Does Baron give itself the +2 Might buff? Also, if a Vilemaw is attacking Baron with more Might than Baron, does the Baron get affected by Vilemaw's ability?

Baron Nashor does not give itself a +2 Might buff.

According to its card text, Baron Nashor's ability specifies: "Other friendly units have +2 [S]." Because it explicitly uses the word "other," the bonus excludes Baron Nashor itself.

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