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dimis
Responsible
Supreme Hero
Digitally signed by FoG
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posted October 04, 2008 06:19 PM |
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Alex,
This should be great, but I am not running it at the moment since I don't see the source code and nobody is reporting here that it works (unless they wait for me ... lol). And yes, a translation would help a lot everyone, coz at the moment I think people have to guess on some parts, plus it's not so friendly if you work with a program in a language that you don't speak; think about it. In any case though, this seems to be like a really really nice work!!! 
By the way, when I was thinking about reversing the program, I had in mind to extract the code, and then create a program that can simulate that behavior. But clearly this isn't necessary if you want results on a game that you play at the moment. I guess just interfering with memory as the game runs is enough, since it gives you online all the information that you might want. I have some questions, but I'll let others comment as well first.
Thanks again for your time and effort you put on implementing this!
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The empty set
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maretti
Responsible
Supreme Hero
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posted March 26, 2009 11:49 PM |
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Edited by maretti at 00:34, 28 Mar 2009.
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If you have a lvl 7 barbarian with basic air, who will be offered magic at lvl 8, what is his chances to get adv air compared to basic earth?
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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 March 27, 2009 04:35 AM |
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Edited by dimis at 07:14, 27 Mar 2009.
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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%
where S is the sum of weights for the skills that you already have. Of course here I assume that there is at least one of the 8 slots free so that you can be offered a new skill.
* If this is not the case; i.e. you got offered Wisdom at level 2 and not again up to now (level 7), then:
If you already have Basic Wisdom, you will be offered Advanced Wisdom (therefore Advanced Air has 0%), and Basic Earth is either 100% or 60% (= 3 / (3 + 2)) depending on whether or not (respectively) you also have Basic Fire. Note that this scenario can happen in theory: You get Wisdom at level 2, and then Basic Air and Basic Fire at levels 3 and 4. edit: Again I assume there is one slot free for a new skill. If all slots are occupied, then in this case you get Advanced Wisdom on your left with prob. 100% and Advanced Air on your right with probability 3/ S * 100%, where S is the sum of the magic skills you already possess. So, if it is only Air, then S = 3, and hence Advanced Air has 100% and will appear on your right. /end of edit
Now, if you didn't pick Wisdom at level 2, then you get Advanced Air with probability 100% and Basic Wisdom with probability 100% (so Basic Earth is 0% this time).
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The empty set
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SAG
Promising
Supreme Hero
WCL owner
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posted March 27, 2009 03:16 PM |
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Quote:
Alex,
This should be great, but I am not running it at the moment since I don't see the source code and nobody is reporting here that it works (unless they wait for me ... lol).
I tested english version of LMOracle, it seems to work. Calculations take a lot time though.
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Ecoris
Promising
Supreme Hero
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posted March 27, 2009 03:37 PM |
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Are you sure that adv air = 100%, dimis? IIRC the game first picks a magic school (using the odds values of the four magic schools); whether it will be an upgrade or not is irrelevant. Then it determines the other skill offer (whether this offer should be a new skill or an upgrade of an already known skill depends on the magic skill offered).
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Xarfax111
Bad-mannered
Supreme Hero
The last hero standing
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posted March 27, 2009 06:33 PM |
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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%
where S is the sum of weights for the skills that you already have. Of course here I assume that there is at least one of the 8 slots free so that you can be offered a new skill.
Thats wrong.
Thats why all the skill tables are wrong. In the described level-up it would be:
Basic Earth: 4/7 * 100% means about more then 50% Chance NOT less then 5%.
It really shows how false the calculations are.
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dimis
Responsible
Supreme Hero
Digitally signed by FoG
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posted March 27, 2009 09:29 PM |
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Edited by dimis at 22:01, 27 Mar 2009.
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Testing. Not just talking this time ...
Short answer: I still think that what I suggested is right.
Long answer: Since I respect you guys and you know that, I was forced to do some testing to verify the things that I remember (I am getting rusty). Ok here we go.
My claim is that if you get offered a Magic School at level 4 which you accept at that level, and you don't get offered a Magic School up until level 7, then at level 8 you will be offered the Advanced version of the Magic School you accepted at level 4 (on your left) given that there is no Wisdom-exception at level 8.
