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dimis
Responsible
Supreme Hero
Digitally signed by FoG
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posted March 29, 2009 08:32 PM |
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Edited by dimis at 22:32, 29 Mar 2009.
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Ok. I did a similar test with Tyraxor.
Here is the save. However, I couldn't verify with this guy the theory of Level 2 Wisdom, and somehow (i.e. selections), at level 5 you get offered Logistics.
We can observe the following though.
When Crag is offered Logistics (in these examples where Wisdom is offered at level 2) he already has Offense, Wisdom, Artillery, and Fire. These sum up to 26.
Regarding Gurnisson (again in the examples where Wisdom is offered at level 2), we have two possibilities.
* One of them has Offense, Artillery, Wisdom, and Fire, which again sum up to 26. Therefore, (this was my conjencture), if there is actually only one tree that starts with Wisdom at level 2, both outcomes on Crag and Gurnisson are perfectly justified.
* The other case is if Gurnisson has Offense, Artillery, Wisdom, Eagle Eye, and Fire. These sum up to 28. Again the outcome is Logistics.
Now let's switch back to Tyraxor.
One of the stories in the save above can give him Offense, Tactics, Wisdom, First Aid, and Earth Magic. These sum up to 28 (like the second case in Gurnisson above). So, if there was a unique tree starting at level 2, I would expect on the very next level up to get Logistics. However, Tyraxor is offered Pathfinding. What the .... ?  (shshshshsh ... don't say it!)
So at that point to me it seems reasonable that there are more than one trees that start with Wisdom at level 2. However  I generated two more examples with Wisdom appearing at level 2, and all three "different" cases actually reflect the same case. It's a pity.
Another example with Yog.
Now the guy can have Offense, Ballistics, Wisdom, Fire, and then he is offered Pathfinding. Now, Offense, Ballistics, Wisdom, and Fire add up to 26. So, if there was one tree with Wisdom at level 2, then the next offer would be Logistics. But it is Pathfinding.
The other funny thing here, is that all these examples are around the other idea that was presented earlier in this thread "if two sequences are identical for the first four level-ups, then they will be identical for the rest level-ups". But of course you know that this has been refuted long time ago.
Now the critical variations between Yog and Gurnisson above (bold indicates what was picked) seem to be the ones that add up to 26 at level 4 and both of them have Fire at level 4. Let's see:
Gurnisson
L2: Advanced Offense - Basic Wisdom
L3: Advanced Offense - Basic Eagle Eye
L4: Expert Offense - Basic Fire Magic
L5: Expert Offense - Basic Logistics
Yog
L2: Advanced Ballistics - Basic Wisdom
L3: Advanced Offense - Basic Scouting
L4: Expert Offense - Basic Fire Magic
L5: Expert Offense - Basic Pathfinding
However, even the very first entry between these two is essentially different, since Offense is given to Gurnisson and Ballistics to Yog. Note that the sum of skills of both heroes is the same initially (18 = 10 Offense and 8 the other skill), so one justification would be if the pairs (Offense, Artillery) and (Offense, Ballistics) would appear in different order. However, the table given by Ecoris directs that the order of these pais is (Artillery, Offense) and (Ballistics, Offense), meaning that Offense is second in every case. So, clearly these two saves reflect two different skill trees.
Unless somebody can come up with a good idea, I once again declare the ghost of "always Logistics" as ... dead! 
What would be particularly interesting is if someone can give us a save with one of the heroes above such that Wisdom is Offered at level 2 but the tree is different from the one that I have in the saves above. That would be very interesting. I believe that you can not do that.
As a consequence, I am also claiming here that if you get offered Wisdom at level 2 with Gurnisson or Crag Hack, then you have a way of getting Logistics at level 5. But this is not because of some rule. It's just the way it is. And it's up to you if you want these sort of skills early in the game so that you can be sure (100%) that you get Logistics.
Closing, in case it is not clear, I claim that there is a unique tree for each hero that starts with Wisdom being offered at level 2 as a new skill. And I would be very interested if you can give us a save with a different tree than the ones I have above for Gurnisson, Crag Hack, Tyraxor, or Yog (any one of them).
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The empty set
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Ecoris
Promising
Supreme Hero
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posted March 29, 2009 10:49 PM |
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Would it not be easier to use LMOracle to look into such matters?
