Passive checks can supplant active checks given enough time

and...

You can retry a failed Ability check only after a Long Rest

My rule:

If you have essentially unlimited time, you may use a Passive score in place of rolling an Active check.

It follows that: If you make an Ability check and fail, you cannot try again for that same task, until after a Long Rest.

Rationale

When your player's character fails at an Active check, say a Thieves' Tools check to open a lock, the player will tell you, "I try again!" When they fail again, they will try again. And again. And again. Eventually, the law of averages says they will finally roll high enough to succeed, but this is tedious for players and DM.

There's a suite of variant rule ideas generally called "Take Ten," where if a character takes enough time (ten minutes, in this shorthand), they will succeed at whatever they are doing. Clearly, this is just a suggestion, because nobody is going to open the DC 30 lock, no matter how much time they have.

I like to give this some structure, by deciding that if the character's Passive score is equal to or higher than the DC for the task, they will succeed, given enough time.

"Enough" time is clearly up to the DM to interpret. Ten minutes seems like a good starting point, but it should vary by the task at hand.

But what about trying again and again when your Passive score is not higher than the DC? In other words, when you can't just take the time and eventually succeed? What's to stop you from rolling again and again until you do, finally, even if it takes a really long time, roll high enough to succeed?

We had a circumstance once where a Rogue was trying to unlock a lock, and failed, then failed gain, then again. She wanted to keep going. We decided, impromptu, to put a limit on the number of times they could try, that eventually it was just too hard for them. I've thought about that, and I don't think that was a good ruling.

Here's what RAW has to say about failing an Ability Check (Basic Rules DDB link)

"Otherwise, it's a failure, which means the character or monster makes no progress toward the objective or makes progress combined with a setback determined by the DM."

Nothing about what happens when you fail, just that you don't succeed. So I came up with a long and convoluted system where if you failed it added 1 to the DC for the next attempt, and if you failed by ten, that increase was permanent (if someone else tried the task), so that eventually you just failed enough that it was so hard you couldn't do it. But that felt like too much trouble, too finicky, and not very 5e to me. Besides, it states that no progress is made, or some progress, combined with a setback. Nothing about going backwards, if you fail. 

But neither does it state, explicitly, that you can just try again. So, I've decided that if you fail, you can't just try again. Radical! If your Passive score is higher than the DC, you can still take the time to eventually succeed, but if you're trying something that is harder than you can normally do, and you fail at it, there's no trying it again. You reached beyond your grasp, and you failed. Nice try.

I'm so mean.

Edit: After some reading and consideration, this does seem mean. So, you can try again, for this task, after a Long Rest. Happy?

Examples

Skill checks:

The Rogue from above is trying to open a lock. The lock's DC is 15, the Rogue's Passive Thieves' Tools is 15. They know that, under my rule, they could take their time and unlock it. But they don't want to wait, so they roll, and fail. Now they can't try again. They could take the time to do it right, since their Passive score is enough, but they can't try to open it right away.

Or, a character is trying to impress a crowd in a tavern by making a long jump. The DC is 15, and their Passive Athletics is 16. They could take their time and eventually succeed, but the crowd will have wandered away by then, so they roll. They fail, and can't try again. Perhaps they landed badly, and have to walk it off before they can try once more, by which time the contest is over.

Ability checks:

You're going "to march or labor for hours without rest," which is an example of a Constitution Check from the rules. In this case, if your Passive Constitution is higher than the DC, no sweat, you take the time (hours) and succeed. If it's not, roll. If you fail, too bad, you can't try again. You collapse and suffer a level of Exhaustion.

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