So, in particular it doesn't really matter if you were offered Air Magic at level 4. The same thing holds if you get offered Earth Magic then, or even Fire Magic then.
If I understand correctly what you are saying, then you imply that at level 8 you will be offered Air with probability 3/ (3+3+2) = 3/8 = 37.5%. Similarly you also imply that Earth has chances 3 / (3 + 3 + 2) = 3/8 = 37.5%, and Fire has chances 2 / (3 + 3 + 2) = 2/8 = 1/4 = 25%. What's the bottom line of all these? Stick to the Magic School that you were offered at level 4. No matter what this Magic School was, then you are saying that I will be offered the same Magic School with probability no more than 37.5% (which is the maximum among all 3). Hence, if I start testing, I should observe something similar; i.e. some times I will be offered the same Magic School at level 8, and sometimes not. On the other hand, my claim implies that every time I will be offered the Advanced version of the Magic School I accepted at level 4. So, all we need is a test that can verify which one of these two cases holds with high probability.
Ok, here is the test. I used Gurnisson on a custom map I made. The map has a pandora box with 10,000 experience points in it. The map can be found here. The results that I am about to discuss can be found here. The saves that generated the results can be found here.
What are those tests about? First of all there are 18 tests on that map. In all of them Gurnisson is offered a Magic School at level 4, Wisdom at level 6, and a Magic School again at level 8. In all of the cases I follow the following strategy (policy) on picking skills: At levels 2, 3, 4, and 6 I pick the new offer. So, in particular I pick the Magic School offered at level 4, and Wisdom at level 6. At levels 5 and 7 I pick the upgrade that is offered.
Based only on that, and from what I understand on what you are suggesting, I should encounter the same Magic School as Advanced at level 8 with probability at most 37.5%. This means that with probability at least 62.5% I will be offered something different. This further implies that I should expect (at least) about 0.625*18 = 11.25 ; i.e. about at least 11 tests that verify your sayings (==> get offered a Magic School different from the one I got at level 4).
However, not even one of the tests actually turned out this way entirely. I am adding entirely here, because at test #14, something interesting happened. I was offered both Advanced Air, as well as Bas Earth at level 8. But which one was chosen first? There is an easy way of figuring this out. My offer at level 7 was Adv Offense and Bas Pathifinding and according to the policy I followed, I picked Adv Offense. However, you can reload the game, and then pick Bas Pathfinding at that level. And now, Earth Magic goes bye-bye. Probably Ecoris can help on explaining this part; I don't remember all the details of his testing right now.
Closing, your suggestion on offered skills at level 8 is even more problematic. Unfortunately I have to be a little bit technical here, but essentially here is what the test does. In each of these 18 tests, it is like we are flipping a coin which comes up Heads (what I propose above) with probability at most 37.5% (according to your interpretation). How likely is such a coin to give you 18 Heads in a row? Well, it goes on multiplicatively, so (0.375)^18 which is less than 0.0000001 = 0.00001%. Hence, if what you imply is correct, I was so damn lucky that I got a sequence of tests which occurs once in about every 10 millions tries... Now, are you willing to believe that this is the case and I am so lucky, or the simpler explanation that I gave above holds?
Again, I might be wrong. But the probability that I am wrong on this due to what you suggest is less than 0.00001%. One example (save) is enough from your side to convince me I am wrong. When you get that, let me know. I wouldn't bet much on that though for the reasons explained above.
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The empty set
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Ecoris
Promising
Supreme Hero
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posted March 27, 2009 10:33 PM |
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Quote:
My offer at level 7 was Adv Offense and Bas Pathifinding and according to the policy I followed, I picked Adv Offense. However, you can reload the game, and then pick Bas Pathfinding at that level. And now, Earth Magic goes bye-bye. Probably Ecoris can help on explaining this part; I don't remember all the details of his testing right now.
That's easy to explain. It simply changes the value of S (the sum of the odds values for all skills the hero does not know). The random number generated to determine the right skill offer simply belongs to another interval.