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dimis
Responsible
Supreme Hero
Digitally signed by FoG
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posted March 29, 2009 10:56 PM |
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True. But what are we looking for?  There is no theory at the moment that we want to check.
As of:
Quote:
Quote:
I assume that the wisdom-bell is not ringing at level 8 as well.
* If this is the case, then:
Advanced Air: 100%
Basic Earth: 3 / (112 - S) * 100%
Both statements are wrong. ...
...
So if air is already given its about 4/7 for the magic fixed skill slot.
Give me one save that justifies this. Just one. Nur eins ist genug.
Quote:
Means that reverse to the opinion in this thread, if you take a magic skill like fire you probability will be much more higher for earth on the next fixed magic offer.
Later the game designers worked on other skills like this too.
I have no clue what you mean. Give me an example with one save. Simple as that.
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The empty set
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dimis
Responsible
Supreme Hero
Digitally signed by FoG
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posted March 29, 2009 11:15 PM |
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Edited by dimis at 06:41, 30 Mar 2009.
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note
And by the way ... Even if you (not particularly you; anyone) ever come up with such a save, then this only proves that my 100% on Air is wrong; not that what you say is correct. Because I have already given examples (and one can generate a whole bunch of them on his/her own), which satisfy what I claim. So, if it is not 100%, then, on average it is above 99.999% So, I can be wrong only in this kind of sense.
Moreover, I think another result has not been appreciated enough. And that is the correlation between the prediction following ANSA (AR) and what I observed empirically with Crag Hack in the past. It is a striking result that we have correlation 0.995. Roughly, this implies that the model we have makes an error with probability 0.0025 = 0.25%. So, even if the model is wrong for all the reasons in the world, it still predicts on average over long examples very-very well. And essentially this is why I reject all the theories everybody is coming up with, but has no way of justifying them.
@everyone: Give me a theory and saves that support your theories. That's all I want and honestly I don't care who is right or wrong. I just want to know and be able to predict. That's the whole story. Can you  The rest is ...
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The empty set
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AlexSpl
Responsible
Supreme Hero
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posted March 30, 2009 08:24 AM |
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Quote:
I tested english version of LMOracle, it seems to work. Calculations take a lot time though.
Minimize the game before running calculations to increase perfomance. The game itself loads CPU badly. With the window minimized it takes about 8-10 seconds to build +15-lvl tree.
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pacifist
Famous Hero
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posted March 30, 2009 11:38 AM |
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Edited by pacifist at 17:04, 30 Mar 2009.
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LMOracle is a very usefull tool! To test with it will take much time but still quicker than the old way. It can alreaby be useful to test if for any given might hero (later test on magic ones) there is always "one" path at least leading to logistics. Later, if answer is yes, test if there is always a path for combo like "earth" and "logistics". Etc. There will be no stats there, just empiric observations that lead to great confidence in skill selection. One must of course see if bad skills can be prevented to achieve that but I think that a main hero can be very good even with a wasted skill for that map (navigation, eagle eye, learning, etc). Maybe then we can sort out some particular correspondence between skills or groups appearing.
One way to test is to start a new map (give the gold necessary at start). Hire every possible hero in tavern that has potential to be a main hero. I will do some tests myself of course, but the more the better . I think it's better that way than to restart map with other heroes since the random factor is the same for all then.
edit : Well this programm is amazing ! You can let him search all combos you like, even the 8 skills you want (considering those you have at start of course). Congratulations AlexSpl for this pearl! .
edit2 : Just one example with the map "all for one", I tested the 8 knights and the condition was to have (logistics, pathfinding, air , earth and tactics). There was a way for each one to have those skills but some weird choices for Sylvia who had to take sorcery once, Christian had to take ballistics and Tyrics luck. The other proposed choices were good skills for main hero so choosing them was natural.
In some cases you couldn't take offense and armorer at the same time but only one of them. So far I never failed to have logistics with main but how is that guaranteed and how to find a scheme there? Maybe restart the map and only test one hero at a time, then with another map the same hero and try already to see in the first level-ups if something looks interesting. If it's only a question of probabilities then at one moment we may have the choice between 2 bad skills and choose the better one and go on with that. that let's time to find the usefull ones. Well knights are dangerous main heroes as they tend to like skills like navigation, luck, ballistic, scholar, etc .
This program is really usefull since you can develop the whole tree of skills and copy paste in another document to study it. The problem is to find a way to predict the good choices or even the good choices minus one .
