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Infernal Pit SpecialChest runs: high probability of Zod and other HRs

Discussion in 'Single Player Forum' started by vmiguli, Apr 10, 2018.

  1. drmalawi

    drmalawi Diabloii.Net Member

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    What I am after is the chance of getting rune X when i start a run (i.e. when I dont even know what kind of set I get)

    But that is ok, I can work it out
     
    Last edited: Jun 7, 2019
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  2. vmiguli

    vmiguli Diabloii.Net Member

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    @Fruit, thank you for posting your results here!

    Now we can evaluate a prosperity of this place in terms of HR-hunting by comparing it to expected theoretical values:

    Code:
    Rune      Prob,%    ExpProbSC,%   CountSC       ProbSC,%
    Zod       0.019       0.0020        1           0.0015 
    Cham      0.025       0.0027        1.7         0.0026 
    Jah       0.076       0.0082        6.26        0.0096 
    Ber       0.068       0.0073        6           0.0092
    Sur       0.102       0.0110        6.08        0.0093
    Lo        0.092       0.0099        5.58        0.0085
    Ohm       0.138       0.0149        8.98        0.0137
    Vex       0.130       0.0140        8.78        0.0134
    Gul       0.196       0.0211        9.06        0.0138
    
    
    Prob, % - probability of a dropped rune to be a certain rune (1 out of 5170 for Zod, etc.; probabilities for other HRs were calculated earlier in the thread – page #3)

    ExpProbSC, % - the theoretical chance to see a certain rune when hitting the SC (with unlimited seeds). The chance to get a runic TC is 14/130 = 10.77%, thus ExpProbSC, % = Prob, % * 10.77%

    CountSC – the established amount of a certain rune for the SC. (for example, for Jah: 12%*4 (Cases #1-3)+ 20%*7 (Case #4) + 30%*7 (Case #5) + 38%*6 (Case #6) = 6.26)

    ProbSC, % - the calculated chance to see a certain rune when hitting the SC (with 65,536 seeds). ProbSC, % = CountSC / 65,536


    At first glance, the conclusions are discouraging for my start-topic. Indeed, only Jah and Ber runes display higher dropping probabilities as compared to other rune-harvesting places; where the theoretical values should be considered (for either monsters or chests without the known final pattern count). Only one sole Zod count (4 total Zod patterns add up to 1 count) is a huge disappointment for my hopes. So, it is always 1 out of 65,536, as it looks like.

    On the other hand, it might be not so bad after all. First, Jah and Ber are the most sought high runes in game and having such a big advantage in probabilities should definitely result in considering Act V SC runs as an alternative for LK for these runes. Yes, I know, 3 patterns for Ber there, 11 for Sur, 6 chests in one run, do the math. But! It was a long time road before the optimal (time-wise) strategy was discovered there, and who knows what is the best strategy here, in Act V? There are 3 chests in three mini-levels: with a proper map the triple chest-run might be something more rewarding. The research has not been done in full to discard the Act V SC rune-hunting strategy as non-profitable. Is there a map of a mini-level that, for instance, spirals around for just a couple TPs to the chest from the portal? We don’t know. Is the S&E lag dependant on the time spent in the mini-level? How get rid of it? Because sometimes there is no lagging. There was no lagging during my long runs on the first Map. Many question for research and investigation.

    Second, Cham probabilities equal its theoretical values. So it comes to a math after all, which is different for each character: what is the less time-consuming way that gives the biggest probabilities for Cham? Counsels, Cows or maybe Act V SpecialChests: killing or running, that is a question. At least, right now there is a new evaluated opportunity for HR-hunting.


    However, I still have doubts that we comprehend the full picture. The main reason for this is the following table of my 9,700 IP SC runs:

    Code:
    Rune      Prob, %    ExpSC(9,700)   IP SC(9,700)
    Zod       0.019       0.20             1
    Cham      0.025       0.26             1
    Jah       0.076       0.79             0
    Ber       0.068       0.71             2
    Sur       0.102       1.07             1
    Lo        0.092       0.96             2
    Ohm       0.138       1.44             2
    Vex       0.130       1.36             0
    Gul       0.196       2.05             5
    HR(Gul+)  0.846       8.84             14
    
    Prob, % - probability of a dropped rune to be a certain rune (see above)

    ExpSC(9,700) – the expected amount of a certain rune from the SC after 9,700 runs. ExpSC(9,700) = Prob, %*9,700*10.77%

    IP SC(9,700) – the actual amount of a certain rune found from the SC after 9,700 runs

    Don’t you think it is too much just for “blind luck”?

