How so? What does it mean for a sandbox to have a GM-authored plot - which is to say, following the definition that Google provided me, GM authored main events . . . devised and presented by the writer as an interrelated sequence?
Yes, that is the definition of a plot. And if you asked your players to write down the plot of your games from the start of the campaign to the present, there'd be a series of interrelated sequences making up the main events of the game.
In this instance, "the writer" is the entire table and not a singular individual.
While you as the DM might not be authoring the plot, there still is a plot.
In a sandbox, more or less by definition, the GM does not author the main events, nor contrive them into an interrelated sequence. To the extent that such a thing occurs at all - and it may not - it is done by the players.
Ummmm... no. That's not what the term means.
Turning to Google myself:
A sandbox is a style of game in which minimal character limitations are placed on the gamer, allowing the gamer to roam and change a virtual world at will. In contrast to a progression-style game, a sandbox game emphasizes roaming and allows a gamer to select tasks. Instead of featuring segmented areas or numbered levels, a sandbox game usually occurs in a “world” to which the gamer has full access from start to finish.
A sandbox game is also known as an open-world or free-roaming game.
https://www.techopedia.com/definition/3952/sandbox-gaming
Nothing in that denotes an absence of a plot. Just not a linear plot. But, when the campaign was done, the players will be able to describe and summarise the plot of the sandbox.
Player agency is a vital part of sandboxes. There's choice. Opposed to railroads where there is none:
http://tvtropes.org/pmwiki/pmwiki.php/Main/Railroading
http://www.urbandictionary.com/define.php?term=railroading
What you seem to be describing is a
player-driven campaign. Which is something entirely different. It's unrelated.
Sandbox and railroad occupy an X-Y axis on a chart. The amount of player agency in the story would be a Z axis. In theory, you could have a player-driven sandbox, but you could also have a player-driven railroad where one or all players have a campaign planned in their head and the DM is just working towards their goal. If in your game 3/4 of the table were mostly passive and one player made all the decisions and drove all the action that would very much be a player-driven railroad.
A brown duck is a type of duck; but a fake duck is not - it's some sort of non-duck.
Similarly, on the face of it a "flexible plot" is not a plot at all. Unless the "flexibility" is confined to minor variations and colour (which is the case eg in at least some APs), in which case it remains GM authored and the flexibiity is merely superficial.
No.
Just no. You're missing the point. Completely.
The DM can present the plot. The villain, the situation, the overarching story. What the campaign is about. Say, finding the Rod of Seven Parts. Or destroying the One Ming in the fires of Mount Dread. Really, every single event occurring in the world that is happening without direct input from the players.
A railroad would be if the players have no real choice but to follow the DM's plan. The can't reject the quest or find an alternate path. There's no choices, and a best only the illusion of choice (no matter if they turn left or right they have the same encounter).
However, the plot
can be flexible. Going left or right leads to very different results. The players might surprise the DM by doing very different things than expected and having cunning plans. They're still going to the same destination (from A to B) but they're taking a very different route than planned. It's not a railroad so much as a flowchart with a set Start and Stop, but a infinite number of branching paths.
A railroad is playing the original Dragonlance modules as written. They're railroady as eff, with even the resolution of some of the villain fights being predetermined.
A flexible plot maintains the War of the Lance and might even start the same, but diverges when the players have other plans. The players say "eff Tarsis. Lets just head north to New Sea and get a boat there". It becomes flexible when the DM decides to run with it, changing the adventure. The overall plot might still be the same (get to the Whitestone Council, find the Dragonlances, get the metallic dragons into the fight, beat Takhisis, win the war) but the events occurring aren't happening as planned. Some of the major beats can still occur, and the DM can still lead the players to some of the major set-pieces, but the players have much more agency to make decisions.
That's an extreme example as it's using prepublished modules and requires more rewriting. In a homebrew situation the same can occur, where the DM has the basic plot outlined in their head and the expected beats, but the players go in the opposite direction while still planning on fulfilling the overall goal presented.
Saying "no" doesn't mean the game is a railroad. It's not taking away a player's choice, it's just limiting their options. Similarly, saying "yes" adds options.
But there are other approaches that are neither railroads nor sandboxes - [MENTION=16586]Campbell[/MENTION] described some upthread, and I responded with reference to actual play experience. There are approaches to play - eg Campbell's "Principle GMing" which are neither railroads nor sandboxes.
Again, there are not just railroads and sandboxes. Things aren't either-or. There's not neat little categories that games solely fit. Games have a range. Something can be mostly a sandbox. Or be 75% sandbox. Or start on the rails and become a sandbox. Or each session could be tightly scripted by the DM but the players make choices at the end of each session that determines the direction the next session.
Correct. That is why, as I posted somewhere upthread, I GM according to "say 'yes' or roll the dice". If nothing is at stake, say 'yes'. But if something - what, in the OP, I called an outcome - is at stake, then a check is framed and the dice are rolled.
Then why do you need a DM?
Seriously.
The players can determine the odds of success just as well as you. The table can agree on the probability and roll. If you're not making any decisions and just randomly determining events in the game, you're redundant. Your players can replace you with random encounter tables and agreed upon probability.
Dump your DM screen, roll up a player character, and move to their side of the table.
Heck, the DMG even has you covered. Read page 269. It's discussed as an option. And you can probably look at many other DM-less games for inspiration.