playBunny: How fast I'm playing my moves does NOT depend on the number of games I'm currently playing. It's not uncommon for me to play 250 games, or more, at once. But it happens only rarely that in more than 50% of the games, it's my move. Typically, when I give brainking my attention (and usually, that's a few times a day), I make moves in all the games in which it's my turn - and if opponents are active as well, in such a session, I play several moves per game (how many will depend on how fast my opponents play).

Of course, it sometimes happen that I'm away for a few days, so I will not make any moves. But that's independent of the number of games I'm playing. 10 games, 50 games, 300 games.