    Well, logically there are only 2 ways:

    (A) That is just luck.

    (B) There was something that had influenced the outcome of my runs in IP.

    To prove (A) is the case I need to reject (B). @Fruit would you be so kind as to help me with this?

    What I have in mind is to find out if the Case-dependant running code could be somehow influenced by other factors, like the map, the monsters around, the # of TPs, etc. The observations that were proven active for LK armor stands, for example. Thus, if the program somehow forces the certain scenario (Case 1-6) after the repeating the same procedure – then the 1-10,000 random roll is NOT RANDOM at all. Thus, if I would stick to Case, let us say, #4 (20%) most of the time – then my runic outcome would be much more rewarding, than if the Cases are truly random. That is my logic.

    Now, the way to prove or invalidate this hypothesis is to check the real outcome for my HR’s patterns and compare the Cases. I hope, Fruit, you will help me out when you get a chance!

    Map #1 (runs 1-2,000)

    Ist_1_IP : Ancient Axe, Demonhide Gloves, Embossed Plate, Full Helm, Mace, Tiara, Tomahawk, Two-Handed Sword

    Ist_2_IP : Balrog Blade, Barbed Club, Battle Staff, Broad Sword

    Gul_1_IP #1: Axe, Blade Talons, Dirk, Breast Plate, Gauntlets, Gladius, Loricated Mail, Splint Mail, Two-Handed Sword

    Ohm_1_IP: Great Sword, Kite Shield, Poleaxe, Royal Shield

    Lo_1_IP : Thul Rune; Breast Plate, Broad Axe

    Cham_1_IP: Eth Rune; Chain Mail, Cloudy Sphere, Great Axe, Maul, Ring

    Zod_1_IP: Bone Wand, Demonhide Sash, Dragon Shield, Heraldic Shield, Light Plated Boots, Partizan, Short Spear (Dragon Shield, Heraldic Shield, Light Plated Boots, and Partizan should be added – video checked)


    Map #2 (runs 2,001-9,700)

    Pul_1_IP: Assault Helmet (n.), Gothic Plate, Morning Star

    Pul_2_IP: Crossbow, Flamberge, Flamberge, Luna, Mask, Short Spear

    Pul_3_IP #1: Bardiche (e./s.), Blade Talons, Crown, Falcion (n.), Giant Axe (l.q.), Mask (l.q.), War Javelin

    Pul_3_IP #2: Bardiche (e./s.), Blade Talons, Crown, Falcion (n.), Giant Axe (l.q.), Mask (l.q.), War Javelin

    Pul_4_IP: Cestus, Ring, Short Spear, Quhab

    Um_1_IP: Amn Rune; Ancient Sword (n.), Hunter’s Guise, Legendary Sword (l.q.), Maul, Military Pick (e./s.), Spiked Club (l.q.)

    Um_2_IP: Simbilan, War Fork, War Hummer (l.q.)

    Mal_1_IP: Flying Axe (l.q.), Hatchet Hands (l.q.), Short War Bow, Plate Mail, Wyrmhide Boots (l.q.)

    Mal_2_IP: Bramble Mitts, Destroyer Helm

    Mal_3_IP: Balrog Skin, Demonhide Gloves, Grand Crown, Hellspawn Skull, Razor Bow

    Ist_3_IP: Tal Rune; Ancient Sword (l.q.), Balanced Axe (n.), Hunter’s Bow, Military Axe, Partizan (l.q.)

