Real WoW example, from BFA around the SL pre-patch:
I wanted the wheel (ground) mount. I learned it was a rare drop from Rustfeather on the Mechagnome island – on the first kill of the day for each character. Wowhead said it had a 1:200 drop rate. So, on average, it drops 1 out of every 200 kills, according to wowhead.
I farmed it. It took me a total of 515 kills. It dropped on my 515th kill.
Would “cumulative probability” have helped me in any way? Who needs it? That plus $3 gets you a cup of coffee.
It doesn’t matter if you believed it would. It’s called applied mathematics and it exists in almost all phases of your life whether you want it to or not. It’s how math works really. It’s just there. Existing.
Drop rates are not cumulative for a large majority of drops in WoW. Meaning that yes the expected number of runs is 13 for something with an 8% drop chance. However it does not mean that you WILL get it on the 13th run. This isn’t bad luck protection like we saw in Legion with the legendaries in that expansion.
Because it is not relevant. Cumulative probability has only applied to things with bad luck protection in WoW. Such as the legion legendaries or the bonus roll coins. In these scenarios, if an event results in a failure (as in you do not get the item), the drop rate increases until it gets close to 100% (i.e the probability converges to 1).
Drop rates for things like mounts (and that includes ones that can be obtained via coin rolls, such as the MoP world boss mounts) are not cumulative. Meaning that it is a static drop rate. And since each event is independent, the drop rate does not change. Therefore it will remain at say 1% for the first time, to the 1000th time if you are extremely unlucky.
Now if the OP had stated that the item they are hypothetically after had bad luck protection applied, then cumulative probability would be relevant.
Like I said… Cumulative probability exists whether you understand it or not. Every time you’ve ever gambled, entered a contest or played the lottery, someone much smarter than you banked on the fact that their knowledge of probability suckered you into playing the game in the first place.
It may exist but it is not relevant here. If it did than you will get a mount like invincible on the 100th attempt since it has a 1% drop rate.
This is the problem. People confuse probability for the actual chance. Yes after 100th attempts the probability of not getting invincible would be (99/100)^100 (each event is independent so you can do this). But that is not equal to 0. It is close, but not equal. Meaning that it is unlikely but it is still possible. It is what causes the coin flip fallacy. Where you think that because a coin flipped heads 10 times the next time MUST be tails. When that is simply not true. People tend to confuse the expected value for the actual value. See it all the time on the bug forums. Where people complain that because they haven’t gotten something within the expected number of attempts, it must be bugged. Sometimes you are just unlucky.
It is why I said talking about cumulative probability is irrelevant in scenarios that do not have something like bad luck protection. Since in a cumulative probability function, the probability increases as time increases. Meaning that over time the probability of an event resulting in a favorable outcome increases with each failed attempt to the point that it converges to 1 at the upper limit.
The above also applies if the events are dependent. The classic example is, “pick a ball in a bag without replacement”. However things like mount drops are independent. Meaning that the previous event has no affect on the next event.
I don’t even know what you’re arguing with me about now. I never said anything would ever reach 100% here in wow. In fact, I never mentioned WoW drop rates at all. I never said anything would reach 100% nor have I agreed with anyone here who said it would. I didn’t say that because that’s not how it works.
Vortimer hit it right on the head with what I’ve been saying. I’m not getting involved with any specific in game drops. I’m just talking pure numbers.
What I’m saying is that people tend to use the probability of an event as justification for saying something is bugged. Basically they say that because they didn’t get an item within the expected number of attempts, the item’s drop rate must be bugged. Because they think unlikely = impossible. Or that the probability is cumulative. When that simply isn’t true. Which is why I brought up the coin toss fallacy.
Using in game drops is called using an example. Talking pure numbers doesn’t really mean anything unless you can give an example. It aids your argument is what I’m saying.
Apply it to whatever you want because no matter what you apply it to, whether it be Mount drops, consecutive dice throws or chances of winning a random drawing cumulative probability will always apply.
It shouldn’t need an example because in any instance the formula is always the same. Probability is probability because the math doesn’t change it.
A single attempt, called a Bernoulli Trial, has an 8% chance of success in the OP’s title question. It will always be 8% on any individual event.
Multiple trials most certainly do involve cumulative probability. The OP’s question was answered correctly by several people in this thread but there are so many wrong answers I wonder if the OP could separate the wheat from the chaff, given that they asked in the first place and so don’t have enough stats to answer on their own.
