Help remembering an author and the name of a sci-fi book?

Ok folks I am trying to remember a book I read . . . probably 20 - 30 years ago. (probably closer to 30 years ago). I get the sense that the book was not newly published when I read it . . . but I might be wrong.

It was a sci-fi book and I am sure I do not remember all of the details correctly which I am about to spell out so there might be some red herrings in here.

It was a book about space travel which was made at near light speed. Near the beginning of the book a guy who was on such a ship was getting examined by a doctor at the end of a journey and the doctor found some kind of teeth issues (like a cavity or something) and made a comment to the effect of "some of those early model ships do not have fluoridated water so this is normal". The main character stays behind on Earth when the ship makes its next voyage. The main character's twin/brother/friend who is now 8 years older than the main character takes his place on the ship (totally not sure about this part)

During the progress of the book this newly arrived traveler is mentored by a guy who is some kind of gaming expert. As near as I can remember the game in question is a math based game which has 3 levels. It is played in a public forum and everyone is playing the same game . . . the first to solve the puzzle (or whatever) earns a monetary prize. The higher the level of the player the higher the prizes. If you are say a level 3 player you are not allowed to go into a level 1 arcade/gaming place/whatever. At one point the mentor intentionally looses a game in order to make sure that he is not hated as much -- I seem to remember that the implication was that this mentor could more or less win any game at will.

There is a drug in the book which after the first use the user becomes instantly addicted. I think prolonged use makes the whites of your eyes turn yellow. This is divulged when the main character is in the presence of the mentor when a "junkie" asks the main guy if he wants a hit/dose/whatever of the drug in question. The mentor explains that this is a choice that everyone must make at some point . . . implying that you have the choice if you want to be a lifelong drug addict or not.

As the book progresses the main character developed a faster than light (FTL) drive and used it to catch back up to his ship -- at which point the main character is now roughly the same age as his twin/brother/friend who took his place.

That is all I can remember . . . does anyone have any insight? I would really like to read the book again and or other books by this author. Thanks in advance to anyone who can help!