Map Management Resource

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Budget_player_cadet wrote:

So uh... I just got this:

...Is that worth running as-is, or should I ID and try to roll it higher?

Flapdrol is correct, follow his advice. Scour and chisel that Bazaar. Chaos spam until you find yourself with a Bazaar with:
-30%+ Larger / 30%+ Packsize
-Magic/Rare/Undead/Bandits
-70% quantity.

This wall is where I'm standing in the path of map science now :)

Adjusted IIQ = (100 + Q) * ((1 + kL * L) * ((1 + kS * S / 100) ^ kpS) * ((1 + kP * P / 100) * (1 + kM * M / 100) * (1 + I / 100) + kR * R / 100) + kB * B) - 100

Q = map IIQ (including quality)
L = 0, 1 - a maze or not a maze
S = 0, 20-50 - larger area
P = 0, 20-50 - pack size
M = 0, 20-50 - more magic monsters
R = 0, 20-50 - more rare monsters
B = 0, 1 - twinned boss
I = 0 or some multipliers for inhabitation prefixes (may be -15 for goats, +15 for undead and +20 for bandits)

kL = maze multiplier - assuming 1 for testing purposes (doubles everything but boss)
kS = area size multiplier - assuming 2 (that is multiplied by 35 on average, resulting in 1.7 multiplier)
kpS = area size power - I don't know how larger area works exactly. If it enlarges both linear "length" and "width", then 1.2-1.5 improvement should be squared and kpS = 2. Assuming 1.
kP = pack size multiplier - assuming 0.6 (that is multiplied by 35 on average, resulting in 1.21 multiplier)
kM = magic monsters multiplier - assuming 0.4 (that is multiplied by 35 on average, resulting in 1.14 multiplier)
kR = rare monsters multiplier - assuming 0.3 (that is multiplied by 35 on average, resulting in 1.105 multiplier)
kB = boss multiplier - assuming 0.1

Most of these values (at least kL, kS, kP) differ from map to map. I assume some arbitrary numbers based on previous discussion for testing purposes.

The formula reflects the ideas that boss loot is not affected by anything but IIQ and twinned prefix and that pack size improves number of magic monters but not rare monsters.

Any comments on the formula and multipliers? Is maze value really that high that single mod blue maze equals 100 IIQ map without a maze? And it can be multiplied by pack, magic monsters and bandits values, all as "more", not "increased".

I'm slowly developing a tool we were discussing. For now it generates all possible maps and calculates adjusted IIQ distribution. It is buggy and slow as hell. I have some ideas and is going to try them in the weekend. The main idea is to calculate probabilities for all possible combinations of Q, L, S, P, M, R, B, I, store them in file, and then use them with different multipliers and formulas. For 20-50 "all possible values" will be limited to 0 and 35 and may include 50 for divined maps. The main issue is that I don't know how mods are generated in game, so my model is not accurate. Not sure if anyone is interested in discussing this "model".

Aight, thanks for the tips. Ended up selling it to Laz for an ex, as I am really low on currency atm.

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SunnyRay wrote:

Any comments on the formula and multipliers? Is maze value really that high that single mod blue maze equals 100 IIQ map without a maze? And it can be multiplied by pack, magic monsters and bandits values, all as "more", not "increased".

I'm slowly developing a tool we were discussing. For now it generates all possible maps and calculates adjusted IIQ distribution. It is buggy and slow as hell. I have some ideas and is going to try them in the weekend. The main idea is to calculate probabilities for all possible combinations of Q, L, S, P, M, R, B, I, store them in file, and then use them with different multipliers and formulas. For 20-50 "all possible values" will be limited to 0 and 35 and may include 50 for divined maps. The main issue is that I don't know how mods are generated in game, so my model is not accurate. Not sure if anyone is interested in discussing this "model".

Yes. Labyrinthine/Massive is unquestionably mandatory. Its effectiveness varies per map unfortunately, so you will have to factor this into your calculations.


I look forward to your results.

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...generates all possible maps...
...main idea is to calculate probabilities for all possible combinations of Q, L, S, P, M, R, B, I, store them in file...

