Just a small addition: favourite games would also save the server from some traffic. For example now I play at first those "favourite games" by clicking at first one of certain type with setting move and go to the next of this type. But when all moves in such games are done, main page reloads again and I process next favourite game this way. This would be prevented by an option of jumping to another favourite game type instead.
Even in current configuration it might be helpful to recognize there are no more moves for games of "this type", so instead of return to main page some page could appear with a choice what game to process next. But I like the idea with favourite games better.
If someone asks why someone would play games which are not his favourites, my answer: I mean there are kinds of games we like to play faster and kinds we like to play slower. Or when one is learning new game he can also play it slower and in spare time may be trying to get some ideas how to play this new kind of game.