It didn’t take long after the release of Phyrexia: All Will Be One for Atraxa, Grand Unifier to make an impact on Standard, Pioneer, Modern and Legacy. As a reanimator target, she’s reminiscent of Griselbrand, making her one of the best creatures ever to cheat onto the battlefield.
Atraxa’s enters-the-battlefield raises the question of how often she’ll provide the type or quantity of cards you need, but math can give us all the answers.
Suppose, for example, that you need to find a specific card to stabilize and that there are four copies of that card remaining in your 50-card library as Atraxa enters the battlefield. Then, the probability of finding at least one copy of that card is 60.3 percent, making you a clear favorite to find the card you need.
This probability could be determined with a hypergeometric calculator – it’s the probability of finding at least one success in a sample of 10 cards from a population of 50 cards containing four successes.
However, when you want to know the probability of finding a specific combination of cards or the distribution of the total number of cards put into your hand, things get a little bit more complicated. For this, we need the multivariate hypergeometric distribution. I explain the details at the end of this article, but first I will provide a tour of eight different Atraxa decks. Using the multivariate hypergeometric distribution, I will analyze two Standard deck lists, two Pioneer deck lists, two Modern deck lists and two Legacy deck lists. For each, I will show the distribution and expectation of the number of cards provided by Atraxa, confirming her power. However, let’s start by building some intuition with a simple example.