If what you are saying is true I am mistaken. I had not thought that you would automatically get an upgrade of an existing magic skill in such a situation. I never got to that in my tests.
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dimis
Responsible
Supreme Hero
Digitally signed by FoG
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posted March 27, 2009 10:57 PM |
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It's easy to verify that what I am saying above is true. I edited the post and I also gave the saves that yield the result of each particular test. All one has to do is download and verify.
Moreover, all those tests can be counted as double, since at level 7 you can pick the new skill that is offered (instead of upgrading that I describe above), and then check again what is offered as Magic School at level 8.
I also went through the code to verify that I remember correctly what is done. If you download internals_mc code, then on file mighty_classes.cpp, the function get_skill_offer () decides which two skills should be offered for the next level up. At lines 1115-1119 I implement exactly this. Which is (modulo some technical irrelevant details): Initially make up your mind on the left offer (upgrade). How can you do that? First check for wisdom exception. If this doesn't hold (like here), check for magic exception. If this holds (like here), then your left offer is an upgrade of the magic schools that you can upgrade. In the example we are talking about we only have Air, and this forces Air to have 100%. The right offer then is decided at random. May be reading that part of the code could actually clear up all the things that I have missed stating.
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The empty set
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maretti
Responsible
Supreme Hero
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posted March 27, 2009 11:04 PM |
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Edited by maretti at 23:05, 27 Mar 2009.
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First of all thank you for the fast answer Dimis.
Im with you all the way. I made a test of my own and was offered the adv magic 100% of the times in more than 10 tries. The only question that remains is: what if you got your basic magic from a witch hut?
I made a test where I took air from a witch hut as lvl 1 and then a box with 10 k xp. In 100% of the time (10 plus tries) I was offered adv air at lvl 4.
This means that if you have some kind of magic at basic or adv lvl you lower your chances of getting a new magic school significantly. So if you find a witch hut early with air its a good idea to get your hero to lvl 4 before you take air from the hut (unless its Crag or Taz). This way you give yourself a chance to get earth at lvl 4 that you wont get if you have taken air from the hut allready.
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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 March 27, 2009 11:26 PM |
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Edited by dimis at 23:40, 27 Mar 2009.
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Quote:
This means that if you have some kind of magic at basic or adv lvl you lower your chances of getting a new magic school significantly.
Exactly. I thought that part was clear through the entire thread. As of the witch huts I haven't tested their impact on "magic-exception"; i.e. whether or not the counter is reset, but your test indicates that witch huts do not reset that counter. I haven't made tests with witch huts, since I wanted to finish first the "pure" part of offered skills; i.e. implement Frank's skill selection mechanism, as well as your suggestion, and in the end also give partial results for all the intermediate levels.
And by the way, there is another interesting alternative that might not have been clear. If both wisdom exception and magic exception occur at the same level, and you can upgrade wisdom, then you are also forced to get a new magic school given that you have a slot to keep it (and of course there is at least one Magic School available for your hero to learn). Note also that this is consistent with the "level-13-exception" described in page 2 of the thread.
All in all, these arguments show once more why upgrading existing skills is a good strategy. And partially it justifies why Frank's skill selection behaved so nicely.
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The empty set
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maretti
Responsible
Supreme Hero
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posted March 28, 2009 12:26 AM |
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Edited by maretti at 00:31, 28 Mar 2009.
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"I thought that part was clear through the entire thread."
Well i hadnt noticed it. Ecoris hadnt either. Xarfax definitely hadnt. (Sorry Xarfax, I couldnt help it) So im not sure it has been mentioned. Anyway its hard to find things in a thread this long. Its faster to ask again
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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 March 28, 2009 12:56 AM |
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Edited by dimis at 01:25, 28 Mar 2009.
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Probably you are right because that's a direct impact of the things discussed above.
To be perfectly honest, I remember that at some point in the past I had also said (probably in another thread*) that I had observed the Magic exception before it was mentioned in this thread by Ecoris. At that point nobody commented on me thinking that I was behaving like a child; i.e. I hadn't actually observed anything and the fact that I seemed amazed on page 2 of this thread was indeed an honest reaction. However, I remember that I had an ace in my sleeve (probably this one - I really don't remember anymore), which could actually prove that what I did (pretending not knowing) was done just so that others get involved with the project and have more testers, because clearly this would speed up the process and that was all I really cared and frankly all that really mattered.
