Entertainment apps are most often not solving an actual problem, per se. I guess you could say that "killing time" is a problem in a way.
For SaaS startups, however, solving a real problem is the core requirement. No one is going to use a product that you make that doesn't address any problem they have.
This doesn't necessarily have to be a problem that they realize they have. When you are creating a new market, you're basically showing people that there is a better way to do something. You are showing a problem that people didn't know existed.
Your odds of success are exponentially higher if you're solving a real problem.
Otherwise you're basically throwing things against the wall hoping something sticks.