Retrieve Planeswalker cards are very nice, however there’s only a couple of them. This is crippling your ability to bring out this powerful Planeswalker.
My suggestions to improve this deck:
- Have more cards in the deck where you are seeking for the Planeswalker to put into your hand (Yanling’s Harbinger). You’re allowed 4 of the same type anyway, and this Planeswalker is pretty powerful. At the least, you can put in 2 more of Yanling’s Harbinger.
- I don’t necessarily like 27 creatures in a hand, only because I enjoy using spells more, so I would have less creatures, and more spells in the decks I build. And if this were my deck, I’d add more Retrieve Planeswalker spells and +X/+Y spells to increase your chances of boosting your creatures more.
- I would remove cards (unless they are dual) that Tap or Return Creature or Draw Cards. And add cards with abilities as I suggested. This would increase the probabilities on your ‘leading abilities’ and remove cards that may make less sense to play together.
- Because you will have a good amount of mana in a small number of rounds, you could afford to increase your weighted average casting cost by removing a few less powerful creatures with lower casting costs, and adding a couple more powerful ones. For me, the obvious choice would be to get rid of a Spectral Sailor and a Warden of the Evos Isle and add two more Air Elementals. All else equal, that would make the Weighted Average Casting Cost 2.22.
Extra topics I may explore in future articles:
Multiple color decks – How many of each type to use?
Shuffling deck techniques (to make things more random)
Suggested ability segmentations
Scoring a deck with arbitrary numbers
Taking into account powerful combo cards
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