Pop growth in 4.0 strongly benefiting gestalts or am I confused? (Solved: Indeed I was confused, it does not, details inside, if you want to check)

[Ilab]

EDIT: It was proven here: Explanation 1 and here: Explanation 2 that my logic was incorrect. So, if you have/had the same doubts as me, go check those threads for some evidence.

For a summary: while the non gestalts might have higher variance they do not significantly lag behind gestalts (or ahead) and are on par, and even in cases when one exceeds the other, the differences are negligible enough that even if one nation is lucky at the end the difference in pops is very small to really matter.


Hi,

I was thinking about this a moment ago and noticed something. If my understanding is correct (which I will briefly explain as it is the basis of the entire post) this is how (summarized) pop growth works:

• growth is calculated based on a certain formula
• the total growth is given to pop groups in a proportional matter, that is, bigger pop groups receive more
• fractional pop growth is not added each month, so if a pop group has 0.5 growth it has a 50% chance to grow 1 pop

What does this entail? Well, 2 example that should be self explanatory:

An individualist empire with 3 species can have for each species several pop groups depending on strata, ethics and factions. Lets assume that each species has 5 pop groups. That means that on a specific planet, you get 15 pop groups in total. Then, lets say that you get 5 total growth. Since it is split among pop groups, each group will get a proportional amount. However, since there are so many pop groups, it is likely that the amounts that each receives (except perhaps for the larger groups, if any) is below 1, and thus proportional. Meaning that pops only have a chance to grow.

On a gestalt, however, pop groups are usually smaller since they have one less strata, no ethics and no factions. So even a hive mind with several (3 to be consistent with the above example) species (not common, but not impossible) instead of having 15 pop groups will only have 6 groups. This means that when receiving the 'growth split' (assuming the same 5 for simplicity) it is much less likely that several groups receive less than 1, and those that do, should not receive tiny numbers.

If this logic is correct, the difference is huge!

You might think that in the end it does not matter, as over a large period of time the fractional growth will tend towards the expected growth, right? Not exactly.

There are some issues. First, a pop that grows will further influence the growth of the group, it can also start to work right now and not in X months. That same pop might start working an assembly job for instance, giving an immediate benefit that compounds.

So, no, the fractional pop might seem ok, but if you get a pop 3 months later, not only I benefited from a pop for 3 months earlier, but that pop also contributed to the economy and the growth itself during that time, potentially making it so another pop can grow.


This means that nations with few pop groups, and specially gestalts, should have a much better growth. If I am incorrect in something, please someone correct me and explain it to me. If I am correct though, this needs to be addressed somehow.

 

[mergele]

I do not understand why you assume that having many low percent chances would be less than having a few high perctages or eve 1 guaranteed. 10 times 10% is statistically over a large number of cases identical to 1. Sure, having more earlier does snowball somewhat, but there is no reason the safe one should be the one charging ahead. 10 times 10% giving you 10 on the first try is equally likely as giving you 0.

 

[aadf97799c]

assembly are far stronger than growth at early game

predator seem to be the only one can get decent growth at mid game

 

[Ilab]

I do not understand why you assume that having many low percent chances would be less than having a few high perctages or eve 1 guaranteed. 10 times 10% is statistically over a large number of cases identical to 1. Sure, having more earlier does snowball somewhat, but there is no reason the safe one should be the one charging ahead. 10 times 10% giving you 10 on the first try is equally likely as giving you 0.

Because it is? You (and I on my post) explained it somewhat similar.

A 10% chance is. in the long run, equivalent. yes.

The issue is that, theoretically you would need to wait 10 months to get a pop. If another empire gets a pop during that time, not only does that pop contribute towards the economy earlier (snowballing among other things) but actually contributes towards further pop growth, since the population matters for growth. It is specially important if said pop takes a job that increases growth somehow, either by increasing habitabilty, assembly or giving some growth bonus.

So by the time that you, statistically, have the extra pops, I not only have said pops, but more because those pops contributed towards growth (and the economy) earlier.

Keep in mind that a gestalt has very few pop groups, while an individualist will have several. So this is not just a tiny difference, we are talking that the difference in pop groups can be of multiples of 2 or 3 under normal circumstance, in some cases more and rarely less.