Moreover, check the first post in this thread at page 3; right here. Essentially I am describing there exactly what you asked. And once again I pretended we had to make some tests to see what's going on. Is it still not clear that I was trying to make everyone interested in the project and I wanted Xarfax to stay around? I pretended once again I didn't know until somebody comes up with the tests (or similar ones) I have above. However, I was ignored. And I didn't mind. I implemented it the right way; or if you prefer, the way that it seems to be more reasonable to explain the level ups.
Ok. Confession time is over. Feel free to give me a -QP for being so lame 3 years ago. I would still do the same thing under the same circumstances.
Best regards to all, and peace.
*May be it had to do with the thread by Xarfax saying bye-bye to this community, may be not. The other reasonable alternative is Russ' thread on Skill Chances. I have to check where I made that statement.
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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 28, 2009 08:08 AM |
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Edited by dimis at 12:27, 28 Mar 2009.
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Tools on Bounding Probabilities
Ok, I am more than certain that some people are trying extensively what I suggested above thinking that 18 examples are clearly not enough to draw conclusions (although even 10 or less are enough). Here I will give you (for those of you who don't know) probably the state-of-the-art tool that you need in order to convince yourselves that even few experiments can make you very confident on drawing conclusions.
The tool is called Chernoff-Hoeffding bound. The variation (I simplified it) that is particularly useful for these sort of tests is summarized in the following equation:
Pr[ |observed_average - true_value| >= a] <= e^{-2Na^2}
Now let me explain all the parameters and then I 'll give examples on how we can use it.
N is the number of tests that you make.
a is the accuracy.
observed_average is the empirical probability of what you are testing.
true_value is the real value that you are trying to figure out (I assume some probability here).
The basic intuition that you don't want many examples to "roughly" approximate one quantity comes from the right hand side of the inequality. As N increases (for fixed a), the probability that your empirical probability deviates from the true value decays exponentially fast; i.e. even when you make one more experiment, then you bound this probability by whatever you used to bound it before divided by e = 2.7...
Example 1
Suppose I have a coin and I want to determine how likely is it to come up say heads (H). Clearly the coin has a true probability p with which it comes up heads (H). Moreover, say that I want to approximate this value with accuracy 0.2 and I make just 10 coin tosses; i.e. a = 0.2, N = 10. Substituting these values on the right hand side, we get e^{-2*10*0.04} = e^{-0.8} which is about 0.45. What do all these numbers mean? Let's make it more specific; say that on those 10 coin tosses you observed 8 heads; i.e. empirical probability = observed average = 8/10 = 0.8. Then the bound tells you that with probability 1 - 0.45 = 0.55 (55%) the true value for p (i.e. the likelihood of this coin giving you heads when you toss it) is within 0.6 and 1.0 (these last two values were obtained by 0.8 by subtracting or adding the accuracy 0.2). Of course this is not a great accuracy, so let's see the following example.
Example 2
Suppose now that we have a coin and we want to be 95% = 0.95 confident that we approximate the true probability p the coin has of turning up heads (H). How many times should we toss the coin to achieve that? For simplicity let's baptize that 95% as "delta" since for other tests we might be ok if it is just plain 90% or 80%.
Well essentially all that we really have to say is that the right hand side is bounded above by "1 - delta" (= 0.05 in this example). This means that we want
e^{-2Na^2} <= 1 - delta
Taking the logarithms and solving for N we get
N >= 1/(2a^2) ln (1/(1-delta))
So in this particular example this last equation gives us:
N >= 1/(2a^2) ln (1/0.05) = 1/(2a^2) ln 20 =about= 1.49786613777 / a^2
So, clearly N depends on a which we still didn't specify.