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buggy and slow as hell

What'd you expect, mate? Just a quick look at the formula shows nothing obviously wrong (I'm a bit busy here, can't take the time to work out details, sorry!) so I'd recommend first improving your algorithm.

I'm 100% sure that it is NOT NECESSARY to generate all possible maps, though doing so is the easiest way to code it. More efficient algorithms left as an exercise to the reader, sorry again, work calls. For an application such as this, I imagine it begins with the choice of programming language or software, what are you using?

I don't even play Path on weekdays any more, and won't for a while. Hats off to people who have both the time and the skills to do such things for the community.

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Kirielis wrote:

I'm 100% sure that it is NOT NECESSARY to generate all possible maps, though doing so is the easiest way to code it. More efficient algorithms left as an exercise to the reader, sorry again, work calls. For an application such as this, I imagine it begins with the choice of programming language or software, what are you using?

It's a difficult exercise, you know, with factors like "3 prefixes max" and 895 prefixes and 746 suffixes (not equal!) in statistics.
Bugs will be hunted, nothing to worry about here.
Programming language is C# for simplicity, can be ported to C++ for performance or Java for portability in future.
I have a work too so maps have to wait 3 days more. Nothing to discuss besides the formula really until I have some real results.

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SunnyRay wrote:

This wall is where I'm standing in the path of map science now :)

First reaction: wow!

My detail comments:
1) maze should be 0.9 instead of 1, as it does not double the boss, and twinned assumes the boss to be 0.1
2) there should also be an I multiplier for skeletons (which is different from undead). I also suspect sea witches to be worse than normal, but am not sure.
3) there are good mazes and bad mazes, where good mazes are about 0.9 and bad mazes an estimated 0.3
Bad Maze: Underground Sea, Mine, Underground River
Good Maze: Temple, Arachnid Nest, Torture Chamber, Waste Pool, Cells, Maze, Necropolis, Crema, Shrine, Shipyard. At this moment we only look at Good Mazes (there are more of them and they are more important)

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SunnyRay wrote:

The main issue is that I don't know how mods are generated in game, so my model is not accurate. Not sure if anyone is interested in discussing this "model".

I am interested in discussing it

Your model is more accurate than we have now. That it is not accurate is OK:
1) many inaccurate assumptions and numbers will go into it
2) right now we don't even know very basic questions like the examples in the next point.
3) after it is done it will have to be abstracted again to come to decision rules that humans can use (not everyone will want put 8 values in an app to see whather it needs to be rerolled, they just want to know: should I reroll:
-Necropolis Maze with no pack/twin/magic/rare and IIQ of 50%
-Cells of 50%, +packsize, +rares and +magic but no Maze
-Gorge of 120% but no other modifiers

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Flapdrol wrote:

1) maze should be 0.9 instead of 1, as it does not double the boss, and twinned assumes the boss to be 0.1
...
3) after it is done it will have to be abstracted again to come to decision rules that humans can use

Ok, let it be 0.9. It is a test value, real application will need different multiplier presets for different maps, may be customizable. Something like 1.7 for Temple etc.

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Flapdrol wrote:

2) there should also be an I multiplier for skeletons (which is different from undead). I also suspect sea witches to be worse than normal, but am not sure.

A lot of values we'll need to set up. I had in mind the same 1.15 multiplier for undead and skeletal and zero effect for sea witches, ranged monsters and multifarious. Should I use 0.95 for sea witches? What is better, undead or skeletal?

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Flapdrol wrote:

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SunnyRay wrote:

The main issue is that I don't know how mods are generated in game, so my model is not accurate. Not sure if anyone is interested in discussing this "model".

I am interested in discussing it

I'll try to describe it then. This is about math and algorithm, but not about actual code.

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SunnyRay wrote:

Ok, let it be 0.9. It is a test value, real application will need different multiplier presets for different maps, may be customizable. Something like 1.7 for Temple etc.

I quibble a bit on maze becaue it is the single biggest factor. For the rest I firmly believe that reasonable estimates are good enough.