So yeah, distributing a certain amount of growth between a lot of pop groups can leave most of them with fractional growth, and a tiny amount at this. Imagine having 0.1, that is waiting 10 months. While if a gestalt instead gets 0.3 that is about 3 months.

You might think it is ok, but over a long period of time, that gestalt would grow MORE than 3 times more pops than you, and that is assuming the same growth, which is unlikely as gestalts (specially hive minds) usually grow faster. Why? Because at 3 months they alredy got 1 pop, another 3 months later, and another 3 months later. by the time you got your first one, they not only have 3 more pops, but they also contribute towards pop growth more.

And yes, the numbers are made up, but with equivalent values in mind, so the hive mind in this example is not growing because of better groups itself, but only because of its groups. Not clear yet? An example:
Imagine that both have 5 pop growth. The individualist has a total of 15 groups, while the hive mind has a total of 3. Imagine that all groups are equally sized to make the math simple.
Each gestalt pop group gets: 5 (growth)/3(pop groups)=1.6666.
Each individualist pop group gets: 5 (growth)/15(pop groups)=0.3333

So, what happens is that, each pop group in the gestalt will grow at least 1 pop each month, with a chance for another one. While in the individualist nation each pop will grow around every three months. Overall it might seem the same. Except that for the gestalt, since the pops are guaranteed, not only will they produce earlier, but also contribute to growth. So after a few months, the gestalt growth wont be 5, but instead 6, rapidly outpacing the individualist. This is the issue. See how, even though they had the same growth, the gestalt rapidly outperformed.

 

[Abdulijubjub]

I do not understand why you assume that having many low percent chances would be less than having a few high perctages or eve 1 guaranteed. 10 times 10% is statistically over a large number of cases identical to 1. Sure, having more earlier does snowball somewhat, but there is no reason the safe one should be the one charging ahead.

Yes.

There's no reason to assume that a guaranteed 1 will average any better than 10 instances of 10%. On average they will be the same (assuming it's done correctly).

10 times 10% giving you 10 on the first try is equally likely as giving you 0.

No.

0 has a (9/10)^10=34% chance. 10 has a (1/10)^10=0.00000001% chance.

0	1	2	3	4	5	6	7	8	9
34%	38%	19%	6%	1%	0.1%	0.01%	0.0009%	0.000004%	0.0000009%

---

Growth does massively favor gestalts, but not for this reason.

Hives get Spawning Pools, letting them spam colonies for a flat +2 growth per planet (like 3.14 empires), and use that to jump start their growth on the planet. And machines of course can assemble full speed regardless of population on the planet, so they just ignore the logistic growth system entirely (though it's so much less profitable for them that they're better off not spamming those colonies unless they have no other avenues for resource investment).

Individualists can get a bit of that for themselves with Clone Vats and Robot Assembly Plants, but those take tech.

 

[Abdulijubjub]

The issue is that, theoretically you would need to wait 10 months to get a pop. If another empire gets a pop during that time, not only does that pop contribute towards the economy earlier (snowballing among other things) but actually contributes towards further pop growth, since the population matters for growth. It is specially important if said pop takes a job that increases growth somehow, either by increasing habitabilty, assembly or giving some growth bonus.

So by the time that you, statistically, have the extra pops, I not only have said pops, but more because those pops contributed towards growth (and the economy) earlier.

This making a mountain out of a molehill. A single extra pop contributes 1/400 growth per month, times planet capacity penalties. So it's around 1/500, or 0.002.

Suppose one empire G has a 100% chance of getting 1 pop, and another N has a 10% chance of getting 1 pop for 10 different pop groups.

~1/3 of the N will roll 0. ~2/5 of the time it will roll 1. ~1/5 of the time it will roll 2. ~1/16 of the time it will roll 3.

Month 1: G grows 1 pop, N gets unlucky and gets no pops
Month 2: G grows 1 pop and has a 0.2% chance of growing a second pop (but doesn't). N gets unlucky again.
Month 3: G grows 1 pop and now has a 0.4% chance of growing a second pop (but doesn't). N gets lucky and rolls 3 pops (about half as likely as rolling two 0s in a row).
Month 4: Both empires have equal pops again.

In the mean time, G got an extra 0.6% chance of rolling an extra pop. But that chance is so tiny that it doesn't substantially change anything.

By definition, ten 10% chances will average the same outcome as one 100% chance. Sometimes it will be behind, sometimes it will be ahead. And while it's behind/ahead, technically that lead will compound... but 1 pop is 0.002 growth.

