Extraordinary and legendary items

[rijackson741]

WORK IN PROGRESS! WORKING ON A GOOGLE SHEETS DOC TO DO THE MATH FOR YOU, THE MATH BELOW IS INCORRECT. DO NOT USE IT!

The math is here: https://andorstrail.com/viewtopic.php?t=6613. It is correct.

[Anku]

The main point is that the monsters you've already killed don't count. You're always starting from zero, no matter how many hundreds or thousands you've already killed.

But I agree that these kinds of calculations can be fun, if only to get a sense in retrospect of how far your experience was from the centre of the curve.

This is not how probability works. Even though every monster has a fixed drop chance based on your Magic Finder level, your chances of obtaining the item DO increase the more monsters youve killed. The formula is: P(A) = 1 - (1 - p)^n when accounting for an unchanged Magic Finder level throughout your hunt. P(A) is the Probability of obtaining the item. p is the drop chance of the monster. n is how many monsters you killed.
Also, you can achieve a 100% drop rate for Extraordinary items by upgrading Magic Finder 18 times for Extraordinary items (this would require 72 character levels) or 198 times (792 character levels) for Legendary Items. It is true that you can never achieve a 100% chance to obtain the item without a 100% drop chance.
However the fact remains that the probability of obtaining the item does in fact increase the more monsters youve killed. We can use the Inclusion Exclusion Principle to determine the probability for any hunt that includes multiple Magic Finder levels throughout your hunt: e.g started with Magic Finder 2, but upgrade your Magic Finder 2 or 3 times before you received the item.
That's what the spreadsheet I just posted does. Unlike the other AT game mechanic posts, this spreadsheet accounts for multiple different levels of Magic Finder, and calculates the probability of obtaining the item based on what you input for monsters killed. The Andors Trail game mechanics post does not account for multiple MF lvls when calculating the total probability. My spreadsheet can give you the total probability of anywhere from 0 to 20 Magic Finder levels, and any combination of them as well.
The only catch is, you have to know approximately how many monsters you killed per each Magic Finder lvl.

[Nut]

Well, you are both right. Probability is a strange thing.

If you haven't started yet, the probability to get at least 1 ring after 1 mio kills is rather high.

BUT if you have done 999999 kills with no ring, the probability to get it on next kill is still 0.01%

[Canuck]

Exactly. Anku's probabilities apply only ex-ante, not ex-post.

The monsters you've already killed don't count, because the uncertainty has resolved itself. Whether you already killed 0 or 10,000 monsters makes no difference in the probabilities: they apply only to the monsters you haven't killed yet.

More here, for anyone interested:

https://en.wikipedia.org/wiki/Gambler's_fallacy

[Anku]

[*][/strike][/strike]

Exactly. Anku's probabilities apply only ex-ante, not ex-post.

The monsters you've already killed don't count, because the uncertainty has resolved itself. Whether you already killed 0 or 10,000 monsters makes no difference in the probabilities: they apply only to the monsters you haven't killed yet.

More here, for anyone interested:

https://en.wikipedia.org/wiki/Gambler's_fallacy

Yes, but just like people confuse independent events with dependent ones, which is what the gamblers fallacy is, many people also misunderstand the gamblers fallacy. The gamblers fallacy does not mean that the more times you do something the probability doesn't increase. If I rolled a dice 100 times, and was trying to get a 6, I would use this formula for independent events to determine the chances I would have rolled a 6 by now:

P(A) = 1 - (1 - p)^n
P(A): Probability for rolling a 6
p: chance of getting a 6 (1/6)
n: number of times I rolled (100)

Probability of rolling a 6 after 100 rolls = 99.99999%

The gamblers fallacy simply means that the more you do independent events, you can never achieve 100%

[rijackson741]

The occurrences in AT are independent. The monsters you have killed have no influence on the current probability of a drop, regardless of what level of MF you had, or have.

if you have had several levels of MF the calculation for the probability that you would have had a drop at some point is fairly simple. If the probability of getting a drop with MF0 is P0, the probability of getting a drop with MF1 is P1, etc. (the spreadsheet I posted will calculate those probabilities for you if you enter the level of MF and you know the number of kills with that level of MF) then the probability of a drop is

P=1-(1-P0)*(1-P1)*(1-P2)...

