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Xarfax111
Bad-mannered
Supreme Hero
The last hero standing
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posted June 25, 2006 08:21 PM |
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Not really Maretti,
you get always offered a magic skill at levl4 when you play a might. After this you get ALWAYS offered a magic skill every 6 level, no matter if you take the first or not.
Knowing this it gives you the following IMPORTANT conclusions for your game!
1. If you take EVERY magic school a Babarian/Beastmaster is offered you have a 100% chance to get Expert Earth.
2. If you dont take the first offered magic school with a Knight or Alchemist your chance of getting Expert Earth tends to subsero.
So if someone complains about his "Hack is not getting Earth", then you know you are facing a wanabee. 
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maretti
Responsible
Supreme Hero
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posted June 25, 2006 08:39 PM |
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First of all: Nice to see you giving your opinion in the library (thought you decided to leave for good)
Unfortunatly its simply not true that you are offered a new magic skill every 6th level when you take magic when its offered. I just tested it and its far from being true (at least with ver. 4.0)
I tested it on about 10 heroes and about half of them got 2. magic school later than level 10.
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Crag rules, Orrin and Ivor suck
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angelito
Honorable
Undefeatable Hero
proud father of a princess
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posted June 25, 2006 08:54 PM |
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I have to admit maretti is right here. I donīt know why and what circumstances are needed, but it really can take 10-15 levels until u get offered a magic skill the 2nd time.
Perhaps it depends on whether u accept the first offer or not.
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Better judged by 12 than carried by 6.
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dimis
Responsible
Supreme Hero
Digitally signed by FoG
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posted June 25, 2006 09:14 PM |
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Edited by dimis at 03:23, 26 Jun 2006.
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Getting along
maretti thank you for the input. Some clarifications though and correct me if I am wrong:
> When a hero gains a level and both Wisdom and Magic Schools should be offered on that level but hero also has at least one skill available for upgrade, then Wisdom has higher priority over Magic Schools and as a result the hero will be offered only Wisdom as a new skill.
> What happens on the above scenario on next level? I mean, if your hero gains one more level is it obligatory to receive as an option a Magic School, or he has to wait for at most 4 level-ups so that he is obliged to receive a Magic School (ofcourse assuming he has no Magic School so far)?
> I think what you describe is for Might heroes, right? Do we know what happens on Magic heroes? I think LegendMaker has said that you are offered Wisdom and Magic Schools on half-the-time (meaning every 3 levels for Wisdom and 2 for Magic Schools), but I could be wrong on what I remember. Legend can you please verify / refute what I remember?
> Binabik, Ecoris, or anyone else, do you have something more in mind? Please share. 
By the way, regarding the assumption I made one post earlier, I was wrong. I thought of a "peculiar" user policy, which is a variation of the ANSA policy:
Quote:
The user selects the offered skill every 2 level-ups (), or every 3 level-ups and only at those times.
Now, if our problem didn't have any exceptions, those numbers would be the same as those by ANSA computed earlier (for Might heroes). However, exceptions might change numbers on probabilities, because under these policies the user might encounter earlier or later the equivalent exceptions: I really didn't go deep into this, but it is not likely I will do so, since this seems not so interesting ...
Finally, so that I don't leave any gaps, let me have a comment on the following:
Quote:
Lets say i made 80 test with a hero classe and in 3 cases i got the same 8 skills. So NO probabilities ...
Well, I don't see what you are trying to say here. I mean that this is the ultimate goal of this thread, i.e. understanding the behaviour of the machine and the offered skills while leveling-up (for every single hero). Perhaps, this was my mistake that I didn't clear it up, though at my very initial post I wrote:
Quote:
This is a scratch place, where various ideas can be discussed and analyzed so that we obtain new verified facts which on a subsequent level will appear on thread "Heroes' stats and skill chances".
Now let me analyze the process of "verification":
1) At first we need smart all-around observations; for instance the weights the various skills have (our cornerstone) and exceptions that occur on various levels. Anything else might fit here but I don't see what else ... Of course suggestions are more than welcome and encouraged!
