Same schema - Single table or multiple tables

[René Simon]

Hello MySQL Community,

we are currently working on a GameBackend System.
The problem we are currently facing and is as follows:
We want to store users for each game and leaderboard entries of each user.

What are the deep level advantages and disadvantages between:
a) Storing all users in one table have the game as an indexed column
b) Creating a users table for each game

The same question goes for the leaderboard entries table

We have around 30 million users and growing and 500 million leaderboard entries and growing.

Of course the basic is to have one schema one table but maybe there are advantages in MySQL to have more smaller tables, regarding INSERTs, ALTERs?
e.g.: If ALTER is blocking a table till it is done, is it done faster for more smaller tables than one huge.
OR
An insert into a smaller INDEX is quicker or does it not make a difference since in the depth of MySQL a table is just nothing else but an abstraction and there is anyway one large "Index" that has the table name as column?

Looking forward to some deep MySQL knowledge why one or the other idea is better or worse.

Thanks in advance.