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http://www.youtube.com/user/alkoriak#g/u
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dimis
Responsible
Supreme Hero
Digitally signed by FoG
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posted March 30, 2009 07:10 PM |
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Edited by dimis at 19:47, 30 Mar 2009.
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Ghosts ...
I don't want to discourage anybody, and indeed I am interested in all those tests. However, let me give some examples that can justify ghosts.
Suppose now a guy comes and claims the following skills are some sort of a "map-skills-group": Logistics, Pathfinding, Scouting, Navigation.
Clearly, all those 4 help on map.
Now here is a strategy in which I pick skills: I will upgrade my skills for the first two levels, at level 4 I'll pick a Magic school, at level 6 I 'll pick Wisdom, and in general I always pick Magic or Wisdom, otherwise I upgrade my existing skills. Let's see a more or less expected scenario of leveling up this way. And so that I make it slightly more particular, I pick Gurnisson.
Levels 2, 3: Upgrade Artillery.
Level 4: Pick Magic.
Level 5: Upgrade Offense
Level 6: Pick Wisdom.
Level 7: Upgrade Offense
Level 8: Upgrade Magic
Levels 9,10,11: Upgrade Wisdom and Magic to Expert level (say magic at level 11).
Level 12: Pick something (among 2 new).
Levels 13,14: Upgrade that something.
Level 15: Pick newly arrived Magic School
Levels 16,17: Upgrade your new Magic.
Level 18: Pick something else (among 2 new).
Levels 19,20: Upgrade that something else.
Level 21: Pick the last Magic School available for Gurnisson among the 2 new skills.
Levels 22,23: Upgrade that Magic School and complete the level up.
Meanwhile, apart from the chosen skills you were presented "new" skills at levels: 2, 3, 5, 7, 8, 9, 10, 11, 12, 12, 13, 14, 15, 16, 17, 18, 18, 19, 20, 21.
Counting the numbers between the commas yields 20.
Clearly, I can prove that the guy who claims these 4 skills form a group is wrong if I can find a level up such the one above that "misses" in every case all four of them. How likely is such a thing to happen?
Let's see. Initially, Gurnisson has Offense and Artillery; they sum up to 18. So initially the remaining skills have weight 112-18 = 94.
Out of those 94 points, 25 are charged to the so-called map-group. This implies that at level 2, Gurnisson is presented with skills other than those 4 with probability 69/94 = 0.734 (about).
Same probability for the next level-up. These two level-ups have combined probability (69/94)^2 = 0.539 (about). Do you see where am I getting at? If I take into consideration all those 20 factors that appear on those 20 skill offers along the way, the resulting product goes to 0. Note that the function (69-x)/(94-x) is monotone decreasing; i.e. whenever you charge one skill to the hero of weight x (or a combination of skills that weigh in total x), then those factors become less and less. So, in particular (69/94)^20 is an upper bound on the probability I am looking for. But (69/94)^20 = 0.002 (about). If you are a little bit more careful when you consider those factors up to level 12 you get (69/94)^2*(67/92)*(61/86)^6*(60/85) which is less than 0.036. Now multiply this with the other 10 level-ups remaining. Clearly each of these factors is upper bounded by (60/85), and (60/85)^10 is less than 0.031. Multiplying now 0.036 with 0.031 gives 0.001116.
Bottom line 0.001116 = 0.1116 % is an upper bound on missing all those 4 skills along the tree that we generated. And if you want a different interpretation of this, this means that we expect to miss all four of them once every about 1000 trees.  Prove that this guy is wrong especially when you know that the trees generated by the game are indeed few (that is a fact that we already know).
So yeah, I claim that we have a skill group: Logistics, Pathfinding, Scouting, and Navigation. Prove me I am wrong now ...
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The empty set
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dimis
Responsible
Supreme Hero
Digitally signed by FoG
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posted March 30, 2009 07:26 PM |
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Edited by dimis at 20:34, 30 Mar 2009.
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More ghosts ...
You want me to make this even worse?
Another guy jumps in the thread and says: "Here is the combat-group guys": Archery, Armorer, Artillery, Ballistics, First Aid, Leadership, Luck, Offense, Resistance, Sorcery, Tactics.
