If it proves as popular as its clear inspiration, this could be a huge boost for Arena as the default digital MTG client
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Battle styles aren't a singular mechanic, but more of a label to designate cards that are designed around a similar theme: for example, Single Strike cards are slower and focus on large, direct damage, whereas Single Strike cards are trickier, messing around with your opponent's resources and keeping them on their toes
Specifically the pokeball which is the most obvious difference
Some also use shipping labels (with the label peeled off, as a poor mans medium when using the heat pen
Some current examples of B tier cards are Go For The Throat, No More Lies, Aftermath Analyst, and Faerie Mastermind