2) Building on the above observations we can generate mechanistic procedures that will allow us to give estimates on probabilities for each hero receiving a specific skill under a very specific policy (so far I am interested in deterministic policies, i.e. you don't flip a coin to decide whether or not you are going to accept a new skill and things like that...). Of course it would be interesting to have probabilities for groups of skills, meaning that you care let's say for about 4 skills (e.g. offense, tactics, air, logistics) and do not care about the rest. This is better and is certainly doable within the ANSA policy; so, for that reason, I might implement this first.
3) On this next level of analysis (which has not been made so far for the ANSA), we need a large sample of actual simulations of hero level-up and results of occurences of various skills or even groups of skills (even all 8 skills).
4) Hopefully, this step is going to be final on our verification procedure. Step 2 above computes the expected probabilities, or in other words the peak of the distributions on the specific events we want to observe (the most likely value our experiment will have). However, we can also estimate the likelihood that we observe something different from what we expect. Then, if we find large discrepancies, we are in the unfortunate situation where we should believe that our model is wrong and hence we have to make more observations, or in other words return to Step 1. 
That's the reason I wrote on my Groups post:
Quote:
... or even if only one hero can be used as a refutation of the above table, then I think we 've made a step forward. We know we have to search more for patterns in the first 8 levels. If, on the other hand, every hero can be used so as NOT to refute table, then again we have made a small step forward because now our assumptions are now better founded.
In other words, we can not be sure that our model is 100% correct but on the other hand we can say with confidence the extent to which we are certain that we have an accurate model.
There is lots of work and testing, so anyone willing to help in any way, is more than welcome! Especially people with lots of experience! 
- dimis -
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The empty set
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dimis
Responsible
Supreme Hero
Digitally signed by FoG
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posted June 25, 2006 09:16 PM |
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Seems that I delayed to finish my post due to various people jumping around in my place this afternoon! I am glad we have a conversation.
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The empty set
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maretti
Responsible
Supreme Hero
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posted June 25, 2006 09:43 PM |
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Edited by maretti at 23:38, 25 Jun 2006.
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Seems you are right that wisdom has a higher priority than magic, and it seems that in the case you are offered wisdom over magic you will be offered magic at the next level (13). I tested it a few times where the above was the result every time but it probably needs more tests to be sure.
You are also right that my observations all regard might heroes (magic heroes dont interest me much )
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Crag rules, Orrin and Ivor suck
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dimis
Responsible
Supreme Hero
Digitally signed by FoG
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posted June 26, 2006 03:05 AM |
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Edited by dimis at 12:53, 26 Jun 2006.
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Level-13-exception - part 1.
My tests show the same thing. In fact, I did some more testing this day, this time trying to keep some log regarding magic offer on level 13. I am certain about wisdom priority and chance that we are wrong on magic offer on level 13 is way lower than 1 / 1,000,000 even if we encounter this "only" on 10 out of 10 tests. Moreover, my tests show that whatever you receive on level-13-exception is independent of the magic school offered at level 4 or 8. I am just saying this because initially my log results showed a match between these 2 offers (which almost drove me crazy). In addition to that, this was also verified with the "lucky" version of level-13-exception which occurs on level 7 because you are offered a magic school on level 2 (and of course NOT offered Wisdom on levels 3-5).
For documentation: I made all my tests with Crag Hack on Complete version @ a Pentium II running WinXP - service pack 2 on a map I created for this purpose. All tests on Rook difficulty and starting bonus was gold for me and my opponent always.
If someone else does similar testing on this exception, please post your results and number of times you did finish with the verification of magic offer. Of course if even only once you encounter an offer other than magic on level 13, stop testing and post your result!
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The empty set
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dimis
Responsible
Supreme Hero
Digitally signed by FoG
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posted June 26, 2006 12:07 PM |
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Edited by dimis at 12:39, 26 Jun 2006.
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Level-13-exception - part 2.
