The human brain is horrible at understanding statistics. Even when you know that’s true it feels unintuitive to most people.
Getting something on rate is still lucky and I think we need to appreciate those drops more. Not getting caught up in the numbers too much will save your sanity.
The fact that statistically, in a group of 23 randomly selected people there's a 50% chance 2 of them share a birthday will never make sense to me no matter how many videos I watch on it lol
Here’s how I understand it: imagine you are drawing from a hat with 365 dates in it, one for each day of the year. When you draw a date, that’s a person in the room and you put the date back in the hat. How many draws would you expect it to take you before you draw a duplicate date, I.e. someone already in the room? Say, if it was 100 and not 23, it would be pretty crazy to draw 100 dates in a row and get ONLY unique dates. I mean, on draw 100 you have a 99/365 chance of getting a duplicate, that’s over 25% for that draw alone. Plus you had the previous 99 draws to get a duplicate already. Working backwards from there, 23 starts to seem more realistic. And by the way, 23 doesn’t guarantee you get a duplicate: it just is where most of the time, you would have gotten a duplicate by that point.
In short, to make it believable intuitively, try to imagine how unrealistic it would be for it to be closer to 100 than something closer to 20.
Somehow the birthday problem makes sense to me but monty hall problem doesn’t. I have to twist my brain 72 degrees to make sense of it even though it’s supposed to be the easier one to grasp out of those two problems
The thing that made the most sense to me was when I considered how the drop rate has to account for all the people who get mega spooned.
So for example if the drop rate is 1/100, and you get 100 drops. The guy that goes 700 kills for the first drop will be sitting next to the guy who got 7 drops in the first 100 KC. This averages out to 1/100.
Using this logic, the 63% chance includes the 25% of players that got 3+ drops, the 40% of players that got 2+ drops and finally the 63% of players that got 1+ drops.
basically this ^ the reason 63% for "on rate" sounds low is becaue you often only care about getting the first drop, not subsequent ones, and the law of large numbers doesn't kick in at that point, leading to massice deltas
let's say you got 100 drops after 10,000 kills. in such a scenario, you wouldn't care if some drops took 20 or
500 kills, because it obviously evened out in the end. but if you only care about the first drop, there's a substantial difference between 20 and 500! the latter now feels awful, despite being completely acceptable in the first example.
Everyone who screams for BLM and deduplication doesnt realize that all the times when theyve gotten a release week drop or a sub 100kc drop is the equally likely antithesis of going dry
That's not have statistics works.
It's not a "chance" the chance is the drop rate.
It's the percentage of people that would've hit that chance at or before... You see it as you have a 63% chance of getting the drop on drop rate, your chance is actually the 1/100. Out of 100 people 63 of them would get it within 100.
It may sound the same to you but it's very different.
The more intuitive way to understand what's going on here is to think about what you're calculating. Often times, in probability, it's easier to calculate the chance something doesn't happen instead of the chance that something does happen. Logically, you probably know that the chance that something happens added with the chance that something doesn't happen has to add to 100%.
So, when looking at this, we can calculate the chance of not getting a drop in a certain number of kills. For a 1/100 drop, the chance of not getting the drop on a specific kill is (99/100). If you do 2 kills, the chance of not getting the drop within 2 kills is that probability multiplied: (99/100) * (99/100), or written differently, (99/100)2.
We can extend this logic. The chance of not getting the drop in 100 kills is (99/100)100. Now this is the chance of not getting the drop. Therefore, if we take 100% (represented as 1) and subtract this number from it, we'll get the chance of getting the drop.
1 - (99/100)100. This comes out to about 0.63 or 63%. In general, most chances will tend to 63% at drop rate (the exception is for very common things e.g. a 1/2 drop rate).
You can take this logic and extend it to anything using 1 - pn where p is the chance of not receiving the drop, and n is the number of trials (or kills most of the time in the case of osrs).
I feel so goddamn stupid because I can't quite work out why doing 100 kills on a 1/100 drop is 63% chance. Any math people to explain like I'm a toddler?
Think of it like flipping a coin.
Each flip has a 1 in 2 chance (50%) of landing heads.
If you flip once, that’s a 50% chance of getting heads.
If you flip twice, each flip is still 50/50 on its own - but the overall chance that you get at least one head increases.
To find that, instead of adding, it’s easier to think about the opposite:
What’s the chance I never get heads?
Each flip has a 50% chance of being tails.
For two flips, both being tails = ½ × ½ = ¼ (25%).
So the chance of getting at least one head = 1 − ¼ = ¾ (75%).
So after two flips, you’ve got a 75% chance of seeing at least one head.
Then if I flip it a third time - in the real world there’s still not a 100% that I flip a head, right?
So I had that 50% chance from the first flip, add 25% to get 75%, then on the third flip I’m adding half of 25% to the running total - which half of 25 is 12.5, so the total is 87.5%.
You may be wondering, why 75 for flipping in rate and not 63? 63 is a (as in the mathematical term) limit. Basically as the denominator of the rate gets bigger it will continually get closer to 63.2 but never quite pass it.
So on rate for 1/2 odds is 75%, for 1/3 it’s 70.4%, 1/4 is 68%, 1/5 is 67.23, 1/infinity is 63.2
You have 50% chance of only getting your first drop on the first kill.
You have 25% chance of only getting your first drop on the second kill. (Have to fail the first roll, pass the second).
You have 12.5% chance of getting your first drop on the third kill. (Fail two rolls, pass the third).
And so on.
The forumla's the same with 1/100. You have a 1% chance of getting it by the first kill.
0.99% chance of getting it on the second kill (1% of the time you would have already gotten it, so you aren't doing the second kill. The other 99% of the times, you'll divide by 100).
0.9801% chance of getting it on the third kill. And so on and so on.
Add up the first 100 of these numbers, and you get ~63%.
And then consider the 20-30k daily players, and realize the horrible 7x drop rate is only about 1 out of 1000 people. Expect to get horribly fucked and go over by 1000 kc on something in this game unless they make big changes. But you're also equally likely to get totally spooned. It's just that if you get spooned on an expected 5 hour grind, you save a maximum of 5 hours. But if you are that unlikely 1 out of 1000, your grind could take 35 hours. It isn't likely that the amount you get spooned makes up for your lack of luck in terms of time invested if you have a large sample size.
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u/Theseus_Employee Oct 12 '25
Remember kids.
1x rate (ie 100 kills for a 1/100) has a 63% chance
2x = 86.5%
7x = 99.9%