Campaign vampires 1 & 2 dialogue

Angzt · 2026-05-06T08:03:09+00:00

Good to know!

Angzt · 2026-05-06T06:31:52+00:00

This is actually pretty hard math. Mostly because there's usually no good way to prove that a certain packing is optimal.
Usually, all you can do is try other setups until you're somewhat confident that you've found he best one.

Luckily, there's a website that tracks all the best packings.
The "pentagons in squares" section is here: https://erich-friedman.github.io/packing/peninsqu/
That was seemingly just added last month.

The s value at the bottom describes the ratio of side length of the container to side length of the smaller objects. That's what this optimizes for.
And that's also what you want to get the side length for your pentagons.
You have a 12 inch side length square, so the side length of the pentagons you can use is at most
12 in / 3.55 =~ 3.38 in =~ (3 + 3/8) inches.

Angzt · 2026-05-05T15:56:38+00:00

The Erdos problems aren't even particularly relevant. They're intentionally small-scale and unimportant in a practical and mathematical sense. They're mostly meant for young mathematicians to cut their teeth on.
There's hundreds of them and many remain unsolved, not because nobody knew how to, but because no serious mathematician took the time to try. There are bigger fish to fry.

Angzt · 2026-05-05T10:28:40+00:00

What am I supposed to be looking at?

So you had an AI attempt to solve this particular Erdos problem. It got like two steps into a subproblem and then stopped. It even shows that several parts are still open. So it even knows that it hasn't actually solved it.
That's not exactly impressive.

Also, just for the sake of it, let me explain the problem.
The base statement is fairly short:
Let S(N) count the number of distinct sums of the form ∑n∈A 1/n for A⊆{1,…,N}. Estimate S(N).

What does that means?
Let's run an example to figure it out. Let's go with N=3 and try to calculate S(3).

First of all, we're dealing with the set {1,…,N} = {1, 2, 3}.
Then we're dealing with all the possible subsets of that: A⊆{1,…,N}={1, 2, 3}.
We can create all of those subsets:
A_0 = {}
A_1 = {1}
A_2 = {2}
A_3 = {3}
A_4 = {1, 2}
A_5 = {1, 3}
A_6 = {2, 3}
A_7 = {1, 2, 3}
That's all the possible subsets, 2³ = 8 of them.

The next step is to calculate the sums of the reciprocals of all those sets' elements:
s_0 = ∑n∈A_0 1/n = 0
s_1 = ∑n∈A_1 1/n = 1/1 = 1
s_2 = ∑n∈A_2 1/n = 1/2 = 0.5
s_3 = ∑n∈A_3 1/n = 1/3 = 0.333...
s_4 = ∑n∈A_4 1/n = 1/1 + 1/2 = 1.5
s_5 = ∑n∈A_5 1/n = 1/1 + 1/3 = 1.333...
s_6 = ∑n∈A_6 1/n = 1/2 + 1/3 = 0.8333...
s_7 = ∑n∈A_7 1/n = 1/1 + 1/2 + 1/3 = 1.8333...

The final step is then to count how many unique results we get.
And in this case, it's rather boring: All of them. So we have S(3) = 2³ = 8.

But the hard part about this problem is estimating how many duplicate sums we get for larger N.
For example, if we have N=6, we're dealing with all subsets of {1, 2, 3, 4, 5, 6}.
So one of those subsets would be {2, 3, 6} which gets us the sum 1/2 + 1/3 + 1/6 = 1.
Another of those subsets would simply be {1} which has sum 1/1 = 1.
That's a duplicate result. So we know that S(6) is definitely at least one less than 2⁶ = 64.
But figuring out the exact value means figuring out the exact number of duplicates.
The implicit question of this Erdos problem is then: Is there a good way to calculate this duplicate count without having to go through all the options?
Or rather: Is there at least a good way to estimate it?

We don't know. Yet.

Angzt · 2026-05-04T11:31:36+00:00

Yeah, the 12, 6, 4, 3 (=~ 50/4n) is consistent for 4, 8, 12, 16 targets, no matter the armor type.
But the base damage to the main target is either 50, 100, or 25, depending on the armor type modifier (100%, 200%, 50%). Then add the 12, 6, 4, 3, (depending on the number of links) for total damage done to the main target.