The law of large numbers kicks in before a one pop lead (on either side) has any meaningful effect.

 

[jedavis]

machines of course can assemble full speed regardless of population on the planet, so they just ignore the logistic growth system entirely (though it's so much less profitable for them that they're better off not spamming those colonies unless they have no other avenues for resource investment)

In terms of the pop-years spent on replicator/roboticist jobs in exchange for future pop-years, right?

 

[Abdulijubjub]

In terms of the pop-years spent on replicator/roboticist jobs in exchange for future pop-years, right?

Exactly. That, and colony ships/empire size. Colony ships are expensive in the early game.

500 energy, 200 alloys, 1 year of building time, 1 year to fly to the planet (it's ~6 months per system crossed in the early game, ~3 months per system later), 2 years to establish the colony and get 100 pops, 6 years to build the next 100 pops and fill up all your replicator jobs, and only then start making pops which actually do some work (after you've now invested 10 years, ~600 energy, and 300 alloys). And you've taken on additional empire size to do so.

You can move in 100 pops to skip that 6 years, but that's just compressing the timeline: you're still paying ~8 years of 100 replicators output and 100 alloys; you're just spending it on another planet.

And of course, the standard comparison for choosing to work a replicator job applies: it takes around 100+20+30=150ish pops of early game replicator, fabricator, and mining drone jobs to run 100 replicators. It takes 140 months (12.5 years) for them to replace themselves, then another 12.5 years for them to pay pack the resources you invested (or missed out on by not having the replicators work another job), and only then do you start turning a profit. The timeline looks better than in 3.14 (building pops continuously makes assembly much better), but it's still a long payoff time before you throw in the 10 years and ~1500 energy just to get things up an running in the first place.

You can choose to spend those resources. And having that option is one of their strengths. But you shouldn't always choose to exercise it (especially if you'd be colonizing planets with 50% habitability on which your pops, including replicators, will be 25% less effective).

By contrast, spawning drones are 2x as effective and also make amenities (while your pops also get passive growth). Spawning drones jump start free growth rather than being the only way to make new pops. And 100 pops working as Spawning Drones pay for themselves immediately, rather than in 25 years, because they're doing double duty as an improved maintenance drone (though that comparison does ring a bit hollow if a planet exists purely to assemble pops, and the amenities aren't really providing for any working pops).

---

Colonizing has a cost.

There was a post a few weeks ago where someone had colonized ~10 planets in the first 25 years, and was complaining that their research was too slow... after they'd almost doubled their empire size and spent nearly 15k energy equivalent on colony ships/assembly just to get another ~500 actual working pops by the end.

Granted, they'd set up their economy to skyrocket from then on (as they now had infrastructure build and pop printers running on 10 planets), but it came at a cost.

 

[Ilab]

I do not understand why you assume that having many low percent chances would be less than having a few high perctages or eve 1 guaranteed. 10 times 10% is statistically over a large number of cases identical to 1. Sure, having more earlier does snowball somewhat, but there is no reason the safe one should be the one charging ahead. 10 times 10% giving you 10 on the first try is equally likely as giving you 0.

It is just what you said. Yes, over a large period of time they 'technically' even out.

The issue is that the guaranteed pops can, among other things, start to contribute towards logistical growth earlier. So those pops might start to contribute more pop growth than the ones that might come several months later.

That is why delayed growth matters, because this is a positive feedback scenario.

 

[Ilab]

Yes.

There's no reason to assume that a guaranteed 1 will average any better than 10 instances of 10%. On average they will be the same (assuming it's done correctly).

There is.

The guaranteed pops will, among other things, contribute to logistcal growth earlier. Those guaranteed pops help push the formula higher and increase growth, which eventually scales. So yeah, technically they are the same, except that this is a positive feedback system.

No.

0 has a (9/10)^10=34% chance. 10 has a (1/10)^10=0.00000001% chance.

0	1	2	3	4	5	6	7	8	9
34%	38%	19%	6%	1%	0.1%	0.01%	0.0009%	0.000004%	0.0000009%

---

Growth does massively favor gestalts, but not for this reason.

