3 what the rules mean by "interrupting"; don't get distracted by the damage-distraction rule
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Once the triggered action has begun, there's nothing the other (N)PC who caused the readied action to trigger can do to "un-trigger" it. The action is taken and the silence spell gets cast.

If this wasn't true, readied actions would be non-functional. The (N)PC could always simply choose to change their mind and do something else to avoid triggering the action. That's just not the way the rule was designed to work.

As for what happens next, the original spell being cast that triggered the readied action to cast silence would be lost. The character has already committed to the action and begun it (else the trigger couldn't happen), so they're in the middle of it:

If the triggered action is part of another character’s activities, you interrupt the other character.

The rules use "interrupt" in the normal English sense: the action is happening and the readied action interrupts it, happening while it's in progress and before it has its effect.

Don't let the part about distracting spellcasters confuse you. It's not relevant to this case. That rule adds to the general case, saying that damage can distract a caster and prevent the spell from being completed. Another way to prevent a spell from being cast would be to ready and action to grab them and cover their mouth, but that's handled by the general ready rule being used to make (verbal) spellcasting impossible. Without the damage-equals-distraction rule, spellcasters could still be prevented from casting by suddenly being gagged or silenced, but they'd be able to keep casting just fine when stabbed – and that's now how the designers wanted stabbing spellcasters to work. It's providing an extra way to inconvenience spellcasters, not the only way.

It might be easier to picture what is actually happening to understand how the rule works:

PC: I'm readying an action to cast silence if Voldemort starts casting anything.

GM: Okay. So Voldemort starts casting power word: kill. He's opening his mouth and pointing at you, but you're ready and you interrupt him with your silence spell. *Rolls saving throw* …Aaaand he failed. He's just standing their with his mouth open like a dweeb with no sound coming out, and the spell fizzles.

They key thing to remember is that the readied action happens before the action that triggers it, but the triggering action still started to happen.

Once the triggered action has begun, there's nothing the other (N)PC who caused the readied action to trigger can do to "un-trigger" it. The action is taken and the silence spell gets cast.

If this wasn't true, readied actions would be non-functional. The (N)PC could always simply choose to change their mind and do something else to avoid triggering the action. That's just not the way the rule was designed to work.

As for what happens next, the original spell being cast that triggered the readied action to cast silence would be lost. The character has already committed to the action and begun it (else the trigger couldn't happen), so they're in the middle of it:

If the triggered action is part of another character’s activities, you interrupt the other character.

The rules use "interrupt" in the normal English sense: the action is happening and the readied action interrupts it, happening while it's in progress and before it has its effect.

It might be easier to picture what is actually happening to understand how the rule works:

PC: I'm readying an action to cast silence if Voldemort starts casting anything.

GM: Okay. So Voldemort starts casting power word: kill. He's opening his mouth and pointing at you, but you're ready and you interrupt him with your silence spell. *Rolls saving throw* …Aaaand he failed. He's just standing their with his mouth open like a dweeb with no sound coming out, and the spell fizzles.

They key thing to remember is that the readied action happens before the action that triggers it, but the triggering action still started to happen.

Once the triggered action has begun, there's nothing the other (N)PC who caused the readied action to trigger can do to "un-trigger" it. The action is taken and the silence spell gets cast.

If this wasn't true, readied actions would be non-functional. The (N)PC could always simply choose to change their mind and do something else to avoid triggering the action. That's just not the way the rule was designed to work.

As for what happens next, the original spell being cast that triggered the readied action to cast silence would be lost. The character has already committed to the action and begun it (else the trigger couldn't happen), so they're in the middle of it:

If the triggered action is part of another character’s activities, you interrupt the other character.

The rules use "interrupt" in the normal English sense: the action is happening and the readied action interrupts it, happening while it's in progress and before it has its effect.

