This thread is for people who want to understand probability better. Please feel free to add your own calculations/knowledge.

My experience as an online poker player (it was my only income for over a year) has thought me a few things that made me understand randomness and probability a lot better than before.

Before we go any further I would like to state: I’m no math-wiz, nor do I claim to be one but a basic understanding how statistics work is necessary for anyone who wants to get this.

First of all if you want to make any claim what so ever about anything, you need a lot of data to support it. Stating any theory (I found X legs, therefore Y) based on a few hours of rifts is plain inaccurate. I would say you need at least 100 rifts before you can do any calculations and see some sort of patterns.

Onwards to probability, a classic example is flipping a coin. What’s the probability? Everybody would agree that you have a 50/50 chance of either heads or tails. You flip the coin ten times and it gets tails every time. So what’s the probability the eleventh time? Some might say that heads is now favored, wrong! It’s still just 50/50. The coin doesn’t know it’s been flipped ten times already; this is the human brain wanting to see patterns and create false assumptions based on past events. It’s not based on the actual thing, you’re still just flipping a coin. Conclusion; just because one event has happened a certain way before doesn’t change the probability the next time it happens.

Time for a Diablo3 example: if you go one hour without a single leg drop, you should not expect to find one the next hour just because of this. What you can say is “after 100 hours I should expect X legs” based on previous calculations.

Some final words; in poker we say that you can only play your best and make correct decisions and then it’s up to the cards. In Diablo3 that translate to you can only change your build and plan your runs to optimize your chances but there are never any guarantees.

EDIT: This calculation (based on 100 rifts) (NOT MY OWN) states that from T4 rifts you will probably find 0,86 legs/person/rift - with 10 min rift time - roughly 5 legs/hour.
Plans and kadela is not included. Rifts were only cleared to guardian.

I've just flipped the coin on tales 5 times in a row, what's the probability I'll do it once more?! (answer 50%)

I'm going to flip the coin on tales 6 times in a row, what's the probability I'll do it?! (answer 50%^6 =~1,56%)

There's a difference in calculating the probability depending where you are and where you're going.

A person flipping the coin the 6th time has a 50% chance of getting tales. However, him getting to this specific outcome (6 tales) is 1,56%. Another fact is that getting to either 6-coin flip combination is 1,56%.

This may not have much to do with probability, but "hours" is a horrible indicator. Unless you are running so badly that the safety net kicks in, drops are based on kills, so things like "number of rift completed" or "number of malthaels killed" is much more sound.

Random does not mean streakless. Take a coin and toss it 100 times. The chance you get a streak of 7 is at least 1/2.

Law of truly large numbers: Just because something is extremely improbable does not mean it is impossible. In fact, with enough samples, the probability of it happening approaches 1. For example, the chance of anyone winning the lottery is very small. However, with so many people playing the lottery, the chance of someone winning the lottery is pretty large.

A imo healthy way of viewing your D3 probability when you play would be something like this:

With my current build and gear one rift on T2 takes me about 20mins, including repairs/selling stuff/whatever. I play 2h every night. The first half hour I'm doing bounties, then the rifting starts. I do roughly five rifts a night. 7*5=35 rifts each week, that is my goal. How many legs that will net me is not important, as long as I put in the time and am focused my goal is reached.

Time for a Diablo3 example: if you go one hour without a single leg drop, you should not expect to find one the next hour just because of this. What you can say is “after 100 hours I should expect X legs” based on previous calculations.

I strongly disagree, there is nothing wrong with adding up events in the past and predicting a better outcome in the future. It's quite simple, if you play twice the time then your chance to get a leganderie is twice as high. If i played for an hour finding no legendary then it is perfectly fine for me to expect to find a legendary in the next hour.

Why?

I'am looking at a timeframe of twice the size than yours. Obviously my chances are better.

In general, no. If legendary drops are independent events, just because you haven't found a legendary in the past hour does not increase your chance of finding one in the next. Whatever bad luck happened in the past already happened, and there will be no "good luck" to compensate for it. Once you have that hour of bad luck, that's it. It's in the past, and will not affect the future (see caveat below). That hour is gone, poof, disappeared, and all you get is gold and XP to show for it. It will no longer be in your time frame. Any thinking otherwise is the gambler's fallacy, and is responsible for leading many men and women's lives to ruin.

There is however a caveat. The safety net in D3 means that the chance of legendaries dropping will increase if you haven't find one in hours, which means that the events are no longer completely independent, should your luck be so bad that you haven't find a legendary in hours.

