I also have two or three interesting ideas in mind, but I think the problem is that most users have enough games to play (PAW, TT, Suicide) or don't even play all three and thus probably won't play a new one.
You are right. So, maybe my first proposal could be changed to following one:
"about a game where you have to predict one winner in a list of 3 to 6 possible matches (selected by the manager, the most tricky ones of the day)
The goal is to have the biggest winning streak. If you lose one day, your counter is reset to 0 and you are allowed to restart another winning streak.
You can skip some days whenever you want. The only mandatory thing is that you can only select maximum 1 match per day.
You can start a new streak whenever you want. Every day, a new updated ranking will be published with current winning streak per player and highest winning streak per player. "
This means that players can play whenever they want. If they want to have their winning streaks when playing only during week-ends, that is fine.