Don't let the part about distracting spellcasters confuse you. It's not relevant to this case. That rule adds to the general case, saying that damage can distract a caster and prevent the spell from being completed. Another way to prevent a spell from being cast would be to ready and action to grab them and cover their mouth, but that's handled by the general ready rule being used to make (verbal) spellcasting impossible. Without the damage-equals-distraction rule, spellcasters could still be prevented from casting by suddenly being gagged or silenced, but they'd be able to keep casting just fine when stabbed – and that's now how the designers wanted stabbing spellcasters to work. It's providing an extra way to inconvenience spellcasters, not the only way.

It might be easier to picture what is actually happening to understand how the rule works:

PC: I'm readying an action to cast silence if Voldemort starts casting anything.

GM: Okay. So Voldemort starts casting power word: kill. He's opening his mouth and pointing at you, but you're ready and you interrupt him with your silence spell. *Rolls saving throw* …Aaaand he failed. He's just standing their with his mouth open like a dweeb with no sound coming out, and the spell fizzles.

They key thing to remember is that the readied action happens before the action that triggers it, but the triggering action still started to happen.

2 what the rules mean by "interrupting"
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Once the triggered action has begun, there's nothing the other (N)PC who caused the readied action to trigger can do to "un-trigger" it. The action is taken and the silence spell gets cast.

If this wasn't true, readied actions would be non-functional. The (N)PC could always simply choose to change their mind and do something else to avoid triggering the action. That's just not the way the rule was designed to work.

As for what happens next, the original spell being cast that triggered the readied action to cast silence would be lost. The character has already committed to the action and begun it (else the trigger couldn't happen), so they're in the middle of it:

If the triggered action is part of another character’s activities, you interrupt the other character.

The rules use "interrupt" in the normal English sense: the action is happening and the readied action interrupts it, happening while it's in progress and before it has its effect.

It might be easier to picture what is actually happening to understand how the rule works:

PC: I'm readying an action to cast silence if Voldemort starts casting anything.

GM: Okay. So Voldemort starts casting power word: kill. He's opening his mouth and pointing at you, but you're ready and you interrupt him with your silence spell. *Rolls saving throw* …Aaaand he failed. He's just standing their with his mouth open like a dweeb with no sound coming out, and the spell fizzles.

They key thing to remember is that the readied action happens before the action that triggers it, but the triggering action still started to happen.

Once the triggered action has begun, there's nothing the other (N)PC who caused the readied action to trigger can do to "un-trigger" it. The action is taken and the silence spell gets cast.

If this wasn't true, readied actions would be non-functional. The (N)PC could always simply choose to change their mind and do something else to avoid triggering the action. That's just not the way the rule was designed to work.

Once the triggered action has begun, there's nothing the other (N)PC who caused the readied action to trigger can do to "un-trigger" it. The action is taken and the silence spell gets cast.

If this wasn't true, readied actions would be non-functional. The (N)PC could always simply choose to change their mind and do something else to avoid triggering the action. That's just not the way the rule was designed to work.

As for what happens next, the original spell being cast that triggered the readied action to cast silence would be lost. The character has already committed to the action and begun it (else the trigger couldn't happen), so they're in the middle of it:

If the triggered action is part of another character’s activities, you interrupt the other character.

The rules use "interrupt" in the normal English sense: the action is happening and the readied action interrupts it, happening while it's in progress and before it has its effect.

It might be easier to picture what is actually happening to understand how the rule works:

PC: I'm readying an action to cast silence if Voldemort starts casting anything.

GM: Okay. So Voldemort starts casting power word: kill. He's opening his mouth and pointing at you, but you're ready and you interrupt him with your silence spell. *Rolls saving throw* …Aaaand he failed. He's just standing their with his mouth open like a dweeb with no sound coming out, and the spell fizzles.

They key thing to remember is that the readied action happens before the action that triggers it, but the triggering action still started to happen.

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Once the triggered action has begun, there's nothing the other (N)PC who caused the readied action to trigger can do to "un-trigger" it. The action is taken and the silence spell gets cast.

If this wasn't true, readied actions would be non-functional. The (N)PC could always simply choose to change their mind and do something else to avoid triggering the action. That's just not the way the rule was designed to work.