Hussar
Legend
/edit - edited the title to reflect facts. 
Now, this is just my opinion, but, for my money, there are three fairly broad criteria that almost all rpg's fall into. I would say all, but, there are so many RPG's out there, there's almost for certain some that wouldn't.
But, these three criteria are useful for distinguishing what defines a game as an RPG.
1. Role Assumption.
The game itself presumes that the players of the game will assume some sort of role (or possibly a small number of roles). This role is usually different from the player's personality in some way - different age, different species, different capabilities, etc. There are mechanics in place in the game which define a character within the fictional game world.
2. Narrative.
Events in an RPG are presumed to follow logically. If you do X, then doing Y should be believably possible. If I take my character to a restaurant, I can order a meal. However, I could not take my character into the middle of a desert and then order a meal. Events follow believable paths.
3. Persistence.
There is an assumption in the game that events that occur in previous play sessions will carry over into the next session and subsequent sessions. Consequences carry over. The player is assumed to continue playing the same role and play can possibly continue for very extended periods of time. Generally, there is no "reset" for players which resets the entire game to be played a second time.
To me, these are the three basic criteria for an RPG.
Something like Monopoly fails to be an RPG, because while role assumption might be arguable, there is nothing in the rules for persistence. When someone wins a game of Monopoly, that win does not carry over into the next game. Every game is closed.
It is possible, however, to alter games to become more and more like a role playing game. Take Warhammer. In a standard Warhammer game (not the RPG), there is no role assumption (at least, the rules don't assume one), and there is no narrative. There's no reason why two forces of X points are meeting in battle. There's no reason why both forces are almost always equal. And there is no persistence.
However, if you take a Warhammer ladder, then you can start to see a role playing game. You get persistence, it's possible to add roles to the leaders of armies (the players) and it's possible to get a narrative. Depending on how much focus you start to shift onto role assumption and the like, you can turn Warhammer into a role playing game.
However, that doesn't mean that Warhammer is an RPG. It's not. It's just that turning a game into an RPG isn't always very difficult.

Now, this is just my opinion, but, for my money, there are three fairly broad criteria that almost all rpg's fall into. I would say all, but, there are so many RPG's out there, there's almost for certain some that wouldn't.

1. Role Assumption.
The game itself presumes that the players of the game will assume some sort of role (or possibly a small number of roles). This role is usually different from the player's personality in some way - different age, different species, different capabilities, etc. There are mechanics in place in the game which define a character within the fictional game world.
2. Narrative.
Events in an RPG are presumed to follow logically. If you do X, then doing Y should be believably possible. If I take my character to a restaurant, I can order a meal. However, I could not take my character into the middle of a desert and then order a meal. Events follow believable paths.
3. Persistence.
There is an assumption in the game that events that occur in previous play sessions will carry over into the next session and subsequent sessions. Consequences carry over. The player is assumed to continue playing the same role and play can possibly continue for very extended periods of time. Generally, there is no "reset" for players which resets the entire game to be played a second time.
To me, these are the three basic criteria for an RPG.
Something like Monopoly fails to be an RPG, because while role assumption might be arguable, there is nothing in the rules for persistence. When someone wins a game of Monopoly, that win does not carry over into the next game. Every game is closed.
It is possible, however, to alter games to become more and more like a role playing game. Take Warhammer. In a standard Warhammer game (not the RPG), there is no role assumption (at least, the rules don't assume one), and there is no narrative. There's no reason why two forces of X points are meeting in battle. There's no reason why both forces are almost always equal. And there is no persistence.
However, if you take a Warhammer ladder, then you can start to see a role playing game. You get persistence, it's possible to add roles to the leaders of armies (the players) and it's possible to get a narrative. Depending on how much focus you start to shift onto role assumption and the like, you can turn Warhammer into a role playing game.
However, that doesn't mean that Warhammer is an RPG. It's not. It's just that turning a game into an RPG isn't always very difficult.
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