“The problem is all inside your head”, she said to me

“The answer is easy if you take it logically

I’d like to help you in your struggle to be free

There must be seventy-eight ways to leave your lover”

Hello and welcome back to TheBoxer’s Corner! I know many of you are waiting for my Expedition Power Base article, don’t worry it is still in the works. It is just taking a lot of time to get where I want it to be. In the mean time I decided to write about a topic I’ve been thinking about for a while: deck size and why it is always correct to play 75 cards.

Some may argue that making an absolute statement is wrong, but I argue that my statement is correct so close to 100% of the time that is will do my readers a disservice to write otherwise. I have yet to see any deck that would benefit from more than 75 cards.

There are a plethora of Magic articles by the amazing writer Frank Karsten about probability and deckbuilding. Rather than simply try to translate those into terms of Eternal I’m going to talk about the theory of deckbuilding. I believe this will be a better approach than throwing a million tables of probabilities at you. I personally don’t learn much when I see a bunch of decimal numbers and feel I can show you how math is at play here without giving you the gory details and focusing on the theory and relations between concepts.

A deck is a set of cards with an order. An order is exactly what is sounds like, a way of ranking things. 1<2, 3<Pi, etc. We also will need to distinguish between different copies of the same card. For example, in a deck with Dragon Forge the second copy of a Weapon may be much less important than the first. Hence I will call cards Torch1, Torch2, etc. Even power has a rank. The 31st Power is less important than the 30th. This order is influenced by the metagame. The metagame is the set of all of decks that are played. The ranking of cards in your deck depends on what decks other people are playing and how common those decks are. For example if only one player is playing some brew, that will have little influence on the order. Or for instance the more Teacher of Humility is played, the higher every copy of Defiance is ranked in your deck.

As a deck builder it is your goal to draw the most high ranked cards in the meta each game. By playing more than 75 cards you are decreasing your odds of drawing the cards that are good in the meta, and increasing your chances of drawing the 76th, 77th, 78th, etc. best cards in your deck. I don’t know about you but I personally prefer increasing my chances of drawing higher ranked cards. By playing 75 cards you increase your chances of drawing good cards compared to playing more than 75 cards. This is the key takeaway.

What about tutor boxes? If I play more than 75 cards I can have more options? As I said above, even silver bullets (niche tutor targets) can be ranked. You also decrease your chances of ever drawing the tutor.

What if I have the same Power ratio? This is one of the most common counterarguments, but it is flawed. Probability does depend on your deck yes, but it more directly depends on the power set of your deck. No pun intended. A power set is the set of all subsets of a set. For example the power set of {0, 1} is {**∅**, {0}, {1}, {0, 1}}. It has 2^n elements, where n is the number of elements in the original set. Opening hands depend on the subset of the power set where every element has size 7. There are way more opening hands possible in 76 cards than in 75! Roughly 1.1 times as many! Multiplying by 1.1 may not seems like much but the number of opening hands in 75 cards is already very large.

Let’s do a small scale example to understand power sets. Suppose your deck was 7 cards and you drew 7 cards for your opening hand. Set aside worries of instantly losing the game for this example. Say it was 3 Power and 4 non-Power. Now suppose you double it’s size. 6 Power, 8 non-Power. Same ratio as before. Now in the first deck you always draw 3 Power and 4 non-Power. In the second deck there exist hands where you draw 0 Power. This is why ratio does not tell the whole story. Even forgetting about ordering, power sets are why you should not play more than 75 cards. Your power base also will get worse as the number of cards increases in the deck. You can only play so many dual Powers and in order to keep the ratio the same you will be less likely to draw dual Powers so this ratio isn’t even a correct concept to begin with.

I used a fair amount of math language in this article and if any of it is confusing I am happy to answer any questions you have about it.

Deckbuilding is about tough choices and honest analysis. To be a good deckbuilder you must be able to find what must be cut when finding room for new cards. Deckbuilding is the art of understanding the metagame and figuring out the ranking of cards so that you can construct a deck. Every deck has an ordering even the most synergistic decks. Every deck has a best card and a worst card. Playing 76 or more cards is playing more bad cards than you are required to. Good players are looking for every edge they can find and playing exactly 75 cards is an easy way to get an edge over anyone who would be a valued cosigner on the Indiana Pi Bill (https://en.wikipedia.org/wiki/Indiana_Pi_Bill). My Influence in Expedition article should be coming soon. I hope you enjoyed this look at deckbuilding theory. *Tusen takk for at du leser* (thousand thanks for reading)!

-TheBoxer