These are 11 skills, and the guy also claims that the priority of this group of skills is less than that of Wisdom as well as that of Magic Schools. We still have 15 skills outside. However, the model most likely can also prove with a high degree of certainty that you meet at least one of them every at most 10 offers or so. So yeah, contradict this guy's claim as well!
edit: In Barbarians these sum up to 63. Remove Offense and Artillery for Gurnisson; they sum up to 45. Now the claim becomes, that once Gurnisson upgrades both Artillery and Offense, you will be offered one of them in at most ... say ... 12 level-ups (the other part of the claim is that between at most 12 level-ups you will be offered as upgrade the Offense or Artillery skill). A similar (not careful) calculation like in the previous case upper bounds the probability of this not happening by (49/94)^12 = 0.0004 = 0.04% = less than 1 every 2000. And you know by the analysis above that it is waaay worse than this upper bound ...
A nice read (for those who haven't done so, so far) is Ecoris post on groups of skills here.
And by the way, I am still waiting for some results from the project found here. I guess I should forget about them entirely ...
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The empty set
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Rainalcar
Promising
Famous Hero
Heroji su zakon
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posted March 31, 2009 12:53 PM |
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I forgot to mention one thing.
It was likely observed that restarting the game lots of times sometimes fixes skill trees, that they start to reappear. I noticed the similiar thing when I tested diplomacy. I don't recall the specifics, but it likely went like this: I placed 20+ AAs on the map and checked for join/flee/fight outcomes on multiple restarts. After a (long) while, ALL of the AAs join outcomes became fixed. All AAs reacted the same way after every following restart, they all became "fixed". I didn't pursue this to see will it stop, and become "random" again.
This feature is likely the most dubious factor to explain, for me at least, for I know nothing of programming. If this wasn't the case, I would say that skill choice is a result of a function with variables of currently possessed skills, their levels, skill weights and some random factor (number) which I don't know how is generated, plus of course, magic and wisdom exception. If this random number was known, I bet it would be possible to predict with 100% certainty the offerings to follow.
Perhaps Alex could help with this? Oracle certainly reads the skill tree all the way, and this means that game has it in memory for the game start, perhaps he has an insight how it creates the skill tree in the first place.
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Ecoris
Promising
Supreme Hero
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posted March 31, 2009 03:12 PM |
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Edited by Ecoris at 15:13, 31 Mar 2009.
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When one restarts a scenario over and over again one will eventually enter a loop in which a certain sequence of outcomes (be it skill offers, monster reactions, and such) will repeat itself.
This behaviour is not unreasonable if the random number generator that produces the seeds is recursive.
I have previously determined the first two random numbers used to determine skill offers for Crag Hack in a specific scenario. That allowed me to make accurate predictions for the first level up depending on the odds values alone. It was very cumbersome to obatin these two numbers, but if one determined more values one would be able to see whether observed results differ from the predictions of our model. Unfortunately LMOracle won't help determine these random values.
If someone has a lot of time at their hands I could describe how I determined the numbers. Having a savegame with a longer part of the sequence of random numbers associated to a hero would be valuable.
Otherwise one can look for patterns in the skill trees LMOracle can provide. But if you don't know what you're looking for it can be difficult to spot anything new.
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dimis
Responsible
Supreme Hero
Digitally signed by FoG
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posted March 31, 2009 07:35 PM |
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Edited by dimis at 20:08, 31 Mar 2009.
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idea
I think the most straightforward use of LMOracle is to generate a bunch of different trees and export them in files. Then feed those files in some sort of a bigger database which we can distribute around with a torrent and everyone can get. Finally, downloading such a database (similar to tablebases used in chess) would allow someone various operations.
One of them is re-computing all the odds values that we have in the previous two tables (AR and AL), or even the rest of the skill-selection-strategies.
But of course the other part of this, is that one can use it gradually during level-ups and make sort of predictions; for example, at level 1 you can not say much apart from the probability each skill has to appear at level 2 over all possible trees. Now, when you feed the program with what was actually offered at level 1, then you will "prune" all those trees that don't start similarly. Eventually, this process would end up in a unique tree which predicts the subsequent level-ups. Of course, there is always the possibility that there is no tree in the database that agrees with all these level-ups. At this point the user has found a new tree/subtree which wasn't observed by the guys who created the database. In this case one has to do is load the save game of day 1, use LMOracle to generate the tree, and submit his/her findings. Hopefully within 6 months of the first release most trees for the interesting heroes will have been revealed.
