If you look through a board game shop, or a list of crowdfunding games, you will find a huge number of games with a printed player count of 1 - 4; so they should play solo, for two players, for three players, and for four players. The reality of this is that the game will be best at only one of those player counts; if you are lucky they still kinda work at the other player counts, but it is practically impossible for any game to provide an equally great experience at all player counts.

Let's look at the reasons why games can't work at all player counts, with some examples: Tainted Grail is a complex narrative game, with a complex, puzzle-like card combat mechanic. That works quite well for low player counts, solo or two players. But for higher player counts the downtime, the time between the end of your current turn and the start of your next turn, becomes increasingly long. Maybe your whole group is low on food, and you decided all together to go to a hunting spot; so every player is doing a combat against a random wildlife creature, some of which are quite hard to kill. With 4 players that might take rather long; and as this is just resource gathering, it doesn't even add to the narrative. A lot of games are in a similar situation: The turn of any given player can be long, there is little to no interaction with other players during that turn, and thus at higher player counts people end up waiting a lot, usually getting out of the flow of the game by looking at their phones.

Familiar Tales, a much easier narrative game designed to be family-friendly, has the opposite problem. It's flow works well for 4 players; but the narrative demands all 4 characters to be in the game, and combat is balanced on that being the case. So for smaller player counts, each player has to play several characters, and there are rules on how to combine the decks if you are playing 2 characters at once. Unfortunately those rules don't work well at all, and make the game rather difficult and tedious. Again, similar things happen with other games that are well balanced for 4 players: The difficulty at other player counts isn't the same, resulting in a very different experience.

Dune: Imperium is a game with a lot of player interaction, especially the worker placement base mechanic, which prevents you from using a space that another player got to earlier. As the number of spaces on the board is fixed, this feels a lot tighter and interesting at 4 players than at 3 players, because at 3 players there is simply less competition. At 1 or 2 players there are rules for an AI/automa deck blocking a space every turn, but that is by necessity very random, and not as interesting as having to guess which space another player would take. Combat, which consists of different players sending different numbers of troops into conflict, is also feeling rather random with the AI/automa, while being much more interesting with 4 real players.

Board Game Geek, the biggest source of information for board gamers, for every game lists the official player count, but also a "community" and "best" player count decided on by poll. For example Tainted Grail is officially listed at 1 - 4 players, community would only play it at 1 - 3, and best is 1 - 2. I used that information to make a list of all my narrative campaign games, to decide which one of them I would want to play with friends in a 4-player group, and which ones would be better if I just played them with my wife at 2 players. But when I go for example to the Spiel games convention and look at a brand new game, which doesn't have much information yet on BGG, it is very hard for me by just looking at the box to decide what the real player count for a game is. The only exception to this is specific 2-player games, like this year's Spiel des Jahres Sky Team, which are more likely to be honest and not pretend that they can be played with other player counts than 2.

While the other information printed on the box, like the playing time, can be somewhat misleading too, the biggest lie printed on a board game box tends to be the player count. Be very, very careful before spending your money on a game if you personal situation makes it that you would be very disappointed if the game doesn't work well for a specific player count. If you only ever play with your spouse and end up with a game that doesn't really work for 2, or you have a larger game group and a game doesn't play well for that, you could be wasting your money.