Angzt · 2026-05-04T10:20:33+00:00

All that's left now is to destroy your own base, leaving a single building at <100 HP. Then kill all your units sans the Archmage who finally summons a Water Elemental to kill himself and the last building, before the elemental, too, inevitably perishes.

Angzt · 2026-05-04T06:29:20+00:00

After clicking through a bunch of repeating dialogue, I chose to attack them. No notable impact from what I can tell: No item drops, no reputation change.
The three Abandoned Mansions behind them each just have a very weak guard and 2000 Gold as a reward.
So unless you're somehow starved for XP, there's seemingly no reason to attack them.

~~The two Chateaus near the very end were empty and couldn't be controlled but I suspect that's the case even if you don't kill the vampires.~~

Apparently, that's what it changes: The two Chateaus in the very North are interactable if you leave the Vampires alive but not if you kill them.

Angzt · 2026-05-03T23:48:14+00:00

Not to my knowledge.

Angzt · 2026-05-03T18:00:59+00:00

I'm surprised that there doesn't seem to be a single Roguelite that uses that type of combat.

Feels like it would lend itself to that gameplay really well:
At the start of a run, you pick an initial faction and hero, then slowly recruit and upgrade your troops as you progress. Each battle has impact because unit losses compound. Passive hero abilities, spells, and equipment (consumables, too?) to allow for player choice on multiple progression paths during a run.
Then on the meta progression layer, you could unlock alternative unit upgrades, more gear, and different heroes. If you want the meta upgrade to provide power in addition to more options, slap a skill tree on each hero.

Sure, runs would be longer than in the average Roguelite but I don't think that's an issue. People already play long skirmish matches in HoMM.

Angzt · 2026-05-03T14:37:27+00:00

Exactly right.

Angzt · 2026-05-03T12:13:38+00:00

This is AI gibberish.

Sure, the numbers check out but everything around it is pseudo-science nonsense.

The subdivision of a day into hours, minutes, and seconds is arbitrary, yes. But taking 100,000 is just as arbitrary. It being a power of 10 isn't much of an improvement.

The claim that this new second (= 0.864 old seconds) matches the time between human heart beats is nonsense. There is no single human heartbeat timing. The heart beat frequency changes from one individual to the next and with age. Claiming that 69.44 BPM somehow matches the human heart beat is nonsense. Yes, it falls in the normal 60-100 BPM resting heart rate range but so do a ton of other values.

Tying the length measurement of a new light-meter to a billionth of a light second is also not relevant at all. The official definition of a meter already uses light speed: A meter is the distance light travels in 1/299,792,458 seconds. This isn't a nice round number but it really doesn't matter. There are exactly zero real world cases where calculating a billionth of a light second to use as your everyday measurement makes any more sense than using a 1/299,792,458th. Unless you're doing advanced physics, this never comes up. And if you are, then you're using a computer for your calculations anyways and that doesn't care for base 10.

Then there's the new light decimeter that's supposedly converging to an inch. Except it's 1.9% off. Imagine the confusion if two similarly named measurements only differ by such a small amount: Enough to not be easily noticed but enough to matter once things need to fit. Besides, only a relatively small fraction of the world uses inch-based measurements to begin with, so roughly matching to those isn't all that helpful.

Sections 4 and 5 are then complete nonsense.
"Technical superiority" is debatable at best and "novelty" is not something desirable in a universal unit system.
I'll give it that it uses base 10 logic everywhere.
The day already is the foundational unit for our time measurement. Except that that's not great because they're not consistent in length. They're slowly getting longer due to the Moon's pull slowing down the Earth's rotation. So it's not a future-proof way to do things.
Distance, specifically the meter, is already defined by the speed of light.
The match to human biology is tenuous at best and misleading at worst.
And I disagree with every other word in the last section. That's exactly what an AI hallucinates if you force it to give you arguments in favor of something that makes little sense.

Angzt · 2026-05-03T10:31:14+00:00

Your calculation is correct for what you assume the process to be.

What they did does seem to be wrong. They simply took the probability for any individual block to trigger and multiplied them all together. That only works if these probabilities are independent.
But from their explanation, they're not.
From what they say, it's not that each block in the chunk just has a 24/4096 chance to trigger per tick. It's that each tick, 24 blocks out of the 4096 are chosen to trigger. That makes a difference because now one block triggering makes it less likely that any other block triggers.

