When I create new games in the "waiting games" section, I always choose random colors. When I accept waiting games from the list, I almost always go with those that have colors set to "random". So, in the long run you would expect the randomness to even out and I would have an equal amount of games with each color.

Now, as you probably know, some games here are very color-biased. As I browse through the games statistics, I find that these games give one side an overall score of approximately 60% or more:
Horde Chess (white 74%)
Cheversi (black 68%)
Maharajah Chess (b 64)
Mancala (w 64)
Pahtum (w 62)
Hasami Shogi (w 62)
Swap Five in Line (crosses 61%)
Battleboats Plus (w 60)
Knight Fight (w 60)
Tablut (w 60)
Swap Five in Line is a little complicated because you have the option to change sides after the first move, so I'll leave it out here.

That leaves nine game types that are very color-biased. When I look at the games I have played of these game types (always choosing "random colors"), they add up to 107 games combined. Of these I've had the "good color" 46 times and the "bad color" 61 times.

My grasp of binomial distribution is a little rusty, but if I get it right, the probability of such an unequal distribution should be less than 10%. So my question is: Is there some kind of trick than I'm missing (and that some of my opponents are not)? Is there some crooked way of side-stepping the randomness?