    Ist_4_IP : Balanced Axe, Cestus, Chain Mail (l.q.), Full Helm, Great Hauberk (l.q.), Light Belt

    Gul_1_IP #2: Axe, Blade Talons, Dirk, Gauntlets, Gladius, Loricated Mail, Splint Mail, Two-Handed Sword

    Gul_2_IP #1: Fascia, Gauntlets, Horned Helm, War Spear

    Gul_2_IP #2: Fascia, Gauntlets, Horned Helm, War Spear

    Gul_3_IP: Amulet, Amulet, Scythe, Spiked Club, War Axe, War Axe

    Ohm_2_IP: Breast Plate, Diamond Mail, Ghost Armor, Ghost Wand

    Lo_2_IP : Fury Visor, Lance, Long Battle Bow, Maiden Javelin, Troll Nest

    Sur_1_IP: Crown (l.q.), Francisca, War Fork (Short Battle Bow came from monsters – video checked)

    Ber_1_IP: Tal Rune; Ancient Sword, Axe, Balanced Axe, Chain Mail, Kite Shield

    Ber_2_IP: Field Plate, Scutum, Ogre Axe, Protector Shield, Ring, Small Crescent, Shadow Bow, Spider Bow (Shadow Bow should be added – video checked)

    @Fruit, I am sorry for asking for such a time-consuming task! If it is too much of an effort, I hope you would figure out how to establish validity of this theory, or disprove it finally. Maybe not all patterns to check? I don't see so far other ways to find out if such a dependence takes place.

    Thank you again for your research!
     
    Last edited: Jun 10, 2019
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  3. pharphis

    pharphis Diabloii.Net Site Pal

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    The sad part is that even with extremely good maps, you will likely never even reach half as many chests per second compared to LK. I wonder if regular objects in certain areas could make up for that? Probably not.
     
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  4. drmalawi

    drmalawi Diabloii.Net Member

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    @vmiguli thanks for summarizing the probabilities from Fruit's research, I will double check when I have time.

    But you are doing some wierd stuff when you wanna compare with your own results.
    Remember these events are Binomial / Poisson distributed, which have a HUGE variance.
    Expected is 8.8 and you got 14. Big deal... expected here just means "most likely outcome". We can approximate the width as sqrt(average) { though we have too small average to do the Guassian limit properly it is still reasonable }
    14 is within 2 sigma from 8.8

    The only way to "experimentally" verify the theoretical probabilities is to let many many players to the same amount of runs and then compare the experimentally obtained distribution with the theoretically one. Or that someone does an insane large about or runs, and then divide the entire run sequence into smaller segments (like sizes of 10-20k each) and then compare the distribution of runes with the theoretical one.

    " as an alternative for LK for these runes. Yes, I know, 3 patterns for Ber there, 11 for Sur, 6 chests in one run, do the math"

    According to fruit's research, there are 2 Ber Patterns and 9 Sur Patterns for p7/8
     
    Last edited: Jun 9, 2019
  5. NarfBG

    NarfBG Diabloii.Net Member

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    Of all the IP maps I rolled (30-ish) while I did my 900 runs, and then casually exploring Abaddon on maps I ran for other purposes, the chest was always at the end of the map with only one circle around it. So that seems to be a constant pattern.

    However, having a special chest on the way to the red portal is a definite and very achievable improvement. In fact, I saw some streamer with a Frigid Highlands map like that - Eldritch -> special chest behind him -> Abaddon, each step within 3 teleports I think.
    On that note, do we know the spawning locations of all act 5 special chests?

    I've noticed that those lags are longer when there are monsters attacking you (no difference between melee or ranged attacks, so it shouldn't be proximity based) and have observed similar behavior during LK runs, racking and Gem shrine hunting.
    As I do lots of Pindleskin farming, I also noticed that sometimes there's S&Q lag there as well and it seems to happen when the Prowling Dead in the open area awaken and come close to the stairs. If I just quickly kill and don't stay to pickup items though, there's almost never lag.
    So, I would speculate that it has something to do with triggerred monsters actively chasing you; perhaps something to do with garbage collection (each monster is a program object, with lots of properties and these things need to be cleaned up from memory).

    Not really ... here's 2 examples why:

    1. Just the other day, I went back to Lower Kurast, still looking for that Ber or second Sur I needed and somehow - first run, first chest I popped - Sur! And this wasn't even the real blind luck ...
    See, knowing how much grind is expected, I was prepared to do LK all day long and so I couldn't just stop there ... it would've felt weird. I went on, and got Lo, Vex, Vex, Ist, Lem, Lem (I know people only count Pul+, but Lem is notable for me), a 24 max damage jewel and 3-4 very good charms within the next 60 runs!

