In the example (simple) game in the post, a player character may be able to pass into the red room and "win", but perhaps there's no condition for returning and the game only terminates when both make it to their individual rooms. If the other character lacks the keys to move through the green and blue doors, then they will be stuck and the game won't terminate. This is easy to guard against in a small game (small state space, easy to manually or mentally compute), but in larger games it's almost trivially easy to cause these sorts of dead-end states. Consider the puzzles of Sokoban, where pushing a block onto certain walls or a corner prevent further progress and require a restart. Now, that's part of the game in that case, but perhaps a designer wants to prevent (in their puzzles) this sort of situation from occurring. This sort of analysis of the game model (states and actions) will help them prevent it.
It is especially important because of how frustrating the resulting loss is; it does not even have the dignity that you get from killing Vivec in Morrowind, where the game informs you "sorry, this game just became unwinnable." You just wander around after doing a bunch of actions that made sense at the time, not realizing that your brother Ralph was twisted up in some crazy voodoo plot. "Yes, Alice, I see that you have pains in your arm that you think come from some voodoo doll, I don't see how that has any relevance to anything though: I've searched this whole damn city and there are no voodoo dolls anywhere." Until later "Oh wait... there was that one alley on the other side of the mob lair, it looked empty at the time but what if that's where Ralph is now?"
See http://ifwiki.org/index.php/Cruelty_scale . Not only do they have dead-ends, but sometimes you don't realize you've hit one until long after you do the thing that set you down the unwinnable path.
Getting rid of dead ends makes some of these games feel like they are on rails. If you try enough combos of everything, eventually you'll progress.
I think its important that there is no state were you just get stuck, you should at least have a game over sequence, so that you know you have done something wrong.
It gets worse -- there are a bunch of tools you go by throughout the game. If you fail to pick up any of them, that one will be the one you need to open one of the final doors.
It's a nasty little game, really.
I guess if I were doing it again nowadays I'd be going for a tool-assisted... umm... speedrun isn't really right here, so win-at-all-run.
...classic Infocom games had plenty of dead-ends :)
Some do by accident, for example if you can proceed to the next location in the game without an object you need to solve the challenge in it and without the ability to return to the previous one.
... no "dead ends". I.e. all player actions will result in a state in which the game is still winnable
- then, yes, fairly common, although not always intentionally.A dead lock occurs when a state is reached and there is no way to exit the state. In complex state machines it is important insure they are 'deadlock free.' Sometimes people use a timeout to recover from a locked state machine, sometimes the system needs to be re-powered.
An adventure game is simply a state machine (or a collection of interlocked state machines). So proving the proving the game has no deadlocks will also prove that the state machine has no deadlocks.