It's not really a mystery how credit cards affect a credit score.

Start here: What's in your FICO score

You will see that there are items positively and negatively affected by applications.

Primarily, the negative effects are in the 10% allocated to "New Credit", including number of inquiries, recently opened accounts, etc.

As others have noted, there can also be positive effects. A major component of the score is "proportion of credit lines used" - i.e. balances vs. total credit extended. As you open more cards, you have more available credit, so your utilization of credit goes down.

Overall, though, none of this really matters, unless you need a mortgage or maybe car loan or rental application in the next few years. If no one will be looking at your score, why does it matter?