For all that we need a parser that converts the files generated by the LMOracle to some sort of database structure (we can discuss the structure here a bit if you want), and then we need another program that reads and computes stuff based on the database it is provided. Do you like this idea? I should also mention that I have no time at all at the moment to work on the implementation, but hey, summer is approaching and I 'll find time to work on something like this. And of course this makes all the weight tables obsolete.
edit: Of course I should mention here that such a database can not be used for the Tournament Edition, simply because there different weights are used. On the other hand, it is straightforward to use internals_mc with Tournament Edition. It's no more than a day's work. And I still like it more as an idea, because it can not be used for cheating.
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The empty set
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Ecoris
Promising
Supreme Hero
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posted April 01, 2009 12:31 PM |
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With such a database, you would then make query like "list all skill selections leading to basic logistics at level 5" and look for patterns?
However, if a player picks up a secondary skill from a Witch Hut, School of Magic, etc. he leaves the "day 1"-tree for good.
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AlexSpl
Responsible
Supreme Hero
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posted April 01, 2009 12:36 PM |
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New version of LMOracle is almost ready. Now the program can construct skill trees really fast. For example, it takes:
- less than 1 second to build a +15 level-ups skill tree;
- less than 15 seconds to build a +20 level-ups skill tree.
Later I'll post the leveling-up algorithm here.
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pacifist
Famous Hero
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posted April 01, 2009 12:47 PM |
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Waw! So there is an algorithm then? It means level-up will be predictable then no? or is it too complex without a computer? That will be the answer everyone seeks
I just made some tests based on initial xp of hero but same xp lead to different tree choices in different games so not right direction to search. I have a conjecture that says : there is always a path to any desired skill provided it's not forbidden. That reduces the trees but how to prove it? I didn't found yet a counterexample.
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http://www.youtube.com/user/alkoriak#g/u
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Ecoris
Promising
Supreme Hero
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posted April 01, 2009 12:52 PM |
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@ pacifist
Due to the sheer size of an entire skill tree it is extremely unlikely that a single skill appears nowhere in the tree. See one of dimis' posts above.
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dimis
Responsible
Supreme Hero
Digitally signed by FoG
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posted April 01, 2009 01:39 PM |
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Edited by dimis at 15:07, 01 Apr 2009.
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Quote:
With such a database, you would then make query like "list all skill selections leading to basic logistics at level 5" and look for patterns?
I don't have to look for patterns (yes, the query for the first part will be there). I was convinced by your proof 3 years ago. Few others get it though.
Quote:
However, if a player picks up a secondary skill from a Witch Hut, School of Magic, etc. he leaves the "day 1"-tree for good.
That's true. So it would be nice to try and exploit your technique (hopefully it will be easier if we have the entire tree since we can work on intervals) on recovering the numbers and try to form bijections between different trees. Either we will find the precise numbers at each level up or we will give small intervals and predict what's possibly next even if somebody bumps into witch huts and so on. So, on a subsequent level we can narrow the intervals by simply bumping into witch huts. At least that's the idea.
edit: The idea of the bijection between trees though won't work because I already gave an example above where the tree starts with Basic Wisdom on your right and if that kind of tree is unique per hero (conjecture) then the whole idea goes bye-bye. It might work partially, or there are equivalence classes among the sequences generated. Anyway, this is science fiction now and I 've got to go. Later
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The empty set
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Ecoris
Promising
Supreme Hero
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posted April 01, 2009 04:13 PM |
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But even if we accept that there are no other skill groups that behave like wisdom or the magic schools, we can't rule out that there are not other exceptions to the basic algorithm.
It'll be interesting to see what AlexSpl presents when he posts the "leveling-up algorithm".
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dimis
Responsible
Supreme Hero
Digitally signed by FoG
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posted April 01, 2009 06:13 PM |
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true / true
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The empty set
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AlexSpl
Responsible
Supreme Hero
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posted April 02, 2009 08:03 AM |
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There is an algorithm that allows you to build full skill tree for any hero. You need just know some initial data.
Initial data (hero's level, seed, etc.) -> Black Box (algorithm) -> Full tree.
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Ecoris
Promising
Supreme Hero
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posted April 02, 2009 05:16 PM |
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But we want to know the contents of the black box, not just its outputs.
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This thread is pages long: 
