Okay. So, lets break it down: What is a Chekhov's Gun, and why does this matter?
Chekhov's Gun is the basic principle that if you describe something, it must be used, and the more description you apply to something, the more important it thus becomes. For example: A novel may contain a scene where the main protagonist meets their love interest for the first time in a large crowd of people. It will likely relegate the entire crowd of people to a single line of description, maybe half a paragraph. The love interest however might get upwards of an entire page devoted simply to describing her every feature, from the way her hair moves, to the colour of the shoes she's wearing. Why? Simple: The love interest is going to be a lot more important and see a lot more attention than the crowd the main protagonist is currently in.
How this applies to role playing? Well, you have a limited amount of time with which to describe everything, from characters to the setting to the plot and more. This means that the more useless purple prose is stuffed in there, the more distractions you have separating you from the meat and potatoes of the story. Like for instance where is your character going, why are they going there, what are they hoping to accomplish, and so on. As a GM this is doubly important: You shouldn't describe an entire city in massive detail if it's just a set piece, if the players aren't going to be there long or if they can't really interact with it much beyond small pieces of it. That's just a humongous waste of descriptive space you could have used on more important things, like who they need to talk to, or who is even around that is relevant to the story for them to talk to.
Keep in mind this is also the number one tool for setting up future interests. For example, your party sees a small thief, in a tavern they are staying in. When they get up to leave a few minutes later, doing nothing about that thief, they realize that the [insert plot important item here] was stolen, and easily connect that to the thief. Now without having to explicitly tell them, they know exactly what to do without you adding anything at all: Chase that thief! How do they know that? Because you put emphasis and description on that thief earlier. Atop this, it's also interact-able because you described it: They could have just as easily pointed out that the thief is stealing things and people in the tavern would have reacted, sparing the party the whole "chase that thief!" sequence of the story by being decent people. Oh look, bonus points, it's a moral choice conflict too... And I had to add... Nothing. I didn't have to tell the player that not reporting the thief's actions was bad. They learn it was bad because the thief then steals from them and runs away with something that was important to them.
Chekhov's guns are, above all, a means by which to create a story in which everything is important, everything has meaning. Because you described the thief in advance that left the power in the hands of the players to decide to act upon it or not. This gave a choice, with inherent meaning, without having to do anything beyond make the thing you described have purpose and point in the story.
This is how a story remains coherent. Every action must mean something, every person described or every object referenced has to be important or "usable" information. Like if you describe the glasses on the bar, a character should be able to use them, like to order a drink, or to smash it over someone's head in an impending bar fight. Every sentence has meaning, and if it doesn't, you just wasted your time and the time of the players who read that sentence, whether you are a player yourself, or a GM. So learning this is very important and greatly enhances your ability to create things that have meaning.
Note that the Chekhov's gun can also be subverted. Ergo why I named the thread "Chekhov's armoury". For instance you can make Red Herrings, which are false trails or false clues. Just be careful not to dead end your players with them.
Hope this was helpful. If you have any questions, feel free to ask.
Chekhov's Gun is the basic principle that if you describe something, it must be used, and the more description you apply to something, the more important it thus becomes. For example: A novel may contain a scene where the main protagonist meets their love interest for the first time in a large crowd of people. It will likely relegate the entire crowd of people to a single line of description, maybe half a paragraph. The love interest however might get upwards of an entire page devoted simply to describing her every feature, from the way her hair moves, to the colour of the shoes she's wearing. Why? Simple: The love interest is going to be a lot more important and see a lot more attention than the crowd the main protagonist is currently in.
How this applies to role playing? Well, you have a limited amount of time with which to describe everything, from characters to the setting to the plot and more. This means that the more useless purple prose is stuffed in there, the more distractions you have separating you from the meat and potatoes of the story. Like for instance where is your character going, why are they going there, what are they hoping to accomplish, and so on. As a GM this is doubly important: You shouldn't describe an entire city in massive detail if it's just a set piece, if the players aren't going to be there long or if they can't really interact with it much beyond small pieces of it. That's just a humongous waste of descriptive space you could have used on more important things, like who they need to talk to, or who is even around that is relevant to the story for them to talk to.
Keep in mind this is also the number one tool for setting up future interests. For example, your party sees a small thief, in a tavern they are staying in. When they get up to leave a few minutes later, doing nothing about that thief, they realize that the [insert plot important item here] was stolen, and easily connect that to the thief. Now without having to explicitly tell them, they know exactly what to do without you adding anything at all: Chase that thief! How do they know that? Because you put emphasis and description on that thief earlier. Atop this, it's also interact-able because you described it: They could have just as easily pointed out that the thief is stealing things and people in the tavern would have reacted, sparing the party the whole "chase that thief!" sequence of the story by being decent people. Oh look, bonus points, it's a moral choice conflict too... And I had to add... Nothing. I didn't have to tell the player that not reporting the thief's actions was bad. They learn it was bad because the thief then steals from them and runs away with something that was important to them.
Chekhov's guns are, above all, a means by which to create a story in which everything is important, everything has meaning. Because you described the thief in advance that left the power in the hands of the players to decide to act upon it or not. This gave a choice, with inherent meaning, without having to do anything beyond make the thing you described have purpose and point in the story.
This is how a story remains coherent. Every action must mean something, every person described or every object referenced has to be important or "usable" information. Like if you describe the glasses on the bar, a character should be able to use them, like to order a drink, or to smash it over someone's head in an impending bar fight. Every sentence has meaning, and if it doesn't, you just wasted your time and the time of the players who read that sentence, whether you are a player yourself, or a GM. So learning this is very important and greatly enhances your ability to create things that have meaning.
Note that the Chekhov's gun can also be subverted. Ergo why I named the thread "Chekhov's armoury". For instance you can make Red Herrings, which are false trails or false clues. Just be careful not to dead end your players with them.
Hope this was helpful. If you have any questions, feel free to ask.