So, say that we want to approximate the probability of turning up heads within 1%. This means a = 1% = 0.01. Substituting we get
N >= 14,978.66
which means that we have to toss the coin 14,979 times. This might sound too much, but essentially we require a very good approximation. For example, if you do such a test with a regular coin that sits in your wallet and the empirical probability of getting heads when you toss it is more than 51%, then you are 95% confident that this coin is biased. In other words, keep the coin and start making bets with people (you bet H). In the long run you 'll earn money by fooling others since it is almost certain that this coin is biased. Of course some caution is needed on the amount of money you bet each time because you don't have an infinite amount of money in your bank account.  In other words, small bets and patience is needed.
Just for the record: There is an even better tool which we can apply, called the central limit theorem. But the above analysis is really simple and we don't gain much with the central limit theorem; so stick on the Hoeffding bound.
Reminder: The table on AL (Always Left) policy was generated for N = 10,000,000. Set your favorite a or delta in the last blue inequality above and see what the other value is.
Quote:
I tested english version of LMOracle, it seems to work. Calculations take a lot time though.
Thanks SAG. I guess at some point I'll check it out.
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The empty set
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Rainalcar
Promising
Famous Hero
Heroji su zakon
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posted March 28, 2009 01:00 PM |
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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%
where S is the sum of weights for the skills that you already have. Of course here I assume that there is at least one of the 8 slots free so that you can be offered a new skill.
...
I knew this from year 2000 (I think) . Don't get me wrong, you know me better then to think I'm teasing you, I love reading your (I mean in plural) posts, highest density of keen observations per square letter around here
And of course the tables are right, it's just that people misinterpret them.
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Ecoris
Promising
Supreme Hero
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posted March 28, 2009 08:55 PM |
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Quote:
And by the way, there is another interesting alternative that might not have been clear. If both wisdom exception and magic exception occur at the same level, and you can upgrade wisdom, then you are also forced to get a new magic school given that you have a slot to keep it (and of course there is at least one Magic School available for your hero to learn). Note also that this is consistent with the "level-13-exception" described in page 2 of the thread.
Are you saying that if e.g. a level 7 hero who took wisdom at level 2 and is now up for a double exception at level 8 will be offered advanced wisdom and a magic school at basic level?
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dimis
Responsible
Supreme Hero
Digitally signed by FoG
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posted March 28, 2009 10:04 PM |
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Edited by dimis at 22:07, 28 Mar 2009.
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Wisdom and Magic exception collision
Exactly.
And since I figured out this was again not clear enough, I generated an example on the same map. Here is the example. And now let's observe some level ups.
L2: Pick Wisdom
L3: Pick Offense
L4: Pick Fire
L5: It doesn't matter what you pick
L6: It doesn't matter what you pick
L7: It doesn't matter what you pick
L8: You are offered Adv Wisdom and Basic Earth Magic
i.e. all 8 different variations above lead to the same result at level 8: Adv Wisdom and Bas Earth.
Moreover:
Variation 1:
L3: Pick Eagle Eye
L4: Pick Fire
L5: Pick Logistics
L6: Pick Armorer
L7: Don't pick Luck because you have no available slot afterwards.
L8: You are offered Adv Wisdom and Basic Earth Magic
Variation 2:
L3: Pick Eagle Eye
L4: Pick Fire
L5: Pick Logistics
L6: Pick Eagle Eye
L7: It doesn't matter what you pick
L8: You are offered Adv Wisdom and Basic Earth Magic
and so on ...
Now the funny thing is that in all possibilities above (even before the variations), at level 5 you are offered Logistics. I don't know if this is the way Xarfax was talking about getting Logistics 100% of the time. It fits well though on the statements that he makes.
Moreover, I don't really like that in all cases above I was offered Earth Magic as a new skill. Can someone check if a similar situation (level 2 accept Wisdom and level 4 accept Magic - which one?) can yield to a different combination of Magic skills. I remember that when I tested this particular example while I was writing the code I didn't write down anything. I just verified that you get Adv Wisdom plus a new Magic Skill so I interpreted it in the obvious way that I have above but seems to be contradicted here.