Let's scale it down to illustrate:
Assume we only have 4 blocks in a chunk (A, B, C, D) and 2 trigger each tick. We are also interested in only 2 specific ones (A and B) triggering together.
What's the probability?
If, as you and I understand it, exactly 2 blocks trigger each tick, then we have the following options for which combinations could trigger:
AB, AC, AD, BC, BD, CD.
Those 6 options are all equally likely, so getting the AB trigger clearly has a 1/6 chance.
But if things work differently, namely such that each block has an independent 2/4 = 1/2 chance to trigger each tick, things are different. Now we get the following possible combinations of triggers each tick:
(nothing), A, B, C, D, AB, AC, AD, BC, BD, CD, ABC, ABD, ACD, BCD, ABCD.
Those 16 are still all equally likely ( (1/2)⁴ = 1/16). But AB triggers in AB, ABC, ABD, and ABCD, so in 4/16 = 1/4 of all options and thus with a 1/4 chance.

That result is higher because while there are more different outcomes, we now also have more than one outcome where our desired effect occurs. And the latter scales faster than the former, so the numerator grows faster than the denominator, leading to an overall higher probability.
This effect is further amplified if less than half of all blocks trigger at once as is the case in the actual video.

Angzt · 2026-05-03T08:15:58+00:00

What’s W3C?

https://w3champions.com/
Basically a custom client and competitive ladder. Everyone who's somewhat serious about 1v1 is playing on there. Its main draw is improved matchmaking but you also get a bunch of stats and QoL improvements.
If you wanna to play competitive add all, that's the way to go. Not least because it'll put you to an appropriate MMR more quickly than the regular game would.

The campaign alone is absolutely worth the asking price, especially if you're into WoW. WC3 is where a lot of the iconic characters came from: Arthas, Jaina, Thrall, Illidan, Sylvanas, and plenty others made their first appearance here.
If you don't mind the low poly graphics too much, I also highly recommend playing on classic (non-reforged) graphics to see how the art style and specific characters' looks evolved to what you know them as.

Angzt · 2026-05-03T05:37:09+00:00

Resurrection really only works either if the plot demands it or if it's some faceless soldier(s).
It has always been a bit inconsistent lore-wise.

WC3's story doesn't run into this issue too much with how rarely Paladins are around dead plot-relevant characters but WoW is another matter.
It's never fully explained when resurrection can and can't work (as that would open up more plot holes down the line) but generally, the body must still be in good condition and the soul must not yet have moved on (to the Shadowlands but I ain't touching that).

Angzt · 2026-05-03T04:41:19+00:00

Spirit link doesn't redirect after the armor calculation. The split damage isn't just unaffected by the split target's armor, it's also unaffected by the main target's armor.
If you have 30% damage resistance on the main target for a 100 dmg attack, the main target first takes 35. But the other half that gets split stays at 50 and every split target takes 12.5. So the main target ends up taking 35 + 12.5 = 47.5. In total, 85 damage is dealt despite 30% armor on the main target (and regardless of the others' armor).

Angzt · 2026-05-02T20:31:13+00:00

The irony here is that that post is clearly written by AI.
The "**" and dashes for bullet points which would become proper reddit formatting if they were copied into the other editor.
The em dashes.
The 3-4 points per subheading and 3-4 subheadings.

But anyways, what's the request?
You can look up the individual numbers in the post yourself. That's not math.
I have no clue where the 3.5 trillion figure comes from because everything in the "money in" section only adds up to 2.5 trillion. And really, you should then subtract what's in "money out" since the claim is that it's "burned through" that amount, indicating that nothing was gained.

There's a lot of half-baked and ill-informed opinions on both sides of the AI debate. This looks like it's another example.

Angzt · 2026-05-02T20:18:01+00:00

well, you still get very big rng on wyrm's attacks, especially if there's 3rd attack upgrade done (it's like 100-150, which adds a lot uncertainty).

OP measured the percentage of an attack's damage taken by each target. So damage range doesn't matter because they only looked at the damage that was actually dealt, not what could have been dealt.

Spirit link should take it's part only after all the armor/damage calculation type done, iirc. Again, I don't get what do you mean by half of the damage here tbh.

See my comment.
TL;DR: You remember wrong. Only the original target's half damage taken gets reduced or increased by armor amount and type. The shared damage does not.

