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And we have a winner! After recieving thousands of entrees with amazing guesses like "2.1357kg" or longer, heavy weights of "8.13kg" or even l33tsp34k estimates of "1.337kg" the correct answer was:
0.690kg (690gr) for both Froggy and the graphics card.

Congratulations goes to: Michael H. from Bischofsmais, Germany!
The lucky winner has been drawn from a handful of correct guesses and will have Froggy knocking at his door with the Sapphire Radeon HD 5770 with 1 GB RAM in-hand soon.
Thanks to all participants and until the next contest.
Your Runes of Magic Community Management Team