    2. About a month ago, withing a single week, I knocked off about 15 items off my holy grail progress, including Tyrael's Might, Mang Song's Lesson, Astreon's Iron Ward, Griffon's Eye, Stormspire, Natalya's Mark, Medusa's Gaze and Spirit Ward. I had already found the super-rare Bul-Kathos set, but got that TWICE during that time as well. And if that's not unbelievable enough, I also happened to gamble Saracen's Chance during that time.

    We as players consider that to be great stuff, but none of these items have anything in common from a programming perspective when it comes to whether they drop or not. Sometimes when it rains it pours.

    I happen to know a thing or to about RNGs and I can say with confidence that you're right on that. Virtually every game (including D2 of course) uses seed-based pseudo-randomness and seed-based mechanics are deterministic by nature. Knowing the starting input seed, every subsequent event is 100% predictable.
    However, we are human and not capable of even translating the graphics we see into numbers, let alone computing them to make predictions on the fly, so with a few barely noticeable patterns, it is effectively random for us.

    Let's say the chosen chest cases are affected by the current map seed and another, in-memory seed (speculating here, but something is variable after all). It is entirely possible to roll a "good" seed that would yield awesome rewards in a (relatively) short timespan. But you still have no way of knowing whether you landed on a path to a "good" one, nor how many seed permutations it would take to get you to the very lucky rolls.
     
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  6. vmiguli

    vmiguli Diabloii.Net Member

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    @drmalawi you are right in your conclusions and your mathematical analysis. It is all within the possibilities, and most likely it is. And I would appreciate if you could check my math - I have not thoroughly checked it myself, just don't have that much time these days.
    However, I have one objection to your logic. You have a fresh cold-blooded look from the "outside". You will manage to explain every possible deviance from the expected values that is performed by one person, and thus has limited amount of data. 9,700 is not enough, 97,000 is not enough, even 970,000 runs will be disputed. But if I had given up to this logic in the very beginning this thread would have died within days. You remember how many people suggested (being absolutely right in their logic!) in the beginning in the thread that it is just a waste of time to pursue a 4.2 billion chest-running? You can check the thread - it is still there. Not in these words, but that is what they meant.
    But I am not a cold-blooded outsider. I am there, inside the game, doing the runs and having that peculiar feeling that "there is something to it". So I continued, and after a long-long time, mostly alone, I have managed to prove that "the stereotypical belief", as I called it once, is not necessarily the TRUTH as it is. You remember that agent Mulder poster? Yes, I want to believe - that was my driving force. And it was not in vain after all.
    Now, IF there is a chance that the character's behavior or other player-controlled modes could influence the "RANDOMNICITY" of the SpecialChest - that would be one interesting discover, would not you agree on that? After all my running experience I have a strong feeling that it is not that simple! As a researcher I try to seek the answers from what is available - and that is not a lot: just 7,700 PoA runs, 9,700 IP runs, several screenshots by my running colleagues, and a sudden great help from a programmer-professional.
    I do want to find the answer to the question: WHY DOES THE ARM-STAND IN LK ALWAYS GIVE THE SAME OBJECT IF YOU RUN TO IT THE SAME WAY EACH TIME and if you choose another path or start fighting - it does not? Do you have an answer to this question?
    This gives me hope, that my feeling about IP SC is not just conspiracy theory. Maybe there is an answer...
    Well, maybe not. But it's fun to explore anyway!
     
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  7. drmalawi

    drmalawi Diabloii.Net Member

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    There are population tests one can do you know.

    Racks have a totally different mechanic than chests, just not only in LK.
    https://www.diabloii.net/forums/threads/item-generation-from-racks.788376/
    post #11:
     
  8. vmiguli

    vmiguli Diabloii.Net Member

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    @NarfBG Thank you for sharing your experience!
    LK arm-stand is a good example of how you can "beat RNG". You chose a map with a needed armor, run until you get a set or unique, use it.
    That is exactly the feeling I was talking about in IP. I FEEL how my behavior forms the future events. Cool feeling, must to admit! Unfortunately, the maximum of my "magic" (that I was conscious of) was forming a mana shrine in a certain place by way I get to it. Worked 100%. It is much more complicated with the SC, but I believe there is also a connection.
     
