This should be unrated games only IMO. Otherwise certain people would only play as White.
Select color during Live Chess
There already is a choice in unrated games, because in the New Game Game Type Settings, you have an option of challenging as Unrated: White or as Unrated: Black.
Oh! Yes, there is! But I just tried it, and no match was found. I guess very few play unrated games.
Maybe it could be made possible to choose color also during rated games, but maximum something like 25 games in a row. Thereafter, the random games following with be 2:1, so that after x number of games, the total number of games with each color would be the same.
What I mean is this (as an example):
I want to experiment with the Latvian Gambit, so I choose to play a rated game with the Black pieces. I keep playing with the Black pieces for 25 games. Now, I'm done with my research of the Latvian Gambit, so I choose Random color games. The next 75 games I'm giving either White or Black, at random, but weighted, so I get the White pieces 50 times, and Black 25 times. All-in-all, I've now played 100 games, 50 games with each color.
Here's a simple idea: allow players to select to play either White, Black or Random in Live Chess! This would be great for experimenting with various openings.
Half an hour ago, I wanted to try out a new opening with the Black pieces, so I started a game, and got the White pieces. I abondoned the game, started a new one and got the White pieces again. I abondoned about ten games, getting the White pieces in all of them. Then I played a game (with the White pieces), and started a new game. Again(!), I got the White pieces. Kind of silly, especially, since I wanted to play Black.
I hope you will consider this. Thanks!