In order to backup our assumptions on level-13-exception we can first notice that assuming there is no exception on that level someone gets a magic school offered on that level with probability:
prob_k = SUM ( weight (magic_school_i) ) / SUM ( weight (available_skill_j)),
where magic_school_i varies over all magic schools and available_skill_j varies over all skills that the hero does not possess on that level.
Moreover, again if we assume that there is no exception on that level, the probability that someone gets offered a magic school N times in a row is:
L13-Probability = PRODUCT ( prob_k ) < [ MAX ( prob_k ) ]^N.
But prob_k is a fraction and (since we can not influence the numerator) is maximized if denominator is minimized.
For that reason, minimum value for denominator when using Crag-Hack is 55 (so far: Offense, Artillery, Ballistics, Pathfinding, Scouting, Tactics, Logistis). On the other hand, numerator sums up to 8. As a result, if we assume that there is no Level-13-exception, then maximum probability for Crag-Hack getting a magic school on that level is: 8 / 55 = 14.55 % = 0.1455.
Hence, if someone tests this scenario 10 times, the probability he has on receiving 10 times a magic school offer on that level (assuming there is no level-13-exception) is around 4*10^{-9}.
Finally, even if someone finds a hero that has ratio 1 : 4 (instead of 8 : 55 that Crag-Hack had), then:
L13-Probability < 955 * 10^{-9} < 10^{-6}.
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The empty set
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Ecoris
Promising
Supreme Hero
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posted June 26, 2006 04:22 PM |
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Edited by Ecoris at 16:24, 26 Jun 2006.
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You should make it clear whether you want to now how the algorithm works (including exceptions) or whether you want to know the total probability of some skill(s) in just one of the slots when all 8 secondary skills have been selected.
Are you sure that you aren't offered a magic school at least every fourth level? At least just the opportunity of improving one you already have?
I did a little test with Ciele (no starting skills at all). At level 2 she was offered Earth Magic. I turned it down. No magic schools offered at levels 3-5. Basic Wisdom/Estates at level 6. Water at level 7.
I think you're offered a magic school (or the opportunity of improving one) at least every four levels and wisdom at least once every six levels, unless they coincide at which point wisdom will have the higher priority. Then, a magic school will be offered at the next level up.
At least I've never did a test where this was not the case, but correct me if I'm wrong.
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dimis
Responsible
Supreme Hero
Digitally signed by FoG
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posted June 26, 2006 05:09 PM |
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Edited by dimis at 17:17, 26 Jun 2006.
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Actually my greatest concern is on the algorithm itself. That's the reason I am seeking for exceptions. And I believe this is the way of predicting the probability a skill has for a hero under a specific policy. If we don't know how the algorithm works, I do not see a way of predicting the desired probabilities unless we settle down to testing (again with a very specific policy when picking skills). But I don't think this has a realistic chance to be ever complete. Of course if anyone else has an idea, please share.
Quote:
Are you sure that you aren't offered a magic school at least every fourth level? At least just the opportunity of improving one you already have?
Regarding the first question, I believe it is clear that you get offered a magic school every 4 levels if not earlier as long as your might hero does not have a magic school so far. As for the second question, I would say this needs testing which I haven't made so far nor have I observed something similar (never really paid much attention on this so far). Perhaps the following can simplify someone's testing: Use a hero that starts out with 1 skill. Follow ANSA policy everywhere except on level 4 when you are offered the magic school and reject it. At level 8 accept magic skill offered. That way you can have 5 skills at Basic and 2 skills at Advanced level or 6 skills at Basic and 1 skill at Expert. At level 9+ do not accept newly offered skill. That way you reach level 9 with all but 1 slots full and 5-6 skills at basic. If you do not encounter a magic skill offer on the very next 3 level-ups (up to reaching level 12), then we simply have a refutation and the "magic-exception" does not carry on on the already selected skills. If it does though, my first impression is that we are in deep ****. Only 1 instance is enough as a refutation (meaning you reach level 12 and no magic school has been offered since level 8). But if we don't have even 1 instance on the refutation, we can bound our certainty on how likely this thing is. The reason I don't pick a skill after 9th level is so that I minimize the chance a magic school has to appear. I hope though this is going to be refuted easily. If not, we'll talk about it again. As for the testing, I'll do it in case someone else does not in the next 4-5 days.