There are many reasons why growth is better for gestalts, but this post is only about the impact of pop groups, in fact, it applies to all nations. A nation with several species and ethics will have more pop groups that one with less species and ethics for example. It is just that gestalts have a guaranteed reduced number of groups since they have 1 less strata, no ethics and no factions.

Hives get Spawning Pools, letting them spam colonies for a flat +2 growth per planet (like 3.14 empires), and use that to jump start their growth on the planet. And machines of course can assemble full speed regardless of population on the planet, so they just ignore the logistic growth system entirely (though it's so much less profitable for them that they're better off not spamming those colonies unless they have no other avenues for resource investment).

This is true, but not the point of this thread at all, only the impact of pop groups.

Individualists can get a bit of that for themselves with Clone Vats and Robot Assembly Plants, but those take tech.

 

[Ilab]

This making a mountain out of a molehill. A single extra pop contributes 1/400 growth per month, times planet capacity penalties. So it's around 1/500, or 0.002.

Suppose one empire G has a 100% chance of getting 1 pop, and another N has a 10% chance of getting 1 pop for 10 different pop groups.

~1/3 of the N will roll 0. ~2/5 of the time it will roll 1. ~1/5 of the time it will roll 2. ~1/16 of the time it will roll 3.

Month 1: G grows 1 pop, N gets unlucky and gets no pops
Month 2: G grows 1 pop and has a 0.2% chance of growing a second pop (but doesn't). N gets unlucky again.
Month 3: G grows 1 pop and now has a 0.4% chance of growing a second pop (but doesn't). N gets lucky and rolls 3 pops (about half as likely as rolling two 0s in a row).
Month 4: Both empires have equal pops again.

In the mean time, G got an extra 0.6% chance of rolling an extra pop. But that chance is so tiny that it doesn't substantially change anything.

By definition, ten 10% chances will average the same outcome as one 100% chance. Sometimes it will be behind, sometimes it will be ahead. And while it's behind/ahead, technically that lead will compound... but 1 pop is 0.002 growth.

The law of large numbers kicks in before a one pop lead (on either side) has any meaningful effect.

And this is correct.
A few details though.
First, you at least realize and agree on the premises. We are in the same page here.
Second, might be correct that the impact of 1 pop is negligible. This however needs testing. The reason for that is that while yes, 1 pop is meaningless, over several planets over several months, it might compound.
Third, I think that the ideal scenario would be to do several tests and see if over a sufficient period of time, these '1 pops' actually have a significant effect. I am doing it already with several test games.

So while I generally agree with you, you can't guarantee that the impact of 1 pop per month per pop group per planet might not indeed snowball, unless you have more data that you have not shared. Because remember, this is an example with 1 planet, during several months and several planets, with sufficient difference in pop groups it does matter.

A much more ridiculous example, just to prove the point: a planet with 10 growth and 100 pop groups will take (statistically) a lot of time to produce the same amount of pops that one with the same 10 growth but only 2 pop groups. And in this (extreme) example it does snowball real hard (the planet with only 2 groups grows 5 per month here, this is obviously much better, on average than the situation on the other planet). So that is the thing: with more realistic numbers, can this really make a substantial difference? That is what I am testing with said test games. Will post the results on this thread once I finish.

 

[Abdulijubjub]

A much more ridiculous example, just to prove the point: a planet with 10 growth and 100 pop groups will take (statistically) a lot of time to produce the same amount of pops that one with the same 10 growth but only 2 pop groups. And in this (extreme) example it does snowball real hard (the planet with only 2 groups grows 5 per month here, this is obviously much better, on average than the situation on the other planet). So that is the thing: with more realistic numbers, can this really make a substantial difference? That is what I am testing with said test games. Will post the results on this thread once I finish.

It is not obvious why two pops groups with 5 each would be better than 100 pop groups with 0.1 each. You just assert that it's the case, and give no justification. Edit: No extra justification

But we can simulate it. Assume every newly grown pop adds 0.002 growth (too lazy to deal with planet capacity, just assuming it's like 10x Budding). The gestalt has its growth divided between 2 groups, the non-gestalt has it divided amongst 100.

import math
import random

def growth(population, groups):
    total_growth = (10+0.002*population)
    growth_per_group = total_growth/groups
    int_growth = math.floor(growth_per_group)
    fractional = growth_per_group - int_growth
    sum_random_growth = sum([random.random() < fractional for i in range(groups)])
    return int_growth*groups+sum_random_growth

def sim():
    gestalt = 0
    nongestalt = 0
    for i in range(100):
        gestalt += growth(gestalt,2)
        nongestalt += growth(nongestalt, 100)
    return (gestalt, nongestalt)

print('growth %d %d' % sim())

And you get roughly consistent results from both (sometimes the gestalt is ahead, sometimes the non-gestalt is ahead).