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The empty set
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Rainalcar
Promising
Famous Hero
Heroji su zakon
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posted March 29, 2009 12:49 PM |
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I never noticed the must appear Logistics rule when I was involved more deeply in this. What I did notice is some fixed trees and loops, I think Binabik metioned it, and in that respect it is possible to guess the skill selection, but I never tried to quantize it for I didn't have a clue how to do it. I cannot check your map Dimis for I do not have the game now, but I would guess that Log appearance is simply based on the specific random seed peculiarity which influences skill offerings. What we don't know is how to decypher how this number translates into game mechanics (at least I don't). For Xarfax is right when he says that there are NO probabilities in Heroes - imo, with perfect knowledge of the game one can predict every single game based on the beginning state, kind of like classical mechanics in physics. In that respect I don't know how the weight tables should be understood. This could perhaps be tested: say you have a secquence of skills ABCDEFGHIJ where letters represent skills, and say that secquence is one of those someone reported as repeating. If this secquence of skills can be reproduced for every game, it would be possible to see how it would change if you change the weight of, say, skill J - would J still appear, or would it be replaced? With enough testing, if it would show that the same secquence will appear every time no matter the changed weights of the skills consisting it, then Xarfax is right and the tables likely play no meaning. Otherwise, the tables are a factor.
I'm rather certain that the same effect, as described for Logistics, should come up for other skills as well, given other applicable random seeds.
Pretty much the same thing goes for Earth magic I believe: it's continued appearance is tied to the map i.e. random seed, not that it somehow bypasses weight calculation compared to other magic shools.
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Xarfax111
Bad-mannered
Supreme Hero
The last hero standing
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posted March 29, 2009 06:23 PM |
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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%
..and
Quote:
, then Xarfax is right and the tables likely play no meaning. Otherwise, the tables are a factor.
Both statements are wrong. The skill table does have a meaning to the probabilities, as if you edit the table you will see other probabilities in the game.
But there are some more things to observe. First the game designer only worked with the skill table. Then they thought that the might heroes would be superior to magic heroes and implemented one game routine that says: Give the might hero every 4th skill a magic skill.
At that point the non-magic skills add up to 100, while the magic skills add up to 12. So everyone that works with 112 is wrong anyway.
In the given example the magic skills add up to 12. Im not sure how it adds up to 12, as for example its earth 4, fire 3 and air 3 something.
So if air is already given its about 4/7 for the magic fixed skill slot.
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.
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dimis
Responsible
Supreme Hero
Digitally signed by FoG
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posted March 29, 2009 07:34 PM |
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Edited by dimis at 22:11, 29 Mar 2009.
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I am glad you are back, but your sayings don't justify what is happening during level-ups. The only way (apart from being offered at random) for a hero to obtain a new Magic School while he already has another one not at Expert level is if he already has Wisdom not at Expert level and Wisdom and Magic exception coincide on a particular level. One example of this was given above at level 8. Another example can be if everything goes on "naturally" until level 12 and in between you pick Wisdom at levl. 6 and Magic at levels 4 and 8. Another one, you are offered Wisdom at level 3 (which you pick), Magic at level 4, advanced version of Magic at level 5, and then at level 9 you are offered Adv Wisdom plus another Basic Magic. And so on ...
Now, returning to the Logistics thing... I did the same test with our friend Crag. Here is the example. Again the guy is offered Wisdom at level 2. Let's see now:
L2: Pick Wisdom
L3: Pick Artillery
L4: Pick Fire
L5: You are offered Adv Fire and Bas Logistics
However, Crag's path is more fragile. Another funny variation though is:
L3: Pick Offense
L4: Pick Fire
L5: Pick Wisdom
L6: Pick Wisdom
L7: Pick Fire
L8: You are offered Exp Fire and Bas Logistics
Anyway, for this part, even if it is true, I totally agree with Rainalcar; i.e. it's just a flaw in the sequence of skills that are offered. Of course Olaf can be right, but it is not because it's an exception (game rule, game routine, call it however you like). Besides, this one we already knew by Ecoris and his testing. And it is apparent here on Crag since Logistics does not appear at level 5, no matter what. For me this is like chasing ghosts like the ones people chase when they are addicted to gambling...
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The empty set
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This thread is pages long: 
