"Is it balanced?" is a question that many game players, and all game designers, ask about a game. But it can mean different things to different people.
Most generally, "balanced" means that a game has—at the outset—an even chance of being won by any player at the table. If the game heavily favors the first player (for example), then the game is unbalanced: it's not fair to the other players.
But there are other ways to consider the matter. A common design problem is the runaway leader, where the first player to gain an advantage will almost certainly win. Even if the chances of winning are even at the start of the game, they may quickly become very uneven.
Some players take this notion to extremes, and consider any game unbalanced if the final scores show much separation. Others reject this idea on the grounds that it renders all of the game except the final few moves irrelevant to the outcome.
One of the reasons I built the Rails Across America simulator was to test the balance of the game. I instrumented the simulator to record scores over runs of thousands of games, and to print out relevant statistics. The results were enlightening, and somewhat depressing.
I was looking for evidence of all three kinds of imbalance. After a fair amount of work I was able to tune the rules and map to the point where there was no significant starting imbalance in the four-player game: all players had a roughly equal chance of winning at the start of the game. (This was not quite as simple as looking at the stats for which player won most. A start-player advantage may only apply to intelligent players, and my so-called AI doesn't qualify. So I was also looking for imbalances in the choice of starting location. Turns out it's a bad idea to start at New York, but when I was done tuning, the other five Major Cities on the board were about equal.)
Next I looked at the scoring curves. What was the range of final scores, what was an average score, how sharply pointed was the bell curve? Also I looked at the bell curve for the point spread: what was the difference in final scores between the winner and the biggest loser in each game? Since I want to avoid a runaway leader problem, but don't feel that every game needs to be really close, I was satisfied with curves that showed reasonable but not excessive grouping of final scores. Often a couple of players may be in a tight race for the win, while one or two others lag behind. Sometimes one player dominates, but certainly not always. That's a good distribution, in my opinion.
So what's depressing about all this? It's good, but only for the four-player game. With five, the game is badly imbalanced—at least one player is screwed from the start. The three-player game is worse. And I learned that the biggest factor affecting the balance is the map itself: merely playing with costs, rewards, and setup would not repair the imbalances. To have a good three- or five-player game, I'll need well-tuned three- and five-player maps. That's upsetting. The more restricted the recommended number of players, the fewer copies will sell. To make it less restrictive I have to add more boards, which adds expense.
Probably the best compromise is a two-sided board, with the 4p map on one side and the 5p on the other, and forget about the three-player game. If I'm lucky and work hard at it, I might also be able to make a subsection of one map serve for three players.
The next question is: Is it worth the trouble? But that's an issue for another post.