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In the 6 months that I've been playing this game, I've never seen the computer mulligan an opening hand. There have been cases where the computer won't even get a land for several turns. Is a computer mulligan even a possibility?

Nope, the computer can't mulligan. If you turn on the "AI Stack Land" option, it will stack the AI's land and ensures that the AI will play a little bit better. Even though the computer can't mulligan, usually it doesn't affect its performance but sometimes the AI will have a noticeable shortage of land.

Hmm... it wouldn't be too hard to determine if the computer could mulligan. Determine the casting curve of cards in your hand for the next 3 turns (e.g., if you have 2 spells you can cast over 3 turns), see if you have at least 2 lands, and mulligan if hand size > 5 && those conditions are false.