I doubt it's possible...

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One of the things I'd like to see, though I doubt it's possible, would be the status of our decks being used against other live players on PvP. Beyond just the narcissistic factor of 'My deck is kicking butt' it could help to identify weaknesses in your current cards. If you're only doing okay with your deck but when it's played by the computer against live players it's getting destroyed it could give you a starting point when choosing new cards or making changes.

I doubt the servers have the ability to track that kind of information but it'd be pretty cool to be able to login and see something like your deck's win/loss ratio against live players.