One of the best ways to fine tune your deck and improve you play is to have a good understanding of the probabilities involved with your deck. This is the first of a series of articles intended to explore some of the probabilites involved in Mtg.
1. I want to see a card in my opening hand. What is the probability of drawing it?
This question can be important if you run a deck that relies heavily on one card in order to win, or if it's better to have a card in your opening hand. This matters to decks running Pyromancer Ascension or Leyline of Anticipation , for instance.
The answer depends on how many copies of the card you're running. Assuming you play a full play set (4 copies), the chances of drawing at least 1 in your openeing hand are approximately 40%.
You get this value by figuring out the chances of drawing NO copies of the card and then subtracting that value from 100%. In this case, the equation is:
2. How does redundancy affect that probability?
Running additional copies of a card that has a similar effect increases your chances of drawing a copy in your opening hand (running Ponder and Preordain , or Roiling Terrain and Demolish for example). The chart shows your chances of drawing at least one of these cards according to how many copies of the card you have in your deck:
As you can see, the most bang for your buck comes in upgrading from 2 copies to 3, as you gain a 10% chance of drawing that card in your opening hand by doing so.
3. If I get unlucky and don't draw the card I need in my opening hand, should I mulligan? What are the chances of drawing the card I need off a mulligan?
As a strategic matter, the answer is going to depend on how much mana you drew and what other cards you drew. If you drew an otherwise acceptable hand, you might not want to turn it in. But if you absolutely, positively MUST have a specific card in your hand, here are the chances of drawing the card off a mulligan, by how many copies you have in your deck:
Your chances of drawing at least one card off a mulligan aren't too much worse than your chances of drawing one normally, but you're still playing the odds.
Next time, I'll brush up on sampling without replacement and talk about the probability of drawing lands.