Thank you Jörg. Since I am trying to get people to make cooperative variants, I will answer comments on the subject. You are very correct to say that any cooperative variant, whether random or not, can be seen as a single player game, but I think that is a strength, not a weakness, unless the game is very shallow (but any game that is very shallow will generally be a failure, whether it's cooperative or competitive, with tic-tac-toe being an obvious exception). Of course, it is preferable in a cooperative game that both sides be necessary for each other in some way, whether by the rules or by the pieces they hold, or by the sheer difficulty of the task. In all cases, playing a cooperative game with two players or more is entirely different from playing alone.