In my series on the DMG, I've commented a few times about Gary's very adversarial approach to refereeing and how it would be totally inappropriate of me to bring that into the games I run with the players I run them for. I don't begrudge Gary his adversarial style (only his apparent belief that all games should be played this way) since it seemed to work well with his players, who are reputed to have been shameless power-gamers; after all, they kept coming back to play, which I hold to be the first test to see whether a referee is doing a "good enough" job.
Part of the reason why I try not to be hard on Gary on this point is that, while I've never had players who engaged in or initiated adversarial play styles in my games, I've talked to players who do look at D&D as primarily a contest of wits and will between players and referees, so I know they exist. When dealing with these kinds of players, Gary's adversarial DM advice starts to make sense!
I bring this up because the recent OSR definitions posts going around include the terms "railroad" and "sandbox," and that reminded me of a conversation I once had with a friend who definitely falls into the "adversarial player" category. For some reason we were talking about airships in D&D and my friend told me that I wouldn't want him in my D&D campaign because he would "mess it up."
I asked him how he thought he would be able to do that and he replied that, while flying in an airship, he would have his PC jump out of the airship, without a parachute or any other velocity retardant, just to watch me scramble to save his PC so that the plot could continue. He didn't seem able to fathom my explanation that, in that scenario, I'd just let his PC die; I went on to explain how I didn't consider myself responsible for writing a plot or ensuring that the plot was actually carried out, but I'm not sure whether he got that or not. I'm actually interested in running a game or two with my friend as a player, just to see how many PCs he'd kill before realizing that I wasn't going to save any of them; I think I'd find that very entertaining.
My point, though, is that our difference in play style and assumptions about plot and the preservation of PCs became clear in the differences between the reaction he expected a DM to take and the action I would take. I think this is actually a pretty good litmus test for whether a campaign is a "railroad" or a "sandbox."
(Keep in mind that litmus tests are helpful, but also pretty crude, devoid of nuance and can result in inaccurate results; to mix metaphors, another way to look at what I'm proposing is that it is a "rule of thumb," a generalization, not a "one size fits all" definition that takes every possible way to run a campaign into consideration.)
If a player in a game (willingly or unwittingly) makes the PC do something that will result in death (or perhaps just merely will result in a result other than that expected by the referee) how does the referee respond? If the referee allows the PC to die without interfering, the game is probably a sandbox game. If the referee scrambles to return the PC back to the referee's expected plot line, the game is probably a railroad game.
Or, to put it more succinctly:
If you save a PC that just jumped to certain doom because you want to save the plot, it's probably a railroad. If you let the PC die, it's probably a sandbox.
Now, I think it's important to remember that the issue of "sandbox vs. railroad" isn't binary but is instead something that can be plotted on a spectrum between the two poles of "sandbox" and "railroad." All the same, this test, I think, provides an easy, quick, if crude, way to determine which pole of the spectrum a campaign or play style is closer to.