Quote:
I did a little test with Ciele (no starting skills at all). At level 2 she was offered Earth Magic. I turned it down. No magic schools offered at levels 3-5. Basic Wisdom/Estates at level 6. Water at level 7.
Yes, this is the "lucky" version of the Level-13-exception (just a name for the exception so as not to write constantly same things). Another "lucky" variation is getting offered Wisdom at level 2 and refute Magic on level 4, when you normally will result in the desired exception in levels 8 and 9.
Quote:
I think you're offered a magic school (or the opportunity of improving one) at least every four levels and wisdom at least once every six levels, unless they coincide at which point wisdom will have the higher priority. Then, a magic school will be offered at the next level up.
At least I've never did a test where this was not the case, but correct me if I'm wrong.
Actually, it is rather difficult not to receive an upgrade of an already gained magic skill. For that reason I proposed the guidelines on a test I have in mind above. That way, many skills will be unupgraded (not at Expert) and hence it will be more likely for the magic skill not to appear in a single test eventually.
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The empty set
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dimis
Responsible
Supreme Hero
Digitally signed by FoG
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posted June 26, 2006 06:30 PM |
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Edited by dimis at 18:34, 26 Jun 2006.
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I think we are in trouble ...
Just did some tests on what you say Ecoris and I am almost certain you are correct (at least for magic schools).
Now the problem is tougher and not only that, but ANSA table might be problematic due to this relation. Have you seen a similar relation between offers made on magic schools on already gained skills and those NOT already gained? I mean do offers depend one-another?
Thanks again for the input.
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The empty set
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Ecoris
Promising
Supreme Hero
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posted June 26, 2006 07:26 PM |
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I did not know about the "magic exception" before I joined HC. After that I've kept an eye on it, and I've never experienced that a hero was not offered a "magic opportunity" (improve/new) at least once every four levels (as long as open slots and or not-expert magic skills remained) EXCEPT the wisdom-magic school exception coincidence. But, again only ONE counter-example is needed to prove that wrong (or a large sample that reduces the probabilty of being mistaken to a very low value to actually prove it).
I do not know if any exceptions exist for other skills. Perhaps this could be investigated by looking at an entire skill tree, and looking for large "distances" between skill appearances. However just like the magic schools we don't know if other skill groups exist. This complicates the problem alot  .
But I agree with you that we should try to uncover as much of the algorithm as possible. I guess all the basic exceptions have been uncovered, therefore searching for other exceptions than those we know of (or uncovering all the details of them e.g. the magic school exception) requires large scale testing:
1. Define null-hypothesis
2. Define alternative hypothesis
3. Conduct tests based un the assumptions of 1.
4. Accept or reject the null-hypothesis based on the results of 3.
and so on.
But above all we should use our common sense. The algorithm cannot really be that complicated.
Could you make the source code you use available, dimis?
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dimis
Responsible
Supreme Hero
Digitally signed by FoG
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posted June 26, 2006 07:33 PM |
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Quote:
Could you make the source code you use available, dimis?
Source code is available even before I made the ANSA chart. So, refer to post on ANSA on first page.
It is also my belief as well that the algorithm can not be much complicated and at least we can get good approximate estimations. However, I also suspect that the ANSA chart is still OK. But I will justify this (again I hope!) early July. I have an important deadline on 30th of June, so till then I can't do much ...
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The empty set
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Ecoris
Promising
Supreme Hero
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posted June 26, 2006 07:39 PM |
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Well, I hadn't noticed. I'll have to read that thread through in detail soon.
I guess I'll run some tests then.
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dimis
Responsible
Supreme Hero
Digitally signed by FoG
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posted June 26, 2006 07:49 PM |
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Edited by dimis at 19:50, 26 Jun 2006.
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A reminder
Just don't forget to read the paragraph "Double Precision Arithmetic and Windows 32-bit Portability". It might save you from lots of time.
