Time to engage my rant zone. This IOTM's capitalization bothers me. The item is classified as the "toy Cupid's bow" -- respecting Cupid's authority as an important individual worthy of capitalization but refusing to make the bow or toy a proper noun. This means that when you start a sentence with it, you have the uneven capitalization of "Toy Cupid's bow", where the bow looks off. And then when it's mid-sentence it looks like toy is a modifier on the true IOTM, the Cupid's bow. This is chaos. A madhouse. The world is askew. At least we can all agree to call it TCB, something that is never used anywhere else. Certainly not for transcutaneous bilirubinometry. That's impossible.
The toy Cupid's bow (which I will consistently refer to as TCB in this article) is a generic familiar equipment, equippable by any familiar. It has the following bluetext enchantments:
While familiar experience is normal, three of these are quite unusual, so they deserve their own descriptions:
20% * ( 1 + 3.5 ) = 90%
probability.)Pretty neat stuff. But how good is it, really?
As I usually do, I will go from least-useful to most-useful applications of this IOTM.
First up: the stagger. This one isn't going to be at all noticeable in a turnsaving sense, but it will be a nice boon for both lower-shiny speedsters who have any trouble with difficult combat survival and extremely fiddly bleeding edge speedsters who want to do 500 different things in each combat. It's always nice to get an extra combat round free of damage. The rest of the benefits are long-winded enough that I am going to add some subheaders...
The next best benefit is the ability to grab familiar equipment. In unrestricted, this is actually a very big benefit; there are multiple familiar equips that save 2-3 turns by themselves, so being able to generate them without any resource expenditure is a fantastic boon. In standard, this is a relatively minor benefit, as there are very few familiar-specific equips that are better than the generic equipment we have. Still, a few beneficial equips may be worth the trouble of picking up.
It's worth noting that there is considerable upside here; there's a very real chance that the TCB gets better as more IOTM familiars join it in standard. As-is, this will save you a fraction of a turn (via more Peace Turkey turns) in a normal run, and (in some lower-shiny cases) save you a turn or two on tower tests or NC hunts.
In a vacuum, +2 familiar XP doesn't sound like a ton. And to some extent, it isn't! But you need anywhere from 550 to 1100 familiar XP on your Chest Mimic every single day to access all 11 of your summon/copies. In this year's standard, that's not a horrible problem; after all, we have a bunch of available wishes we can use to stack familiar XP, as well as the new boost from the Leprecondo. But without those wishes or the condo, we are in a much more tenuous place; runners who don't own the Cursed Monkey Paw or the Book of Facts will need every incremental experience source to boost the mimic. And +2 for combat isn't bad! To do a few relatively simple numbers...
To get the numbers for 11 summons rather than 11 copies, simply double the last two numbers in each bullet. Two things should immediately stand out, though. First, if you expend 1-2 wishes, TCB's familiar experience is paltry; it makes up such a small portion of your experience that you barely need it. Matters are a bit different for the "just Leprecondo" scenario; if you go for 11 summons rather than just copies, that saves you 18 familiar turns, which is about 0.75 turns if you convert that into most of a handful of split pea soup.
For most with full shiny sets, this is going to be about where you land. If you lack shinies but still have a hungry Chest Mimic to feed, you'll probably benefit most from the TCB; it is a massive boon if you lack other means to shove familiar XP into that monster. (It also synergizes with the Emberiza Aureola; TCB cuts the familiar turns needed for your yellow ray from 93 to 32, making it relatively straightforward to charge up in the 50-turn cooldown if you happen to be missing a Roman Candelabra. Nice!)
This one is -complicated-. I'll start with the main message I want to communicate in this section.
If you want an item drop, and you cannot cap it, TCB will virtually always be superior to any other piece of familiar equipment at getting that item. Ergo, you should have the TCB locked in during any part of your run where you are looking for uncapped items. Period.
If you take away nothing else from this section, take that away. Now that I've given you the core message, let's get to my favorite part: infuriatingly dense prose and diagrams aiming to prove and explain -why- the TCB is self-evidently valuable in those situations. Hooray, math! Everyone loves math!
Let's begin. Here is a table showing how much the TCB increases your effective chance of getting the drop.
This reveals one important fact: the TCB is most effective if you have a 50-50 chance of getting the item. This is somewhat intuitive, if you think about it; at >50% item drop, you are more likely than not to never encounter the 2nd roll at all, and at <50% item drop, the compounding probability does less work for you.
