There should be a way to go back and instant replay a prior game so you can see what you did or just show your friend. This should not be hard for Blizzard to save the moves of each game and let the Hearthstone client play them back later.
Sometimes I want to show a friend a particularly cool match and there is no way to go back and replay an old match.
Note; this is not interactive. It’s simply a playback of prior games with a fast forward and rewind buttons so you can skip through the move series. This would NOT reveal the other player’s cards or deck.