There is another version of source code there.
Thank you in advance for any help.
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The empty set
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maretti
Responsible
Supreme Hero
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posted June 26, 2006 08:28 PM |
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Edited by maretti at 21:13, 26 Jun 2006.
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I ran a few tests on this new info and it seems you guys are right.
Magic is offered every 4th level (if not earlier) as either a new skill or as adv or exp in an allready existing magic skill. This matches the fact that you are offered a new magic skill every 4th level if you dont pick what is offered.
This means that the chances of being offered a 2nd magic skill increases if you choose adv and exp asap in the magic skill you allready have. It also means that if dont pick adv or exp magic you risk never being offered a 2nd magic skill. Very interesting.
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Crag rules, Orrin and Ivor suck
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angelito
Honorable
Undefeatable Hero
proud father of a princess
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posted June 26, 2006 09:04 PM |
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Quote:
...So if someone complains about his "Hack is not getting Earth", then you know you are facing a wanabee.
But this is only half the truth i think. After reading the theories of dimis and Ecoris, it could probably run like this:
Level 1 = advanced offense
Level 2 = expert offense
Level 3 = basic path (other offered skill was balistics)
Level 4 = basic air (other was advanced path)
Level 5 = advanced path (other was basic wisdom)
Level 6 = expert path (other was basic armorer)
Level 7 = advanced air (other was basic log)
Level 8 = expert air (other was basic artillery)
Level 9 = basic balistics (other was basic first aid)
Level 10= advanced balistics (other was basic tactics)
Level 11= expert balistics (other was basic wisdom)
Level 12= basic fire (other was basic resistance)
Level 13= advanced fire (other was basic log)
level 14= expert fire (other was basic balistics)
level 15= basic scouting (other was basic estates)
Level 16= basic earth
So u got offense, path, air, fire, balistics, scouting and earth. But to keep the chances high getting earth offered, u refused Log, Tactics and Armorer. Call me wannabe, but i canīt think of any situation where i would refuse Log or Tactics in the first 10-15 levels of my main.
So if i would have chosen Log, Tactics and Armorer in the above mentioned situation, i would have ran out of levels to reach basic earth i think, coz if i then get a magic skill offered ONLY every 4th level (coz in between, i get offered new skills or advanced/expert existing skills), i have basic air level 4, advanced air level 8, expert air level 12, basic fire level 16, advanced fire level 20....game over, coz now i have 7 skills on expert, and the next level will prolly give me 2 new (bad) skills and NO earth
So is my theory complete nonsense (), or could it happen like this?
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Better judged by 12 than carried by 6.
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maretti
Responsible
Supreme Hero
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posted June 26, 2006 09:10 PM |
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Even if you pick magic every time its offered you can run out of levels:
Lvl 4 basic air
Lvl 8 adv air
Lvl 12 exp air
Lvl 16 basic fire
Lvl 20 adv fire
So you can never be sure to get earth with any might hero.
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Crag rules, Orrin and Ivor suck
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angelito
Honorable
Undefeatable Hero
proud father of a princess
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posted June 26, 2006 10:52 PM |
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I had your listing at first aswell, but itīs not quite accurate, coz every time when u have all present skills at expert and only the magic one not, u get this magic skill offered. (if u have expert offense, expert log and basic air at level 6, u will get offered the next magic skill, advanced air, on Level 7 and not on Level 8.....and so on).
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Better judged by 12 than carried by 6.
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maretti
Responsible
Supreme Hero
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posted June 26, 2006 11:09 PM |
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You are right. If you want earth at any price you can get it by choosing an exsisting skill every time magic isnt offered. But in a real gaming situation you wont pick skills like that and then you cant be sure to get earth.
But with this knowledge you can give yourself a better chance in some situations, for example if you at lvl 7 is exp in 2 skills and have basic magic then you can choose magic at level 8 and 9 if no very good new skills are offered at these levels. The downside to this tactic is that you will be offered 2 new skills at level 10 which might lead to a slot waisted.
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Crag rules, Orrin and Ivor suck
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