Coin Toss: Not fair?

Has anyone studied the probability of the coin toss, and whether it is fair? For grins I kept track of 30 battles. Of those 30, I started first in 10 of them, and second in 20. There is only a 3% chance this could have happened if the coin toss is 50/50 (fair). Can we accuse Rovio of "cheating" all of us by stacking the odds in the game's favor so we have to spend LC to reset our birds after three losses?
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