  9. vmiguli

    vmiguli Diabloii.Net Member

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    @drmalawi Thank you for the link! That is exactly what I meant for IP SC:
    "when the map seed is established and another seed that is based on time"
    I just want to check those 10,000 RANDOM events, what is the seed that starts it dependent on???
     
  10. Fruit

    Fruit Diabloii.Net Member

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    While you guys are tossing around fancy math, I tend to approach it more simply. :p

    Imagine flipping a coin 10,000 times; you can expect ~5,000 to land heads, ~5,000 to land tails. But how would the pattern look? If H = Heads and T = Tails, would it look something like so?
    Code:
    H-T-H-T-H-T-H-T-H-T-H-T-H-T-H-T-H-T-....
    Well no, from experience (or brains) we know that you will see streaks of X and streaks of Y; perhaps a streak of 6 tails in a row, perhaps 10 heads in a row, etc.

    The same idea can be applied to our (chest) running: You do 10,000 runs and have an "unlucky streak"; you find a couple of high runes, but perhaps only half of what you expected. Or in stead, you do 10,000 runs and you find almost twice as many as expected.

    So in situations like this, where you have 4 different sets of 65534 patterns, you probably need millions and millions of runs to gather data that is sufficient to verify any theories. Because let's say it was claimed that the probability of a high rune is 10 in 100, and you do 10 runs, but no high rune has dropped; would that mean that the 10 in 100 is incorrect, and the real probability must be lower? Of course not. Similarly, you can do 10 runs and 3 high runes drop, but that wouldn't necessarily mean that the probability is in fact higher than 10 in 100.

    My point is that, unfortunately, 9,700 runs is almost nothing, considering.



    And while what @NarfBG mentioned is an important aspect, I'm not so sure there is much, if any bias coming from the "master seed":

    The master seed, usually dubbed "game seed", is the fuel for randomness, and even the map seed is created from (seeded by) this game seed. This game seed is what RTB would've been referring to; a number that is generated by some formula, and as input/seeds it takes a few timers. (I'll refrain from posting the exacts, as that just may cross that line into code-discussion territory, but let's just say it calls a few Operating System functions that retrieve the values of certain timers.)

    The map seed will then of course be overwritten by your character (if applicable), but the map seed is actually not used for a whole lot, other than the actual "world generation" (or however to call it).

    Now, besides generating the map seed, the game seed also generates an "object seed", which is used for a bunch of object-related stuff (mostly initializing certain object types), though in most cases it is the game seed that generates the initial/starting seed for a unit (player, monster, missile, item). Then, whenever a unit needs a random roll done, it is usually its own seed that fuels the random roll; think of things like the to_hit formula, damage rolls, AI checks for monsters, item drops, etc. (Missiles sometimes use the seed of their source rather than their own seed, for example for the to_hit roll.)
    Armor Stands and Weapon Racks are exceptions, as these two objects use the seeds of the segment that they spawned on. Segments are indirectly seeded by the map seed, and I specify indirectly here because, as you know, route and monster spawns (which are seeded by the game seed) both have an effect on the seed of a segment, thus also on the mentioned objects. (There may very well be more exceptions, but I only know of these two objects that work like this.)

    Lastly, a simple but critical aspect to seeding is that whenever a seed is generated, or a random roll is done, the seed that was used in that process will be updated. This ensures that seeds don't stay the same, thus ensures that results will continue to vary. Randomness!



    Now, the famous limited seed of chests is generated/seeded by this "object seed" that I mentioned. This means that on your way to your sparklychest, everything that uses this object seed will end up playing a role in what seed the sparklychest ultimately ends up with. The random roll of 10,000 also is seeded by this object seed.

    I couldn't tell you exactly all the objects in the game that make use of this object seed, but I can tell you that there are plenty, and some of them continuously use it, for example certain kinds of fire patches on the ground, and certain fiery things in lava. This object seed is typically used to "initialize" many kinds of objects (including chests), so as you move around the world, many objects you move past that seem to have absolutely nothing to do with the sparklychest or superchest that you eventually end up at, they will actually all have an influence on its pattern. Both the game seed and this object seed are global, so you can not somehow escape this randomness; it is shared for all acts, areas, etc.