Having said that, it's worth emphasizing that a 25% increase in the "chance you actually get the drop" is extremely different than a +25% item drop modifier. Let's start by explaining the basic math. In the evil eyes example I gave above, when first describing the mechanic, you are going for an item at a 20% drop rate. If your item drop is +200%, then you have a 60% chance of getting the evil eye -- or, more aptly, a 40% chance of missing it. To calculate the probability you get a hit on one of your two evil eye rolls, you can measure the discrete probability of two failures by doing 1 minus P(MISS) to the 2nd power (since you get 2 rolls). That's (1 - (1 - .6) ^ 2) = 84%
-- 24% higher than the 60% chance of rolling it in just one roll. But if you have +350% item drop, and you already have a 90% chance of hitting the evil eye, those two rolls get you from 90% to 99%, just 9% higher.
Now that I've walked through how the math works, here's a more complex table that (hopefully) finishes the explanation in a more powerful, tangible way.
Here, instead of going with the final probability of an item dropping, we are showing the probabilities broken out by both your base drop rate (in the columns) and the bonus item drop % (in the rows). The orange column block gives you the probability you snag the item with one roll -- that's without the TCB. The teal block gives you the probability you snag the item with two rolls -- that's with the TCB. Then the yellow block represents the difference between those two numbers in terms of how the TCB impacts your raw chance to find the item, which is then transformed into the increase in your +item% that you would need to buff up with to achieve that corresponding increase in your chance to find the item.
Now that we've synthesized all this information together, a few things jump out as true:
Having said all that, there is an important caveat I have to give to this whole exercise. If you miss multiple items, the TCB reroll will be assigned randomly to one of the items missed. What this means mathematically is actually pretty complicated, but in effect, this neutralizes some (though certainly not all!) of the value that TCB gives you. A good rule of thumb for handling this is that you can divide the probability increase by the number of items you expect to miss. So, let's use the evil eyes example above; both the Spiny and Toothy variants in the Defiled Nook have a 10% drop rate item, and if you miss the 20% item drop, you will (probably) miss the 10% item drop; thus, instead of increasing from a 60% chance to an 84% chance at +250% item drop, you divide the +24% chance by two, for +12% chance, getting you from a 60% chance to a 72% chance. That's worth an extra 60% item drop rather than 120% item drop; still good, and better than any other familiar equip for getting the drop. But not quite at that super-high-power zone.
To put a finer point on it with an explicit example, let's approach the actual turns-saved impact in the Defiled Nook. Let's say that you can guarantee a +250% item boost, but no higher. You have some unlimited banish you can use on the party skelelton, so you'll only hit it once. You get 1 evil per monster, and 3 evil per evil eye drop you can snag. Without the TCB, you would expect the Nook's 37 evil to require (roughly) 14 kills; you'd expect just around 8 evil eyes (for 24 evil from the eyes) and 14 evil from the kills. However, with the TCB, you'd expect the Nook's evil to require 12 kills; you'd expect around 9 evil eyes (for 27 evil from the eyes) and 12 evil from the kills. That's an (expected) savings of 2 turns, which will go down as you increase the item drop you hit the nook with but go up as you have less and less item drop.
Overall, the TCB's item reroll is a bizarrely complicated tool that helps improve your runs probabilistically rather than in the explicit, measurable boosts that we often see with things like delay burn, free kills, and other discretely measurable effects. It is still useful, though. Here are the primary places that I'd expect it to save real turns for the intrepid speedrunner:
There are many tools in the ascender's toolbox to help with these drops. But the general gist of it is that the TCB is almost certain to save 1-2 turns on the ambient assistance it gives during some of the harder item drops in a run. The best way to think of it, in my view, is an always-on piece of familiar equipment that should be locked to your familiar any time you aren't capping a drop you have any desire to get. Luckily, you're almost always going to have it on anyway, which makes it a complex tool that's pretty easy to play with.
I'm not going to make a huge habit of doing this, but it is probably a good idea to mention the non-standard familiars whose equipment is particularly useful to snag with your TCB in the event you are doing an unrestricted speedrun. These are:
We'd rate the toy Cupid's bow a tier 3 IOTM. It is an IOTM that is -significantly- better the less shiny you are, cutting variance aggressively for players who have to contend with a lot of it. Still, at the highest shiny realm, I'd expect about half a turn saved by the familiar-specific equipment, a turn saved by the familiar experience, and 1-2 turns saved by the item drop reroll functionality. It's nowhere near the power level of most standard IOTMs these days, but it is a highly complex and very cool item with several novel effects, a few comfort features, and a rare familiar XP boost. Go to Mr. Store and buy it today!
... wait, it's March? Well, my wife and I welcomed a newborn a few days after this came out, so I will blame my daughter for this and move on to the next one. Surely it will be simpler to write than this beast!
... /checks Leprecondo OH DEAR GOD WHAT IS THIS