I have a habit of designing my multi-player games for a "sweet spot" of four players, and then testing and tweaking to see whether they will also gracefully support more or fewer players. While I don't recall this being a conscious decision, it makes sense to me. Four is a nice, balanced number: two couples, or a family with two kids. It can mitigate the excessive downtime that some games suffer with more players, and avoids the two-against-one dynamic that can ruin a lot of three-player experiences.
But I don't want to design exclusively for four. Any game will sell better if it can be labeled for "3 to 5" or "2 to 6" players. And any game will be more popular if it actually works for the given range. (All experienced gamers have seen games that really don't play well at the low or high end of the claimed range.)
So recently I broke from my usual simulated four-player rail game sessions, and tried a five- and a three- player to see what would happen. I'm pleased to say that the game survived, and seemed playable. But unsurprisingly the game gives a different experience with different numbers of players.
With four, I've tried to tune things so that the winning player will likely connect all six cities, and build a switchyard: the two highest-scoring achievements. Usually two of the remaining players will get one or the other goal, but not both; and one player will get neither. This makes for vigorous competition to link up the cities, which is one of my design goals. It also often results that most players have little money left at the end of the game: although money is also worth victory points, you're usually better off spending it on connectivity or switchyards if you can. The losing player may actually finish with the most money, having been unable to spend as much of his income on connectivity and switchyards as the others; but sometimes such a player prospers so well just making deliveries that his cash hoard pulls his score up into the middle of the pack.
In the three-player game, there was much more elbow room. All players were able to connect all cities, which soaked up more time and money than in the usual 4p game. It was a less competitive, more open game. I found that I prefer the four-player experience, but some players may enjoy the easier, free-wheeling nature of the 3p game.
In the 5p game, the board was crowded and tight, and competition for connectivity was fierce. Only one player connected all six cities. Also the board filled with track rather faster than in the 4p game, so players could tell early on when (for example) it was clearly impossible for them to reach New York or Seattle. That meant more concentration on switchyards: five were built, and one player built two. This game ended with a lot of money in circulation, because more players were simply making deliveries in the late game rather than building.
Unsurprisingly, the game seems to have a different character depending on the number of players. With three, it's relatively open and easy-going. With four, competition is tight but most players are going to be able to do well. With five, money is tight in the early game as players race for connectivity, then piles up in the late game as players concentrate on lucrative deliveries.
J. C. Lawrence says a game should end when the winner is clear. I think he's right, so I was watching these games to see whether they ended too soon or too late. In the 4p game, 20 rounds seems exactly right. (I originally had a variable end-of-game trigger based on running out of goods, but decided it didn't work well.) I'm prepared to alter the 20-round figure for the 3p or 5p games, but so far it seems to hold up. The 5p game, for example, might have ended at 17 rounds; but then some serious new delivering and building took place in round 20, enough to convince me that the final three rounds weren't empty activity.
Another way to balance the game for different player counts is to alter the map. A smaller map for a 3p (or 2p) game, a larger one for 5 or 6. I haven't gone there yet, but of course I have the possibility in mind. Completely different maps is one way to do it, but it might also work to vary the main map by adding or removing junctions and connections. But before I go there, I want to shake down the current design some more. When (if!) I'm really comfortable with the 4p game, I'll look harder at variations to improve the experience with other player counts.