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If it matters to you let’s work through those different scenarios.
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It's funny. People complained about how the cook example is so terrible so I asked them to provide alternatives. The closest I remember is that it wasn't a cook in the room, it was a guard wandering by or a nosy neighbor. Just shifting from a cook to a different individual doesn't really change anything. Then there's the house rule that successfully picking the lock is whisper quiet and if you fail apparently you decided to knock on the door instead or something. Add in the actions taken completely separate from the sleight of hand check like the squeaky hinges on the door that apparently opens of it's own accord on a failed check to open the lock or the cat in the room that, once again, only exists if you fail.
There are rare times when I will simply take a timeout and clarify the options the characters have, what the characters know, perhaps ask for a roll to give the players a hint. But that's because the game has bogged down and the people at the table are getting frustrated. I don't remember the last time that happened, as I said it's rare. If they're having fun discussing options and what to do I let them have at it. It's their game and it's up to them to move it forward.
Providing "better" examples of fail forward shouldn't be hard. If people use fail forward in their games give some examples of what that looks like. I'm still probably not going to use it because I don't see my job as a GM to push the narrative forward and definitely not on a failed action. But instead of repeatedly saying that the example I found is flawed, perhaps try providing an example that is not flawed?