Running 10,000 trials, the average I got was 1105.8694 for the gestalt and 1105.9087 for the non-gestalt. Another 10k and g=1105.7682, n = 1106.0666.

There is no large scale trend toward the gestalt (with fewer groups) growing faster just because its growth has less variance. They are roughly equal on average (though the non-gestalt varies much more wildly).

Now, they could (somehow) have a bug, where it doesn't truly turn e.g. 0.1 fraction growth into a 10% chance to add a pop. But that's a different thing from the math leading to fractional growth being disadvantaged.

 

[Dr Pippy]

For a visual representation of the math that @Abdulijubjub is doing (I think):

I banged out a couple relatively quick and dirty python functions to compare exact population growth (i.e. don't round off the fractional part of pops grown) vs. the random method that's in the game (i.e. use the fractional part to calculate the probability of growing an extra pop). It turns out they're pretty much indistinguishable over the long haul. Running over 1200 months, with a planet capacity of 10000 and an initial population of 1000:

But since there's a random component to the random method (go figure), maybe this one trial happened to get lucky. So I ran 1000 trials of the random method and looked at the difference between each trial and the exact calculation:

You can see that it does spread out by +/- 50 pops or so over the course of a hundred years, but there's no overall tendency one way or the other.

 

[Ilab]

It is not obvious why two pops groups with 5 each would be better than 100 pop groups with 0.1 each. You just assert that it's the case, and give no justification.

First: I did provide a justification, whether you accept/saw it or not is another thing. Now, if you mean that you did see it but think that the justification is incorrect (which can be ofc, and according to the rest of your post seems to be), that is another thing. But I did provide justification, correct or not.

But we can simulate it. Assume every newly grown pop adds 0.002 growth (too lazy to deal with planet capacity, just assuming it's like 10x Budding). The gestalt has its growth divided between 2 groups, the non-gestalt has it divided amongst 100.

import math
import random

def growth(population, groups):
    total_growth = (10+0.002*population)
    growth_per_group = total_growth/groups
    int_growth = math.floor(growth_per_group)
    fractional = growth_per_group - int_growth
    sum_random_growth = sum([random.random() < fractional for i in range(groups)])
    return int_growth*groups+sum_random_growth

def sim():
    gestalt = 0
    nongestalt = 0
    for i in range(100):
        gestalt += growth(gestalt,2)
        nongestalt += growth(nongestalt, 100)
    return (gestalt, nongestalt)

print('growth %d %d' % sim())

This was a good idea, perhaps I should have tried this instead of running some test games :v

And you get roughly consistent results from both (sometimes the gestalt is ahead, sometimes the non-gestalt is ahead).

Running 10,000 trials, the average I got was 1105.8694 for the gestalt and 1105.9087 for the non-gestalt. Another 10k and g=1105.7682, n = 1106.0666.

I tweaked it a bit (by making starting pop not 0 and use real values and add more iterations for a longer simulation), and I do get an advantage more often than not in favor of the gestalts. A screenshot of just some of the returns:

(Parts blurred because you know xD)

And while this does not mean much in practice, I did another modification to compare when one number was bigger than the other and they where often similar, but still the gestalts where a bit on top (though minimal difference), also it might just be luck as I did not run as many trials (for some personal-hardware reasons). But I have no reason to not believe what you say, and if you ran it and got those results, then it is good enough for me.

In any case, even if my results where somehow better/more accurate/whatever the differences where so minimal that it should not matter in any real scenario.

There is no large scale trend toward the gestalt (with fewer groups) growing faster just because its growth has less variance. They are roughly equal on average (though the non-gestalt varies much more wildly).

I guess that is why I saw the behavior at first. Perhaps just some streaks on one over the other.

Now, they could (somehow) have a bug, where it doesn't truly turn e.g. 0.1 fraction growth into a 10% chance to add a pop. But that's a different thing from the math leading to fractional growth being disadvantaged.