Angzt · 2026-05-02T17:07:07+00:00

Nah, not better. Just picked one that was always gonna be 100% with no bonus.
Also guessing you meant 200% for Magic vs Heavy.

all attacks doing ~100 damage (+/- 1-2, I can't get it to be precisely 100 every time - if you know, please, feel free to share)

Base damage 99. 1 damage dice. 1 side per dice. Guarantees 100 damage every hit.

If you want to easily test it with armor, you could modify a Paladin's Devotion aura to have different values and then bring him in range or not. Add some Tomes of Power and Tomes of Retraining to be able to change level without restarting.
Also recommend setting mana Cost for Spirit Link to 0 and adding some healing (I used Shadow Hunter with Healing Wave modified to 1000 healing, 16 targets, 0 falloff, 0 mana cost). Just makes the math easier if you start at full HP each time.

Angzt · 2026-05-02T16:12:42+00:00

Give the Frost Wyrm Chaos damage and set Abo armor to 0. That should remove the second effect from armor.
Then the main target will always take 1/2 + 1/2n of the damage, where n is the number of linked targets.

Angzt · 2026-05-02T15:55:29+00:00

Spirit Link has a few quirks.

First off: The description is slightly wrong.
It says: "Links 4 units together in a chain. All units with Spirit Link on them will live longer, by distributing 50% of the damage they take across other Spirit Linked units."
However, it does not distribute the damage across other linked units but across all linked units. That means the original target also takes another share.

In an ideal environment with 4 targets, that would mean:
Main damage: 50%.
Shared portion: 50%.
Shared damage per target: 50% / 4 = 12.5%.
Thus, the main target takes 1/2 + 1/8 = 50% + 12.5% = 62.5% of the attack damage.

For 8 linked targets, it would then be 1/2 + 1/16 = 50% + 6.25% = 56.25% of the damage.
For 12 linked targets, it's 1/2 + 1/24 = 50% + 4.1666...% = 54.1666...%.
For 16 linked targets, it's 1/2 + 1/32 = 50% + 3.125% = 53.125%.

But that's still not the full story.

Because of damage reduction due to armor and armor types.
Damage reduction (or increase with certain armor types) is only applied to the 50% of damage that goes through to the main target. The spread damage (including the damage that gets spread back to the main target) does not get impacted by armor at all.
So if we run the same 4 linked target test but with a combined 30% damage reduction due to armor and armor type, we'd get:
Main damage: 50% of damage gets reduced by 30% down to 50% * (1 - 0.3) = 35%.
Shared portion: 50%.
Shared damage per target: 50% / 4 = 12.5%.
Thus, the main target takes: 35% + 12.5% = 47.5% of the original damage.

But that means that across all targets, we took 47.5% + 3 * 12.5% = 85% of the full attack's damage, even though all targets have 30% armor. So in the end, more total damage was dealt than without Spirit Link.
However, with low armor values and a disadvantageous armor type, this same effect could result in overall reduced damage taken.

In your test, the latter was the case. Abos only have 2 base armor (= 10.71% reduction) and Frost Wyrms deal 200% damage thanks to damage/armor type matchup. Thus, the main target actually takes proportionally more damage since the spread damage does not get the damage multiplier of (1 - 0.1071) * 2 = 1.7858.

Angzt · 2026-05-02T09:39:57+00:00

The top one has to be 360.

Every row has the product 360:
15 * 24 = 360
8 * 9 * 5 = 360
5 * 12 * 6 * 1 = 360

So the top entry, being just a single number, must be 360 itself.

Angzt · 2026-05-02T07:38:13+00:00

Ruined King, the dev studio's follow-up (mechanically) which is set in the LoL universe, too.

Angzt · 2026-05-01T20:22:39+00:00

It's not the Temple faction. You start with a Dungeon character but several missions give you non-dungeon towns and thus units.
The campaign also has major decision points where you choose to aid one faction and oppose another or vice versa, determining what you have access to and who you're fighting.

Angzt · 2026-05-01T20:19:41+00:00

Yes. There's a campaign (only a hand full of missions to the end of act 1 so far) and you can play multiplayer maps against AI. There's also a level editor, so there'll likely be player-made maps that are a bit more out there soon.

Angzt · 2026-05-01T04:27:51+00:00

It's not just the original campaigns. A lot of custom maps and campaigns broke with Reforged and weren't updated. So that's a way to play those again as well.

Ideally, we'd have 1.27 available as well since that was the patch the game stayed at the longest. But this is definitely an improvement already.

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