Path of Exile: Talisman Crushing

The current temporary league running in Path of Exile is called the Talisman league, and the new mechanic added for it is the addition of a new item type: the talisman. You can equip a talisman into the neck slot instead of an amulet. They have the twist that they're all corrupted, so you can't craft them in any way, but their implicit property is selected from a new pool of properties which are way more powerful than the normal amulet implicit properties.

These properties are divided out into 3 different tiers of talismans. The first tier are found sporadically on monsters out in the wild. There are also altars that can spawn which allow you to crush 5 tier 1 talismans into a tier 2 talisman. Or 5 tier 2 talismans into a tier 3 talisman. Or 5 tier 3 talismans into a portal to a challenge boss fight. Kill that boss and scoop up a tier 4 talisman which has two implicit properties!

The level of the resulting talisman is based on the average level of the talismans used as input, with a twist. The highest level one is worth 50% more than it should be worth, and the lowest level one is worth 50% less than it should be worth.

There's a challenge for killing the boss while the boss is at least level 80. The easiest way to make sure this happens is to just use 125 talismans which are all level 80. But that requires killing things in tier 11 maps at the very lowest. Is there a way to abuse the weird averaging to cut down on the number of 80+ talismans I need to find to do this challenge? One talisman is going to be the lowest tier 1 of the lowest tier 2 of the lowest tier 3. That means it's only going to be worth 1/8th as much as a true average talisman. One talisman is going to be the highest tier 1 of the highest tier 2 of the highest tier 3. It's going to be worth 27/8th as much as an average talisman, or 27 times as much as the lowest.

There's also the question of rounding... How does it work? Does a talisman remember decimal points, or is it rounded at each step of crushing? And is it rounded up, down, or properly?

If there is no rounding things are pretty straightforward. Getting a single higher level talisman is worth a ton. An 81 talisman lets your lowest level talisman fall all the way to 53! Unfortunately only one talisman can get such a big benefit. Here's a breakdown of the 125 talismans and how many points they could be worth:

Points	Quantity
1	1
2	9
3	3
4	27
6	18
8	27
9	3
12	27
18	9
27	1

I guess the way to think about it is you can earn points for each talisman above level 80 that you can spend to offset some underleveled talismans. The really common situations are going to be trading 12 points for 4 pointers, so assuming you can get a decent selection of 81s you can afford thrice as many 79s, or an equal number of 77s, or any such combination. But it feels like you really don't want to be using too many very low level ones. You get a lot of 79s, but once you dip down even lower you're paying a lot of points.


Can we actually discount rounding? How can we find out? I guess it's time for some quick testing...

Ok, things are now clear. I crushed 8 talismans (7 sets of tier 1s, 1 set of turn 2s) and things followed very simple rules. Rounding happens the way it should and decimals are not carried over.

This means you can gain or lose some levels depending on how you crush. Ideally you want to always be creating a level X.5 talisman, so it gets rounded up to X+1. Stay away from creating an X.4 talisman.

Adding on to the stuff above, we can shave off a full 5 levels from each 'lowest' talisman in a given transaction and end up in the same spot for free. Or a couple levels off of one of the middle talismans. And since the effects bubble forward, you can actually end up shaving an awful lot off of the talismans that get crushed into the lowest tier 3 talisman.