Yeah, no, I was not considering any possible bug (even if there is, which I do not know) into this. Only the supposedly expected behavior.

So indeed I was confused, as I considered in the title.

At least now I do not have to finish the remaining test games, yay!

Also, this is the kind of arguments/replies I want/like (and that people should strive for when possible, just saying you are wrong but without explaining why just creates extends the discussion without really adding much). People saying that you are wrong because whatever, but not providing a backing argument don't really help. So this is a good answer that proved that I was wrong.

Kudos!

 

[Ilab]

For a visual representation of the math that @Abdulijubjub is doing (I think):

I banged out a couple relatively quick and dirty python functions to compare exact population growth (i.e. don't round off the fractional part of pops grown) vs. the random method that's in the game (i.e. use the fractional part to calculate the probability of growing an extra pop). It turns out they're pretty much indistinguishable over the long haul. Running over 1200 months, with a planet capacity of 10000 and an initial population of 1000:

View attachment 1319544

But since there's a random component to the random method (go figure), maybe this one trial happened to get lucky. So I ran 1000 trials of the random method and looked at the difference between each trial and the exact calculation:
View attachment 1319547
You can see that it does spread out by +/- 50 pops or so over the course of a hundred years, but there's no overall tendency one way or the other.

Yeah, I also checked @Abdulijubjub logic. And I did some tests myself playing with the numbers, not because I didn't believe, but rather to see if some changes in some numbers/length significantly affected the outcome. And I arrived to the same conclusion as you both. The differences are negligible enough that it does not matter.

I thank him and you for the solid answers. This is what I would like, people really engaging and trying to explain/prove why something is or is not in a certain way. not just saying it is not like that, but without solid arguments.

Thanks to both!

 

[Abdulijubjub]

First: I did provide a justification, whether you accept/saw it or not is another thing. Now, if you mean that you did see it but think that the justification is incorrect (which can be ofc, and according to the rest of your post seems to be), that is another thing. But I did provide justification, correct or not.

Fair. Sorry, I guess what I was thinking was "The claim is in dispute! You can't just take a more extreme version of the original setup and say it's obvious why the claim is now true, without expounding any further!". But you're right, you definitely gave a justification (though I disagreed).

I tweaked it a bit (by making starting pop not 0 and use real values and add more iterations for a longer simulation), and I do get an advantage more often than not in favor of the gestalts.

Technically, starting with 10 base growth and "0" pops is the same as starting with 5000 pops (at these rates). The two should be identical because I'm simplifying it by ignoring planet capacity (though I don't think that changes anything).

For a visual representation of the math that @Abdulijubjub is doing (I think):

I banged out a couple relatively quick and dirty python functions to compare exact population growth (i.e. don't round off the fractional part of pops grown) vs. the random method that's in the game (i.e. use the fractional part to calculate the probability of growing an extra pop). It turns out they're pretty much indistinguishable over the long haul. Running over 1200 months, with a planet capacity of 10000 and an initial population of 1000:

View attachment 1319544

But since there's a random component to the random method (go figure), maybe this one trial happened to get lucky. So I ran 1000 trials of the random method and looked at the difference between each trial and the exact calculation:
View attachment 1319547
You can see that it does spread out by +/- 50 pops or so over the course of a hundred years, but there's no overall tendency one way or the other.

This is better evidence that the variance is symmetrical.

Much more helpful than just comparing the higher/lower variance setups and seeing that they come out to the same number (on average).

 

[Ilab]

Technically, starting with 10 base growth and "0" pops is the same as starting with 5000 pops (at these rates). The two should be identical because I'm simplifying it by ignoring planet capacity (though I don't think that changes anything).

Yeah, you are right. I initially did it together with changing the length to see if by changing some numbers, it had any significant effects in the variance, but in the end it gave the same results. But you are right that it does not matter, was just me trying some silly things xD.

In retrospective, I think that the core issue with my entire logic was attributing to much impact to the effect of a pop in terms of further growth. It made sense that the moment that one nation exceeded the other in some pops it would eventually 'explode' in growth. But indeed in practice the effect of it is so small that the other one catches up before there is time for those pops to have any real effect.

This topic however, has sparked my curiosity in a couple of things (not entirely related to this, but related to growth overall). I like the new system but the UI is not there yet, and the fact that some info is hard to discern does not help sometimes.

Again, thanks for taking the time for explaining it!