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SunnyRay wrote:

The first step is more about research and less about usability. The research itself will hopefully give some answers. Then we'll see if that answers seem correct or not, and either proceed to the step two or look for a better model (or better researcher :) ).

Agreed. I just wanted to point out that we will lose accuracy down the road, so making it hyper-accurate to start with may not be useful.

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SunnyRay wrote:

A lot of values we'll need to set up. I had in mind the same 1.15 multiplier for undead and skeletal and zero effect for sea witches, ranged monsters and multifarious. Should I use 0.95 for sea witches? What is better, undead or skeletal?

It may be undead, since this will automatically cause a large number of necros to appear who tend to be blue/yellow quite often. Forget what I said about skels and witches, unless Lyralei has some input.

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SunnyRay wrote:

The main value I use is "Total" column in Kripp's(?) file.

Have you guesstimated "Monster skils chain" and "chilled ground" in? Are there more (I think not)?

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SunnyRay wrote:

All 4-mod map probabilities are then multiplied by 7/12, 5-mod by 4/12 and 6-mod by 1/12.

Question: Are there maps with 3 prefixes and 1 suffix? Or 1 prefix and 3 suffixes? Or is it always 2-3 suffixes+2-3 prefixes?

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SunnyRay wrote:

There is a negative effect of this. I have to generate the same map multiple times with different mod orders, getting huge performance drop. When I tried to generate each set of mods once and then multiply by factorial, I realized that probabilities of different orders are different in my model.

I may be *way* off (a pity Scrotie won't set me right), but if I generate only maps in "sorted" order why would my result be different?

So in my generation process I assume that once I have chosen prefix 2 for a map as first prefix, I can then only add prefixes with 3 and higher to that map, since the case with prefix 1 is already covered when I generated the maps that started with prefix 1.

So when you start with prefix 2, you remove prefixes and 1 and 2 from the list of prefixes, normalize the sum of probabilities of the remaining prefixes to 1 and redo. So you would only generated maps that are sorted.

It may well be that the probs no longer add up to 1, so you have to normalize them to 1.

WARNING: probably some statistics PhD will give a devastating counter-example. It may well be worth it to do this with a very small subset and see if the numbers come out the same in both cases.

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SunnyRay wrote:

The model does not include "expected number of chaoses to roll a better map", but this addition is relatively easy.

I still don't know how to exactly formulate this. I have to reread what Scrotie wrote and think.

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Flapdrol wrote:

Have you guesstimated "Monster skils chain" and "chilled ground" in? Are there more (I think not)?

I used chaining = splitting (48), of ice = of fire (76). A guesstimation that may be way off. It's also possible that introduction of 'of ice' reduced frequency of 'of fire', and they are both 38 now.

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Flapdrol wrote:

Question: Are there maps with 3 prefixes and 1 suffix? Or 1 prefix and 3 suffixes? Or is it always 2-3 suffixes+2-3 prefixes?

I was sure 3+1 is possible, need confirmation.

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Flapdrol wrote:

I may be *way* off (a pity Scrotie won't set me right), but if I generate only maps in "sorted" order why would my result be different?

First I coded it as you describe (without normalization, because I wanted a fair 1 as a proof that I'm doing it right). Then I saw strange numbers. Then I came up with this example:

Imagine PoE with only 2 map prefixes (p1, p2) and 1 map suffix (s1).
Transmutation has 3/4 to roll 1 mod and 1/4 to roll 2 mods.
We've got 30/30/40 total quantity of mods.

I roll p1 with probability 30/100=0.3, then roll s1 with probability 1, product is 0.3.
I roll s1 with probability 40/100=0.4, then roll p1 with probability 30/60=0.5, product is 0.2.
Then I divide these numbers by 4.

If I generated p1 first, I would get 1.5 times more p1s1 maps than if I generated s1 first. Normalization wouldn't change that. Clearly, the order I put mods in my app should not affect outcome.

Something is still wrong... When I roll s1 first, I think its probability is 0.4, but it's actually 1 for two-mod maps. This may be what I was doing wrong, not generation of sorted maps. Something to think on. I'm not PhD unfortunately, I abandoned my thesis years ago.