[Anku]

The occurrences in AT are independent. The monsters you have killed have no influence on the current probability of a drop, regardless of what level of MF you had, or have.

if you have had several levels of MF the calculation for the probability that you would have had a drop at some point is fairly simple. If the probability of getting a drop with MF0 is P0, the probability of getting a drop with MF1 is P1, etc. (the spreadsheet I posted will calculate those probabilities for you if you enter the level of MF and you know the number of kills with that level of MF) then the probability of a drop is

P=1-(1-P0)*(1-P1)*(1-P2)...

Yes I misunderstood what independent and dependent meant. I knew each kill was an independent event, but I thought that because when u kill 300 monsters with Magic Finder 2 and 500 with magic finder 3, and the game still counts total monsters killed as 800 that the combination of both events was "dependent". I didn't realize that dependent in this context would mean that the 500 monsters killed with Magic Finder 3 would retroactively or dynamically alter the chances of the the previous 300 monsters with Magic Finder two. Luckily, the spreadsheet I created correctly assumes the events are independent. I am editing my previous post now.

[Anku]

The occurrences in AT are independent. The monsters you have killed have no influence on the current probability of a drop, regardless of what level of MF you had, or have.

if you have had several levels of MF the calculation for the probability that you would have had a drop at some point is fairly simple. If the probability of getting a drop with MF0 is P0, the probability of getting a drop with MF1 is P1, etc. (the spreadsheet I posted will calculate those probabilities for you if you enter the level of MF and you know the number of kills with that level of MF) then the probability of a drop is

P=1-(1-P0)*(1-P1)*(1-P2)...

Omg, when I read your formula I was so worried that my spreadsheet was incorrect, because I used the inclusion exclusion principle formula for it:
P(A or B) = P(A) + P(B) - P(A and B)
Luckily, when writing the script for my spreadsheet, it assumes all events are independent (thank God I didn't make them dependent), and thus the two formulas are analogous and produce the same result.
No rewriting script for me! The spreadsheets math is correct!!!! Yayyy!!!

[Canuck]

The gamblers fallacy simply means that the more you do independent events, you can never achieve 100%

The main point of the Gambler's Fallacy is that past probabilities don't affect future probabilities.

If you haven't started rolling the dice yet, the chance of rolling a 6 at some point in the next 100 rolls is (as you mention) something close to 99.99999%.

If you've already rolled the dice 99 times without getting a 6, the chance of getting a 6 on the 100th roll remains 1 ÷ 6, or approximately 16.7%.

[Anku]

The occurrences in AT are independent. The monsters you have killed have no influence on the current probability of a drop, regardless of what level of MF you had, or have.

if you have had several levels of MF the calculation for the probability that you would have had a drop at some point is fairly simple. If the probability of getting a drop with MF0 is P0, the probability of getting a drop with MF1 is P1, etc. (the spreadsheet I posted will calculate those probabilities for you if you enter the level of MF and you know the number of kills with that level of MF) then the probability of a drop is

P=1-(1-P0)*(1-P1)*(1-P2)...

I have a love/hate for you right now. OMG ugggghhhh. Based on your formula you just provided:
P=1-(1-P0)*(1-P1)*(1-P2)
I was able to write a simple equation in the function bar on Google Sheets that does the EXACT same thing as my 70 line script does, which took me 3 days to write btw... THE EXACT SAME MATH, but way simpler. I spent all that time researching inclusion exclusion principle, trying to find spreadsheets that had it incorporated, or pre existing functions, only to end up spending 3 DAYS writing a script for it that I DIDNT EVEN NEED! AHHHHHHH!!! I'm so frustrated. Here is the equation you can put into the function bar, if you want to add it to the game mechanics spreadsheet that you quoted earlier, so people can determine chances based on multiple Magic Finder levels. The equation accounts for blank cells.
=IF(COUNT(F2:F22) = 0, "", ROUND((1 - PRODUCT(ARRAYFORMULA(IF(F2:F22<>"", 1 - F2:F22, 1)))) * 100, 2) & "%")
You would obviously replace F2 and F22 with whatever cells you have designated on the spreadsheet. Hope you incorporate it!