    So anyway, I suppose my point is just that the overall randomness really is quite strong, as so many things end up affecting so many other things in the world; the "main seeds" are constantly being updated, sometimes even when "nothing" is happening. However, as @NarfBG pointed out, it is pseudo-randomness after all, and therefore it is possible that there is a certain bias towards (a) certain sparklychest case(s). This does not seem likely to me, but I wouldn't just trust my own gut feeling on this.


    @vmiguli If you're asking me to check which case each of your patterns came from, then it would help if I knew which player number they were found on? (If you can't remember, then I'm afraid I'll have to pass on your request. :p)

    @art_vandelay and I made a list a little while back. I presume all of these are known already, but I don't think there are any others:

    superchests:
    Code:
    Frigid Highlands
    Glacial Trail
    Halls of Anguish
    Halls of Pain
    
    sparklychests:
    Code:
    Drifter Cavern
    Icy Cellar
    Abaddon
    Pit of Acheron
    Infernal Pit
    
     
  11. drmalawi

    drmalawi Diabloii.Net Member

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    @vmiguli you said you are a researcher - then behave like one - no feelings, just facts, ok? As a professional physicists, I am a bit ashamed of your behavior in this thread actually.

    @Fruit the distribution over number of heads when you flip 10000 coins will be Gaussian with average at 5000 and standard deviation sqrt(5000) = 70 (well 71 but lets keep things simple).

    Thus 68% will get between 5070 and 4230 heads, 95% will get between 5140 and 4160 heads.
    Not only do we need the average value, but also the spread to conclude if we are lucky or not.
    This means that not only the average needs to be verified , but also the shape.

    If you flipped a coin 10000 times and you got 7000 heads, I would say that the coin is not balanced, you are cheating or something that influences the random nature of the even.
     
  12. vmiguli

    vmiguli Diabloii.Net Member

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    @Fruit Thank you for explaining the seeds! A year ago I tried to get some info about RNG and its use in the games, however your info about the seeding process exceeds all the "wikipedia" info I got by myself. Thanks again!

    And all my runs were made in player7 mode, if you could check it. Despite that after your message I am pretty sure that there will be no abnormalities.

    @drmalawi you don't have to be ashamed by other people personalities. Apparently, you are different, and you believe that you KNOW how the TRUE researcher should behave. However, forcing others (by any ways) to appear the way you want them to look like is not the best approach. Proven by history of 20th century.
    As for my "feeling" that got you so annoyed, as I can judge, well I tell you - it is normal for researcher to have an intuitive lead when the territory is unknown. There is nothing mystical or shamanic to it, it is just a feeling of where your research should turn when there is only a handful of data. It is not successful every time, of course, but it gave me some unexpected great results in my profession in the past; and here also: we have this conversation because I trusted my intuition and continued the research despite all the presented "facts" that my efforts were pointless.
    So, making a long story short:
    1. Facts and logic are keystones of the research. If you don't have enough facts you use logic and, sometimes, follow your intuition (if you believe there is any).
    2. You accept all people as they are in their diversity with their views on logic, temper, emotionality, research, game-running, etc. and you do not try to change them just because you think that their attitude is WRONG from your point of view.
    Can we agree on that?
     
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  13. maxicek

    maxicek Moderator Single Player

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    Breathe people, let’s not escalate please.
     
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  14. Fabian

    Fabian Diabloii.Net Member

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    drmalawi,

    Thanks for taking over.
     
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  15. ffs

    ffs Diabloii.Net Member

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    Out of curiosity – based on the patterns we now know thanks to @Fruit, is it easy for you math specialists to give "break even" points in comparison to other areas?

    For example, how fast do we need to pop an A5 chest in order to break even with, say...
    • ... 20 second dual campfire LK runs for Ber?
    • ... 20 second Trav runs for Jah/Cham?
    • ... 180 P5 Cow kills per minute for Zod?
    From my perspective, benchmarks like that are what's actually decisive when it comes to whether or not it's worth it to run these chests.
     
  16. drmalawi

    drmalawi Diabloii.Net Member

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    It is straightforward to do such calcs :) Gimme a few days and I will make it happen

    but the breakeven will depend on the run speed of chests, or are you after the "expectation value" only?
     
