I don't really understand the universal hatred for "rail-roading" players. I like having a couple avenues to chose from but "sandbox" games I've played in have been pretty awful.
Maybe it's because I'm more of a writer than a gamer, but I like to make a character, get presented with clear goals (perhaps with a few possible ways to reach that goal), and then go after that goal. The goal will ideally lead to the next goal and form an arc.
I have never found the game where we a dumped into a city and asked what our characters do next.
Maybe I'm just misinterpreting the terms. Can someone explain the appeal?
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I think you are misinterpreting the terms, or at least taking the counterpoint (i.e. sandbox) to the extreme where there is no direction.
Sandbox can be "Here are 6 plot seeds. Introduce them to the characters and see which ones they are interested in/pursue."
At the extreme end of the Railroad Train, you can eliminate meaningful player choice. The story comes to a standstill unless the players do/participate in "X event/encounter".
This is particularly loathed in RPGs as you're playing a game where the player has complete control over the characters actions. The mechanics define chances for success and failure, but unlike a board game or video game, a PC can conceivably try a lot of things, approach problems differently than the GM anticipated, or go in completely different directions. This is a huge part of the appeal of RPGs to many players.
On the flip side of the screen, many who hate/dislike railroading have encountered THAT GM. Yes, THAT guy. The one who wields his GM authority as if he is the omnipotent god of the setting. Many have experienced situations like:
Player 1: "I go to the market to see if my contacts can obtain maps of the old temple from before the castle was built above it."
Player 2: "I search the libraries of the wizard's guild in search of the same."
GM: They don't work.
Player 2: "You didn't even roll any dice!"
GM: Look, you're not going to find anything like that. So quit screwing around and go to the Duke's party like the NPC said you should."
An extreme example, but only slightly exaggerated in some cases.
Another prime, non-RPG related Railroad: Exhibit A,
Star Wars: The Phantom Menace. You know the podrace? Well, Lucas was hell bent on having it. Couldn't really work it gracefully into the story, so were supposed to believe these 2 highly trained warrior-diplomats, when faced with a mechanical issue on their starship can find no other possible scenario for obtaining a replacement part other than letting a 10-yr old boy participate in a life-threatening race. But it was cool, wasn't it?
The definition, and more importantly, the degree to which plot, story, or outline crosses over into railroad varies by player/group. I used to plot my adventures and campaigns much more than I do today -- mainly b/c my players thought of things that I hadn't anticipated. Should I have penalized their creative problem-solving or their desire to embrace role-playing or charater development just so an encounter could go as I envisioned it? No. They're not following a script, after all.
Plots are fine. Plots with limited choices are fine. But give your players the ability to take unexpected routes with your plot. For critical encounters you may have to give them the illusion of choice (all avenues lead to same point/nexus). That's ok, too. After all, you are putting work into the adventure.
If they won't take your plot points, move on -- but show the consequences in game:
That princess they didn't rescue? She was sacrificed to a dark god and now the royal family is in disarray and the threat of civil war now exists as opportunitic nobles seek to take advantage.
Etc.
On the other end, embracing the sandbox can be a whole lot of fun, too. Some of the greatest adventures, characters, and moments in gaming in my campaigns came about b/c my players took a route or made a choice I didn't anticipate. Also, I've found players are much more invsted in the story and it's outcomes when they've chosen it, rather than be told: "You've been hired to do X."