So the rate of drop can intersect, yes. that would mean that a very low stability card, if not studied right away, would push down to the bottom of the pile. That’s a good thing. You’ve already forgotten it, give it up. If you didn’t get to it early, then you missed out.
But the total retrievability lost will never intersect on the forgetting curve.
In other words, the derivative of the forgetting curves will intersect and change priorities if you wait time to study two different cards, but the forgetting curve itself never will. So priorities can change if you wait, but the priority today is robust using PRL.
If you wait to study both, then D could end up being pushed to a higher priority. That doesn’t mean D lost more retrievability than A since day 1, that could never happen. That would just mean D will lose more in the next day than A will.
Just look at the retrievability graph where there are multiple S values on the same graph (I’m digging for it and haven’t found it yet, but I know it exists). The different lines intersect at 0.90 and never intersect again.
Edit: @sorata Here it is. Not the exact same formula R is currently using, but the shape is close enough to the same to make my point.
@sorata Let’s say in your example A is the blue line and D is the green line. D will at some point be steeper than A (because A flattens out faster), but it will never be lower.
So if you’re at day 0 and you’re wondering which to study today, you will always lose more R with A than D, no matter what future time frame you wait, so you should study A.
If you’re at day 30 (not sure D is actually steeper there but let’s pretend it is for the sake of argument) and you haven’t studied either yet, then at that point you’ve already lost a bunch of R for both, you will now lose more from that point with D than A and you should study D first.
But at any given point on that graph, PRL will tell you which you need to study first.
@sorata Ugh ok, your intuition isn’t completely wrong, and now we’re getting really into the weeds. At the point where they both have R = DR, what I’m saying is true, PRL will always be correct, no matter the time frame.
IF the current day is, let’s say 3 days before their PRL will be equal (before their derivatives intersect), then what you’re saying could happen. You’ll lose more R in a 1 day time frame with A, but you’ll lose more with D in some longer future time frame. Not sure that can be accounted for. I’ll think about it. Pretty sure at that point you’d have to do some kind of analysis on your own personal study habits to optimize and that’s just not worth the effort imo.
@L.M.Sherlock I’ve figure out what’s been bothering me about the structure of your simulation, and it’s a pretty simple fix. These graphs triggered it:
You’re stopping the simulation way too early. It seems like, and correct me if I’m wrong, you’re stopping the sim as soon as all new cards have been introduced. At that point there’s still a huge backlog for most of the sorts and you don’t really know all the cards that well.
What should probably be done is you simulate until all the cards’ R value is above the DR, which is going to be much later than all the new cards getting introduced. Then, we can see how much total time it takes to get there.
I know you’re going on vacation so I’ll try to do it myself in the meantime.
It would take long, but that’s the point you want to get to. In real life you’re probably going to always be adding new cards, so you might never get there, but in the sim we’re using a set number of new cards and the goal is to know them all. The sim in its current set up is stopping way before you actually know the cards well at all.
The question is how long, and which sort reduces that time the most?
The main problem may be not how long it will take, because some leeches will be lapsed again and again. If you’re lucky, the simulation will go through them soon.
This metric would be more robust: how long it will take to wait the average retrievability exceeding the desired retention?
We can easily try both, but I know I’d rather see how long until I have all cards above the DR and there’s no backlog. @sorata It wouldn’t have to be the day there are no cards due, it would be the day that your 80 reviews covers what is due that day.
Oke, now with the length of the simulation adjusted like you and @L.M.Sherlock suggested, shouldn’t we also account for these potential variables inside the simulation as well, or are they irrelevant?
1- Backlog Size
2- Number of New Due Reviews per day
3- Average True Retention per day
4-New cards per day
Backlog size will be zero when the sim ends. New cards per day will stay at 20, until they run out. You wondering what the average ends up being by the end? I think that will basically tell you the same thing (or be useful in the same way) as total days.
