II.
In order to make valid assumptions, I had to calculate the probabilities based on treuseclasses.txt data and then compare it to the obtained results.
Code:
TC Prob3 R01/Prob1 Probability01, % R02/Prob2 Probability02, %
Runes 9 180 Lum/3 1.622 Ko/2 1.081
Runes 10 360 Fal/3 0.822 Lem/2 0.548
Runes 11 720 Pul/3 0.414 Um/2 0.276
Runes 12 1066 Mal/3 0.280 Ist/2 0.187
Runes 13 1519 Gul/3 0.197 Vex/2 0.131
Runes 14 2170 Ohm/3 0.138 Lo/2 0.092
Runes 15 2941 Sur/3 0.102 Ber/2 0.068
Runes 16 3957 Jah/3 0.076 Cham/1 0.025
Runes 17 5170 Zod/1 0.019 N/A N/A
Probabilities 01 and
02 (in %) show the chances of runes 01 and 02 of the corresponding TC being dropped WHEN this TC is chosen. I use
italic to distinguish TC rune probabilities and dropping rune probabilities (no italic). (Unfortunately, the table code does not allow
italic in the body of the table – be aware: it is supposed to be
italic!)
So, when the game decides to drop a rune an algorithm goes from TC Runes 17 [1/5171 (0.019%) for YES for Zod + 5170/5171 for NO] to Runes 16 (next TC). Then analogously it chooses either 3/3961 (0.076%) for YES for Jah followed by 1/3961 (0.025%) for YES for Cham or 3957/3961 for NO to go to Runes 15. And so on… It repeats the cycles until the first YES or it reaches TC Runes 1.
This is the way how I got
Probabilities 01 and
02 (in %). Now, by adding up these
values (for each TC) we can calculate the total chances for all HRs (or Lum+ runes). Again, these chances are NOT for the chest but for a dropped rune to be a HR.
Prob(Pul+) =
Prob(Zod) +
Prob(Cham) + … +
Prob(Pul) = 2.005% – a calculated probability of a dropped rune (Act 5/Hell) to be a HR
Prob(Lum+) =
Prob(Zod) +
Prob(Cham) + … +
Prob(Lum) = 6.078% – a calculated probability of a dropped rune (Act 5/Hell) to be Lum+
At the same time, in order to get a probability of any PARTICULAR rune to appear from any dropper (Act V/Hell) we have to multiply A*B, where A is a probability of appearance of a rune from this object, and B is a probability of a dropped rune to be this PARTICULAR rune. For example, the probability of Lo rune in IP SC = 14/130 * Prob(Lo).
Prob(Lo) = [1-(1-
Prob(Zod))*(1-
Prob(Cham+Jah))*(1-
Prob(Sur+Ber))*(1-
Prob(Ohm))]*
Prob(Lo)= [1-(1-1/5171)*(1-4/3961)*(1-5/2946)*(1-3/2175)]*(2/2175) = 0.00092 or 0.092%.
It should be repeated that all the calculations above were based solely on data from “treusureclasses.txt”.
Now, we can obtain an expected number of all HRs for 100 dropped runes, or in my case, for 600 dropped runes or 6,000 runs. In fact, the SCs in Act 5mini-levels produces on average 1 rune in 10 runs, which is very convenient for the calculations
. Indeed, both the theory (14/130 = 10.77%) and my experience (10.5% Abaddon Map 1; 10.9% PoA Map 2; 10.5% IP Map 1 and 10.0% IP Map 2) lay in full accordance, allowing me to round it up to 10% for easy handling.
The following table gives a comparison between the calculated values and the experienced PoA / IP results.
Code:
Rune Prob, % Exp(6,000) PoA(6,000) IP(6,000)
Zod 0.019 0.12 0 0
Cham 0.025 0.15 0 0
Jah 0.076 0.45 1 0
Ber 0.068 0.41 0 2
Sur 0.102 0.61 0 1
Lo 0.092 0.55 1 0
Ohm 0.138 0.83 0 1
Vex 0.130 0.78 2 0
Gul 0.196 1.18 1 2
Ist 0.185 1.11 1 2
Mal 0.278 1.67 1 1
Um 0.271 1.63 2 2
Pul 0.408 2.45 4 3
HR(Pul+) 1.988 11.94 13 14
Lem 0.533 3.20 2 6
Fal 0.806 4.84 1 5
Ko 1.029 6.17 6 8
Lum 1.568 9.41 7 8
Lum–Zod 5.924 35.56 29 41
El+Eld 3.843 23.06 22 17
Prob, % = Probability, % – is a chance for a dropped rune to be a certain rune
Exp(6,000) – Number of expected runes for 6,000 SC runs
PoA(6,000) – Number of runes found in PoA (6,000 runs)
IP(6,000) – Number of runes found in IP (6,000 runs)
Unfortunately, there was no constant “runic shower” this time, and the obtained data appear much closer to the expected values than when I got my first IP SC runs experience. Nevertheless, I consider these results supporting my theory of better chances of HRs in the IP SC. Remember, I started doing these runs solely in attempt to prove that there are more parameters in D2 that influence a probability of a dropped rune, and IP is a champion among other chests. I got the results that confirm that! Yes, this is just 6,000 runs, it is not enough to make the final conclusion, but my results exceed the expected numbers by 15-17% (in terms of number of HRs and Lum+). And IP is definitely better than PoA, as it was better than Abaddon in my first trial. However, this could be statistically proven only by multiple participants and many, many more runs…
So, if I am correct, and there is a parameter that increases a HR probability for the IP SC than only one of two following scenarios could be realized:
A. Extra HRs come by additional rune generation (increased chances of TC Runes 17 appearance). In other words, it means more runes in general from the SC.
B. Extra HRs come in expense of other runes within the same TC Runes 17 – Runes 1 sequence. In other words, better quality of the dropped runes.
My running experience does not support A. As I showed above, runes were dropped in 10% cases like the theory suggests. I have not seen any deviation from this number in either mini-level.
Thus, B is the case. To check this hypothesis I calculated the total amount of all El +Eld runes (TC Runes 1 class); as it should be lower than the theoretical value.
Prob(El+Eld) = (1-
Prob(Zod))*(1-
Prob(Cham+Jah))*(1-
Prob(Sur+Ber))*…*(1-
Prob(Nef+Tir)) = (1-1/5171)*(1-4/3961)*(1-5/2946)*…*(1-5/7) = 0.03843 or 3.843%.
After 6,000 runs (600 runes) one should expect 23 El & Eld runes basing on the treasureclasses file. Well, I got only 17, which is 26% short. I suppose that might be another tiny piece of evidence for my theory.
I do not know what the final truth is; I am just modeling the satisfying explanation. Hope, one day it will be enough data gathered to be certain in according conclusions!..
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