Thread for people that like probabilties

Hello,

Recently someone posted a thread about probabilities. I remembered that I calculated quite a few some years ago and some of them changed with R155.
So only for those who care: Numbers

Chance to find a Hammer or Axe with 2xDamage% and 2xDamage: 1/64

Chance to find a Hammer or Axe with 3xDamage% and 1xDamage: 1/128

You might think now, that is not too bad, but wait! Hammers and Axes have only 4 possible enchantments. All other weapons have 5, because of possible weapon speed. So let’s do this again:

Chance to find a normal weapon with 2xDamage% and 2xDamage: 1/156

Chance to find a normal weapon with 3xDamage% and 1xDamage: 1/312

Not fair, you might think now. Why do Hammers and Axes have better chances for certain combinations? They don’t, since they drop only 1/3 as often as for other players 1h or 2h weapons drop. If you take this into account, the probabilities for normal weapons are even better.

What to make with all of this? Simple, stay flexible with your items enchantments. Once you try to find an item with 4 identical enchantments, you are probably proper screwed.

You want only crit on your weapon adornment, so 4xCrit with 5 differnt entchantments possible? : 1/625
Luckily they reduced the possible entchantments to 4 again with R156. So you ideal crit items is "only" one in 256.

Good luck with that! So maybe stop searching for one items and rather have multiple build ideas that work. Cheers!

Any thoughts?
You are welcome

 

hi

I would like to see your math behind the probabilties, if I may

 

Yeah, I would also like to see the math behind it. But here is mine so, assuming axes have 4 possible enchants with the same probability of 25% or 1/4 it would be. To get 2/2 dmg/dmg% combo.
The number all possibilities, including order = 4^4=256
The number of desirable possibilities = 4!/(2!*2!) = 24 / 4 = 6.
The chance of getting Axe with 2 lines of dmg and 2 lines of dmg% is 6/256=3/128 ~ 2.34%

Same for the 'weapons', with 5 possible enchants. = (4!/(2!*2!)) / (5^4) = 6/625

and so on. I guess @wizzo90 counted like this: 1/2 * 1/2 * 1/4 * 1/4= 1 / 64

My math gives better chance, so you decide which you like

UPD: guess we can also use the formula from Bernoulli distribution. for 2x2 Axe combo:

Chance to get exactly two damage lines: ( 4! / (2! * (4 - 2)!)) * (1/4)^2 * (1-1/4)^(4-2) = (24/4) * 1/16 * 9/16 = 54 / 256

Chance the other two lines are the dmg% = 54/256 * 1/3 * 1/3 = 6/256=3/128

 

You all assume the opportunity to get each enhancement possibility is equally distributed. Anecdotal evidence suggests this is not true. Some enchantments seem to be more prevalent than others. Ask anyone that has opened 300 shields to get a 2/2 or 3/1, or anyone looking for 3 lines of speed on boots. Key words there are obviously "seems" and "anecdotal." Hard to prove or disprove without sufficient data.

Additionally, and as a challenge to all my awesome math geek bro's, if you want to make it even more complex, set a threshold for a GOOD enchantment. Not just a 2/2 axe, but a GOOD 2/2 axe.

 

Yes, i agree with BigPapa. You are assuming that enhancement classes have equal/balanced probability.
All empiric evidence says clearly that's not true, for instance damage % increase line is surely less-weighted than pure absolute damage increase line.

But, as general method to build an idea of "what can i expect" from an item, that's a good starting (medium ) point.

Further, in stats & numbers related to DSO, i'm always -and only- interested in statements like this:
After X runs/try, what is the probability that i will NEVER get that single 'item' in these X runs?

(possible substitution of 'item':
piece of keen/roshan/yachak/spark
piece of generic unique set
predator/equivalent
mortis mask/equivalent
and so on ...)

 

@Zamvel7
Sebastian got the math right. Additionally I subtracted the number of Items that would not surpass a normal pink item based on a normal distribution around an average. Since the average in R155 is pretty low my numbers are around 33% lower than Sebastian’s.

@BigPapa
I am not posting chances to find outstanding items, especially after R155. My threshold is more like a trash bin for items that don’t count as legendary. Yes, I have low standards^^

@Excalibur
That might very well be. Personally I don’t see a weighting of enchantments on weapons. But they sure exist on other items, such as speed on gloves and so on, so they might exist on weapons too.
If you like negative statement you just can distribute them from 1 and multiply that number as often as you try.
So 1-(1/64) for example is 63/64 or about 0.98%. Let’s say you have 100 items to open that is (63/64)^100 or about 21% you are unlucky.
I personally find that a bit depressing to look at, but it is basically the same information.

 

I'm perfectly aware of independent events calculation , happy to see that you manage it as well as i can. This was really a 'suggestion' for any BigPoint Dev lurker that reads this thread, not for you

Getting the number of 'negative results percentage' could be easier to calculate and shows to them the immediate evidence that the probability of being unlucky in a insane amount of runs is too high.
It's not the 'same information' according to me, since BP is managing the drop rate as a worst-shifted rate. So it's the negative perception that rules over the positive perception.
In other words, you are getting most of time a too little satisfaction once you drop an item (no more useful, cause it took too much time to drop) compared to the amount of anger/frustration every time you drop nothing.

That's the essence of the power showing the negative result numbers instead of the positive achievement.

 

I like the probabilities ... only if they are in my favor.