Mysql – I have one table for users, one for a collection of games. My users can own one or many games. How to structure that in the database

If you're designing an OLTP database, you should really design it in third normal form initially. If, once you've done that, you find that you can make measurable performance improvements by denormalizing something and there is no other way to get those improvements, it makes sense to denormalize selectively. It does not make sense, however, to denormalize to first normal form proactively.

I don't really understand why you expect that adding a mapping table would be problematic. Yes, you'll need to join to it. But that's what a relational database was built to do-- it joins tables very very efficiently. Plus, you won't have to constantly parse the delimited string to figure out the T2 keys. And you will be able to create a foreign key that ensures that the T2 keys in the mapping table are valid and that you don't have keys in your delimited string that don't map to a valid row in T2. I don't really see the downside.

If you have a separate mapping table and you want to return a single row of data to the client with the T1 data and the T2 keys (which seems awfully suspicious-- the T2 keys are only useful if you are going to subsequently use them to query T2 in which case you almost always want to just let the database join to T2 in the initial query) you can always pivot the data in the mapping table to return a delimited string of T2 keys. I certainly wouldn't recommend that but it can be done.

Yes, I believe you are on the right track. The gameDate and gameScore fields are more a part of the game entity and not the player, so they should be on the Gametable. Besides, bridge tables should really only contain the related ID fields.

If gameDate and gameScore were on the PlayerPlaysGame table, they would only be dependent on the gameID and not the playerID. By definition, this would constitute a partial dependency, and would violate second normal form.