    Last edited: Jun 10, 2019
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  17. Fruit

    Fruit Diabloii.Net Member

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    @drmalawi
    Thanks for the correction! Shame I couldn't even do the simple thing correctly; all I was really trying to point out is that you can expect to see streaks like that, so after a relatively short amount of coin flips you will not have sufficient data that verifies whether a coin has a 50% chance to land heads and 50% tails.

    @vmiguli
    Unfortunately, it's inconclusive. :<

    For example,
    Cham_1_IP: Eth Rune; Chain Mail, Cloudy Sphere, Great Axe, Maul, Ring:
    Case 4
    Code:
    ---------------start_seed: 51880
    Gold
    Oil Potion
    Maul (Magic)
    Flawless Ruby
    Gold
    Key
    Gold
    Gold
    Gold
    Gold
    Rejuvenation Potion
    Bolts
    Cloudy Sphere (Magic)
    Gold
    Gold
    Oil Potion
    Great Axe (Magic)
    Super Healing Potion
    Key
    Ring (Magic)
    Eth Rune
    Gold
    Chain Mail (Magic)
    Super Healing Potion
    Gold
    Cham Rune
    Flawless Emerald
    Super Mana Potion
    Super Healing Potion
    
    Case 5:
    Code:
    ---------------start_seed: 51880
    Gold
    Oil Potion
    Maul (Magic)
    Flawless Ruby
    Gold
    Key
    Gold
    Gold
    Gold
    Gold
    Rejuvenation Potion
    Bolts
    Cloudy Sphere (Magic)
    Gold
    Gold
    Oil Potion
    Great Axe (Magic)
    Super Healing Potion
    Key
    Ring (Magic)
    Eth Rune
    Gold
    Chain Mail (Magic)
    Super Healing Potion
    Gold
    Cham Rune
    Flawless Emerald
    Super Mana Potion
    Super Healing Potion
    

    As you can see, this pattern is shared between case 4 and case 5.

    Another example,
    Lo_1_IP: Thul Rune; Breast Plate, Broad Axe:
    Case 1 (2, 3)
    Code:
    ---------------start_seed: 10530
    Arrows
    Antidote Potion
    Super Healing Potion
    Super Mana Potion
    Breast Plate (Unique: Venom Ward)
    Thul Rune
    Greater Healing Potion
    Super Mana Potion
    Gold
    Gold
    Broad Axe (Magic)
    Lo Rune
    Arrows
    Gold
    Grand Charm (Magic)
    Scroll of Town Portal
    Gold
    Gold
    Long Bow (Magic)
    Gold
    Scroll of Identify
    Greater Healing Potion
    Breast Plate (Magic)
    Key
    Arrows
    Gold
    Gold
    Gold
    Gold
    Gold
    Healing Potion
    Healing Potion
    Mana Potion
    Mana Potion
    
    Case 4
    Code:
    ---------------start_seed: 10530
    Arrows
    Antidote Potion
    Super Healing Potion
    Super Mana Potion
    Breast Plate (Magic)
    Thul Rune
    Greater Healing Potion
    Super Mana Potion
    Gold
    Gold
    Broad Axe (Magic)
    Lo Rune
    Arrows
    Gold
    Grand Charm (Magic)
    Scroll of Town Portal
    Gold
    Gold
    Long Bow (Magic)
    Gold
    Scroll of Identify
    Greater Healing Potion
    Breast Plate (Magic)
    Key
    Arrows
    Gold
    Gold
    Flying Axe (Magic)
    Gold
    Gold
    Gold
    Scroll of Town Portal
    
    Case 5
    Code:
    ---------------start_seed: 10530
    Arrows
    Antidote Potion
    Super Healing Potion
    Super Mana Potion
    Breast Plate (Magic)
    Thul Rune
    Greater Healing Potion
    Super Mana Potion
    Gold
    Gold
    Broad Axe (Magic)
    Lo Rune
    Arrows
    Gold
    Grand Charm (Magic)
    Scroll of Town Portal
    Gold
    Gold
    Long Bow (Magic)
    Gold
    Scroll of Identify
    Greater Healing Potion
    Breast Plate (Magic)
    Key
    Arrows
    Gold
    Gold
    Flying Axe (Magic)
    Gold
    Gold
    Gold
    Scroll of Town Portal
    
