Also, this card didn't activate when I lost.
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About Lich's Mirror: I tested it and it does work. When you'd lose, it shuffles everything back, you draw seven and go back to 20 life. One thing to keep in mind is that it doesn't remove poison counters or commander damage. If you lost to 21 commander damage or 10 poison, the Mirror kicks in, but you still have that damage or poison, so you lose again right after (now without the Mirror). That's how the card works in real Magic too. Do you remember how you lost? If it was something else, send me your log (Settings → open log folder) and I'll take a look.