I've been working on a card game where cards are played either for points or used for their special abilities. The game runs really smoothly with 2 people and is very "tight." I've gotten feedback though that a 2-player only game is harder to sell than a 2-4 player game. having the 3 and 4 player game follow the same rules as the 2 player game has not worked well. The importance of a player's decisions is lost with so many other players' turns happening between his or her turns. I solved this by making a 4-player version that involves 2 teams, each holding half of the 2-player hand size and teamates having limited knowledge of their partner's cards. This also is a fun game, and I enjoy it, but it really is more like a variation of the 2-player game than it is like a scaling up of the 2-player game. The 3-player game involves a team playing against an individual, and requires a tweak to the scoring to balance the team against the individual. The 3-player game is not "broken" but it is weak. In summary I can imagine a reviewer in the future writing "The 2-player game is great, and the 4-player variation is also pretty good, but I would not recommend playing the 3-player variation."
My greatest fear is that if I put "players: 2-4" on the side of the box, that someone will play the 3-player version, find it meh or awkward, and never play my game again. What I really want is people to judge it on the 2-player experience, and then find the 4-player experience to be a neat variation that gives some flexibility to player count.
My real question, and maybe you can't answer it for me, is whether I market the game as a 2 player game and include rules for a 4 player variation, market it as a 2 or 4 players game (is that odd "2 or 4"?), or market it as a 2-4 player game and hope that the word gets out that it is "recommended with 2 players"?
It wouldn't be the first 2 or 4 player game.
It's more flexible than 2 players but less flexible than 2-4 so it is still a small drawback. Better than listing it as 2 player and having them find out that its 2 or 4 only after they purchase it.
1) Figure out a way to make the 3-player game as strong as the others, then market as being for 2 to 4 players.
2) Market it as, "For 2 or 4 players". Be clear, and put the three-player game in as a variant, making a small note in advance of its issues.
I prefer the first, but I suspect the second is the more probable path.
I would suggest you take a look at one game I found a year ago on some forum, or so... Carolus Magnus (and I print&played it). It is for 2-4 players, just like the one of yours. While being listed as 2-4 players game, the main part is the two player game with an extension to play in teams 2vs2. The 3-player game is a bit different game. It doesn't involve the fight for rule between two factions, but three, and the game feels different, as the player has less to do (I personally would allow even more competition). I think this is about the same as your problem.