    Case 6
    Code:
    ---------------start_seed: 10530
    Arrows
    Antidote Potion
    Super Healing Potion
    Super Mana Potion
    Breast Plate (Magic)
    Thul Rune
    Greater Healing Potion
    Super Mana Potion
    Gold
    Gold
    Broad Axe (Magic)
    Lo Rune
    Arrows
    Gold
    Grand Charm (Magic)
    Scroll of Town Portal
    Gold
    Gold
    Long Bow (Magic)
    Gold
    Scroll of Identify
    Greater Healing Potion
    Breast Plate (Magic)
    Key
    Arrows
    Gold
    Gold
    Gold
    Gold
    Gold
    Healing Potion
    Healing Potion
    Mana Potion
    Mana Potion
    

    You probably had the pattern from case 4, 5 or 6, and not from 1, 2 or 3, but still, nobody can tell which one it really was.

    Last example,
    Ohm_1_IP: Great Sword, Kite Shield, Poleaxe, Royal Shield:
    Case 4
    Code:
    ---------------start_seed: 24781
    Poleaxe (Magic)
    Kite Shield (Magic)
    Gold
    Greater Healing Potion
    Gold
    Super Healing Potion
    Gold
    Gold
    Super Healing Potion
    Royal Shield (Magic)
    Greater Healing Potion
    Gold
    Gold
    Scroll of Town Portal
    Arrows
    Ohm Rune
    Great Sword (Magic)
    Gold
    Super Mana Potion
    Gold
    Rejuvenation Potion
    Gold
    Scroll of Town Portal
    Gold
    Super Healing Potion
    Gold
    Gold
    Super Healing Potion
    
    Case 5
    Code:
    ---------------start_seed: 24781
    Poleaxe (Magic)
    Kite Shield (Magic)
    Gold
    Greater Healing Potion
    Gold
    Super Healing Potion
    Gold
    Gold
    Super Healing Potion
    Royal Shield (Magic)
    Greater Healing Potion
    Gold
    Gold
    Scroll of Town Portal
    Arrows
    Ohm Rune
    Great Sword (Magic)
    Gold
    Gold
    Gold
    
    Case 6
    Code:
    ---------------start_seed: 24781
    Poleaxe (Magic)
    Kite Shield (Magic)
    Gold
    Greater Healing Potion
    Gold
    Super Healing Potion
    Gold
    Gold
    Super Healing Potion
    Royal Shield (Low Quality)
    Scroll of Town Portal
    Arrows
    Ohm Rune
    Gold
    Gold
    Gold
    Gold
    Gold
    Healing Potion
    Healing Potion
    Mana Potion
    Mana Potion
    

    Probably case 4 or 5, but who knows which one?


    So as you can see, there are patterns that are shared between cases, and for plenty of your listed patterns it's just not possible to know for sure which case they came from.
     
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  18. drmalawi

    drmalawi Diabloii.Net Member

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    What one can do is to divide that 10k flip coin sequence into smaller (but still reasonably large ones say 1k each) segments and each segment would have different number of heads. The average for each segment should be 500 and the standard deviation sqrt(500) = 22(.4)

    So about 7 of those segments should have number of heads between 478 and 522, and practically all of them between 456 and 544 :)
     
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  19. vmiguli

    vmiguli Diabloii.Net Member

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    @Fruit Oh man, that is unfortunate indeed. That is the only logical evidence I could come out with having those screenshorts on hand. I thought that different "blocks of codes," as you say, would result in different patterns. In fact, we even don't know now the total amount of patterns since, apparently, some of them belong to multiple Cases. Anyway, thanks a lot for finding that out!
    And for Zod, are there 4 different patterns or only 1 for all 6 Cases also?
     
    Last edited: Jun 10, 2019
  20. Eriklop

    Eriklop Diabloii.Net Member

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    I think this thread is fascinating, i love how you guys bump into each other. What i as a total science/math noob see is that the question that vmiguli asked himself and others in this thread was good enough to get people to join the discussion. And i think that is the essence of good science (asking a good question and bring it into a public discussion). You have to ask the a good question. And its equally good that people help/push the topic into a direction that helps get the question solved. Ive learned new stuff from reading it.
     

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