Average # of Kills to get a Card

You probably forgot to tell your bot to pick up pecopeco cards.

The best thing to do is not think of the card dropping while you hunt stuff. It's more fun that way.

Chance for a card drop in a kill = 0.02%

chance of not getting a card drop in a kill = 100% - 0.02% = 99.98%

chance you will NOT get a card in 2 kills = 99.98% * 99.98% = 99.96%
chance you will NOT get a card in 3 kills = 99.98% * 99.98% * 99.98% = 99.94%

etc.. etc.. This multiplication works because each kill is an independent event. The card drop rate doesnt change because you killed one before; you still have the same 0.02% chance each kill. Each kill is independent from the previous kill.

Now we can use this property to find some interesting numbers.

Chance of not getting a card in N kills = 99.98% ^ N (multiply 99.98 with itself, N times)
note: best way to do this is (0.9998 ^ N) * 100 to get the right percentage.


Chance of NOT getting a card in 1000 kills = 81.87%
Chance of NOT getting a card in 2500 kills = 60.65%
Chance of NOT getting a card in 5000 kills = 36.78%
Chance of NOT getting a card in 7500 kills = 22.31%
Chance of NOT getting a card in 10000 kills = 13.53%


Now that we know our chances of NOT getting a card, we can just subtract this percentage from 100% to get our changes of GETTING a card in that many kills. For example, Chance of getting a card in 1000 kills = 100% - 81.87% = 18.13%.


Chance of getting a card in 1000 kills = 18.13%
Chance of getting a card in 2500 kills = 39.35%
Chance of getting a card in 5000 kills = 63.22%
Chance of getting a card in 7500 kills = 77.69%
Chance of getting a card in 10000 kills = 86.47%


So you still have an almost 14% chance of not seeing a card in 10k kills.

Statistics. It works, son.



EDIT: Want to figure out how much kills to almost guarantee a card?

1 - (0.9998 ^ N) = 0.99999 (99.999%)
-(0.9998 ^ N) = 0.99999 - 1
-(0.9998 ^ N) = -0.00001
(0.9998 ^ N) = 0.00001

N = about 57559 kills

http://www.wolframal... ^ x) = 0.99999

Edited by SciasXIII, 02 December 2011 - 10:50 AM.

I dont understand why people think that 0.01% means you'd get an item within or on 10,000 kills. (assuming 'item' is 0.01%)

0.01% doesnt add to its drop rate on your next kill, it is STILL 0.01% drop rate PER kill.
not where when you kill 2 mobs it becomes 0.02% (0.01 + 0.01)

your drops on these 'item' are based on luck of your day. not in your statistic numbers.

Edited by coast9982, 03 December 2011 - 03:15 AM.

I dont understand why people think that 0.01% means you'd get an item within or on 10,000 kills. (assuming 'item' is 0.01%)

0.01% doesnt add to its drop rate on your next kill, it is STILL 0.01% drop rate PER kill.
not where when you kill 2 mobs it becomes 0.02% (0.01 + 0.01)

your drops on these 'item' are based on luck of your day. not in your statistic numbers.

Yes you are correct, each kill is an independent event; I've explained that above.

But you cannot say that the statistics numbers are somehow incorrect without showing proof. You have a certain probability for an event occuring and there are certain properties of that probability that make analyzing the long term possible.

If you don't understand it, that's fine; but don't say its wrong if you don't know what you're talking about.

All the numbers I give are % chance - there is still a chance that you get unlucky, but that chance does get smaller and smaller as you kill more enemies. In this case it just takes a lot of enemies.

Edited by SciasXIII, 03 December 2011 - 01:21 PM.

Yes you are correct, each kill is an independent event; I've explained that above.

But you cannot say that the statistics numbers are somehow incorrect without showing proof. You have a certain probability for an event occuring and there are certain properties of that probability that make analyzing the long term possible.

If you don't understand it, that's fine; but don't say its wrong if you don't know what you're talking about.

All the numbers I give are % chance - there is still a chance that you get unlucky, but that chance does get smaller and smaller as you kill more enemies. In this case it just takes a lot of enemies. :)

you already said %value doesnt added to its next kill count.
but you are calculation is based on reversed calculation 99.98% * 99.98% instead of 0.2% + 0.2%
whats the difference here?


99.98% * 99.98% on 2 kills = 99.96% not getting card
vs
0.02% + 0.02% on 2kills = .04% chance of getting card

99.98% * 99.98% * 99.98% on 3 kills = ~99.94% not getting card
vs
0.02% + 0.02% + 0.02% on 3 kills = .06% chance of getting card
when you said 'each kill is an independent event'


there is no denying that you are given more OPPORTUNITY to get these drop if you KILL MORE. YES. (obvious, everyone knows that)
you get more 'chance' because server rolls more dice for you if you kill more.
but that doesn't mean % will ever change.

again, if you agreed 'each kill is an independent event'
how can you calculate anything with above statement?
its simple. there is only 1 solution. each kill is 0.02%.
nothing more.

Edited by coast9982, 03 December 2011 - 02:41 PM.

Over 9000... I kid not sadly. 1 in 10,000 is the drop rate if I read correctly.

there is no denying that you are given more OPPORTUNITY to get these drop if you KILL MORE. YES. (obvious, everyone knows that)
you get more 'chance' because server rolls more dice for you if you kill more.
but that doesn't mean % will ever change.

again, if you agreed 'each kill is an independent event'
how can you calculate anything with above statement?
its simple. there is only 1 solution. each kill is 0.02%.
nothing more.

You answered your own question buddy! All I am calculating is that OPPORTUNITY. Just as you said, there are more dice rolls. If you roll the dice enough times, you will get that "6" you want! And that part is calculable.

Each kill is 0.02%. But if you kill 58,000 of a single monster, I can almost guarantee that you will get a card!

The difference between doing the addition vs the multiplication is that you lose the independent event property with addition. The multiplication is saying something like, what is the % chance that = (this kill I got no card) AND (this kill I got no card) AND (this kill I got no card) ... for many many kills.

So it means that when I kill 10,000 archer skeleton in one attack, there's a chance that 1 card will drop if the rates is 00.01%?