Mathenagics: Episode 3

By: Joseph Davis

Hi, I’m Joseph, and welcome back to Mathemagics. The goal of this series is to help you level up your deck building whether you’re new to the game or just trying to improve your brews. We’ll be exploring important aspects of deck design and diving very lightly into the math behind it, so you know not just how to build a deck, but why some deckbuilding choices are better than others. This week we’ll be building on last week’s article by talking about how many copies of a card you should be playing.

 

This week’s article deviates slightly from the last two in that is isn’t about arriving at your deck’s “plan” on time. Instead we’ll be looking at some math and then discussing why you might consider playing a certain number of each card. For the purposes of this article we won’t be talking about what turn you are likely to draw a card on. Instead we will be looking at how many draws before you are likely to draw the card.

 

Here are some tables:

 

Draw One Copy

 

1 played 2 played 3 played 4 played 5 played 6 played 7 played 8 played
31 cards 18 cards 13 cards 10 cards 8 cards 7 cards 6 cards 5 cards

 

Draw Two Copies

 

1 copy 2 played 3 played 4 played 5 played 6 played 7 played 8 played
43 cards 31 cards 24 cards 19 cards 16 cards 14 cards 13 cards

 

Draw Three Copies

 

1 copy 2 played 3 played 4 played 5 played 6 played 7 played 8 played
48 cards 38 cards 31 cards 26 cards 23 cards 20 cards

 

 

For this article we are looking for the point at which you are more likely to draw a copy of a card than to not have drawn a copy of the card. Our decision point when generating these tables is thus > 50%. For the first table we are looking at how many cards you need to draw to be > 50% likely to draw one copy of the card, and similar for drawing 2 copies and drawing 3.

 

You may notice something strange about these tables: we are going above 4 copies of a card. This is not just talking about Rat Colony or other exceptions. This is to account for playing two copies of a card which serve the same purpose such Ionize and Sinister Sabotage. While the cards are different and have slightly different color requirements, they are both 3 mana counterspells with minor upsides, so a deck playing 3 of one and 2 of the other can really be counted as playing 5 copies of that effect. This often explains why you may see a deck running 4 copies of one effect and 1 copy of a similar effect on a different card; it approximates playing 5 of the effect.

 

The other thing to note is that some of these numbers are lower than 7 cards. This means that for any opening hand of 7 cards you are more likely to draw a copy of that effect than you are to not draw a copy of that effect. Another important point is that drawing two copies of a card (or effect) is very hard. To get two copies of card in your hand in the first 10 turns of the game you need 6 copies of the card in your deck.

 

What does all of this really mean for deck building, though? Do you simply always put 4 copies of any card you like in your deck? The answer is as always, it depends.

In decks without many ways to draw extra cards per turn, we can look at the tables as basic turn outlines. When playing 8 copies of a card, we are likely to start with a copy of the card, and by turn 6 are likely to have drawn a second copy. With 6 copies of a card, we are still likely to start with a copy, but become likely to draw our second copy on turn 9. When looking at a linear system like this, we see why playing 4, 3, 2, or 1 copy of a card is a fine sliding scale. At 4 played, we are likely to draw our first copy by turn 3 whereas with 3 played it’s turn 6. When playing 2 cards it becomes likely to draw a copy by turn 9, and we just are flat out unlikely to draw a singleton before the game is over.

 

To decide how many copies of a card to play, think about those milestones and when you are likely to want the card the most. If your deck does not plan on the game going past turn 5, you should be looking at 4+ for your business cards, but if your deck looks to go much longer and slower, you can tune down the numbers.

 

So how do you draw extra cards? Is that power only reserved for blue? Should other colors always be playing 4+ copies of all of their cards to have any chance of drawing them? The answer is no. You can consider any card that adjusts what you are drawing as “drawing a card”. This means a scry from Treasure Map will help any deck draw an extra card (since you will either keep the card you want on top, or put an undesirable card to the bottom). Surveiling and exploring both are mechanics which will behave as functional draws, as well as effects like Vivien Reid or Adventurous Impulse, or even Fetchlands in older formats.

 

When building your next deck, keep these principles in mind and ask yourself these questions:

1) Which of my spells do I need to see in a game to win? Do I want multiple copies of it?

2) Are there any ways I have to draw cards or filter through my deck?

3) Can I play extra copies of certain cards to duplicate important effects?

 

These three questions should help guide how many copies of a card or effect to play in your deck. Remember, you either need to play a lot of copies or filter through a significant number of cards to be likely to draw more than one copy of a card in a reasonable window.I hope you’ve enjoyed your third lesson in Mathemagics, and I’ll be back with another one soon!

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