Finding Magic: The Gathering archetypes with Latent Dirichlet Allocation

I do not even try to describe the archetypes — I only show it a collection of decklists and ask for the number of archetypes to be found.With LDA, we can discover what cards are associated with what archetype..Perhaps we ask it to describe all decks in terms of three archetypes and it returns lists of cards corresponding to aggro, combo and control decks..Or, for example, if we ask it to find five archetypes it might simply cluster cards into the basic colors: white, blue, black, red or green.More interestingly, we also get the probability distribution of cards in an archetype..This means that for each archetype, there are card-and-probability pairs where all the probabilities naturally sum to one..Continuing with the example above, we might find that the most popular card in the blue archetype is Snapcaster Mage, the next most popular one is Serum Visions, then Dispel and so on.Draw, go.Finding the distributions analytically is usually hard and involves estimating intractable integrals..Methods from a discipline called Bayesian inference are used to get the best guess of how the distributions look like from what we know..In this case, “what we know” is our set of decklists which helps us get a good estimation of what the underlying archetypes look like.Learning by exampleAs a general rule in statistics and machine learning: the more data we have, the better estimations we can make..Getting good data is usually a difficult task..Since we are giving the algorithm more and more examples of how decks look like, it will become better at understanding a format the more decklists it sees.Angel of MTG Decks was so kind to supply us with data for this article..The data set I will analyze for this article consists of 500 Modern decklists from recent tournaments.I should emphasize here that the data consists of raw lists of cards..The AI does not receive any information about deck names, who built it, where or when it was played, whatever..Just 500 lists of 75 cards.Determining archetypesNext, we decide on a number of archetypes to find.. More details

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