Time for a Diablo3 example: if you go one hour without a single leg drop, you should not expect to find one the next hour just because of this. What you can say is “after 100 hours I should expect X legs” based on previous calculations.

Actually, you should. Blizz has a timer in there to account for cold streaks.

In general, no. If legendary drops are independent events, just because you haven't found a legendary in the past hour does not increase your chance of finding one in the next.

False, Blizzard said that there is a timer that is increasing your chance of getting a legendary.

False, Blizzard said that there is a timer that is increasing your chance of getting a legendary.

Read carefully the entire post that I wrote. Anyways, most people should not see the caveat. It does not kick in until after many hours, not a mere 1 or 2. For all intents and purposes, we can assume them to be independent.

Lets say you have done 100 hours of rifting. and you have been taking notes along the way.
Lets say in those 100 hours of rifting you have done 600 rift
That means you on average have done a rift every 10min sometimes longer other times shorter.
Lets also say you have gotten 150 legendarys from those 600 rift

That means using my awesome calculation you have around 25% chance of getting a legendary everytime you finish a rift.
Since you take around 10m per rift you can say that after 2 hours of rifting I have a chance of getting 3 legendary's I allso have a chance of getting more than that and less that.

If you go in with this mindset then you won't get dissapointed.

Now I have not done 600 rift in 100 hours this is arbetary numbers.

My experience so far is:
17 legendary's
13 legendary plans
After 81 rift

That means on average:
21% chance of legendar's per rift
16% chance of plan per rift

Since I take around 15min per rift
I have on average a chance of getting 4 legendary's every 5 hours.

That means when I do rifting I do not expect to get 1 every hour but I do expect to get 1 within 5 hours since the chance to get on is within than time span on average is 4 times higher

The problem is that we don't really know how fast or often the timer kicks in. Hypothetically, if we average a 50% chance to get a legendary after 1 hours of solid playing (i.e. X rifts, Y monsters killed, Z elites, etc), and the timer only starts increasing after say two hours of no legendaries, then yes, most of the time our legendary drops are independent. (Again just an example.)

It's my impression from blizzards comments that the leg drop rate doesn't even *start* increasing until a decent dry spell has occurred. But again, I'm reading between the lines of what Blizzard is saying.

Time for a Diablo3 example: if you go one hour without a single leg drop, you should not expect to find one the next hour just because of this. What you can say is “after 100 hours I should expect X legs” based on previous calculations.

Actually, you should. Blizz has a timer in there to account for cold streaks.

That's misleading at best because you're implying that the "falisafe" mechanism grants you a legendary, automatically, after a certain timeframe. I'm pretty sure that the blues described it as scaling up your chance to find a legendary based on how lucky you are, and never as a guaranteed legendary after X hours.

So the idea that you could make a statement that after 100 hours you should have X legendaries because of the failsafe is..... misleading at best.

EDIT
Why are quotes all jacked up? This new forum software leaves a lot to be desired.

In general, no. If legendary drops are independent events, just because you haven't found a legendary in the past hour does not increase your chance of finding one in the next. Whatever bad luck happened in the past already happened, and there will be no "good luck" to compensate for it. Once you have that hour of bad luck, that's it. It's in the past, and will not affect the future (see caveat below). That hour is gone, poof, disappeared, and all you get is gold and XP to show for it. It will no longer be in your time frame. Any thinking otherwise is the gambler's fallacy, and is responsible for leading many men and women's lives to ruin.

No, the hour isn't gone, didn't poof nor disappear. It is still in the system and effects it. In fact you do need the time, or more precisely the amount of rolls and their outcome to determine your prediction for the future.

No, the hour isn't gone, didn't poof nor disappear. It is still in the system and effects it. In fact you do need the time, or more precisely the amount of rolls and their outcome to determine your prediction for the future.

The only effect on the system is the safety net, which is usually inconsequential. Other than that, it is gone. Read up on gambler's fallacy.

Onwards to probability, a classic example is flipping a coin. What’s the probability? Everybody would agree that you have a 50/50 chance of either heads or tales. You flip the coin ten times and it gets tales every time. So what’s the probability the eleventh time? Some might say that heads is now favored, wrong! It’s still just 50/50.

Unless, of course, the reason that you flipped ten tails in a row is that the coin is biased. There is a point when you need to start considering that maybe the chances aren't the 50/50 that you were assuming.

Not meaning to endorse any of the crazier tinfoil hat theories we seen thrown around here, but it's something to bear in mind. As you said in your first point, though, you need a lot of data before making such claims.

Unless, of course, the reason that you flipped ten tails in a row is that the coin is biased. There is a point when you need to start considering that maybe the chances aren't the 50/50 that you were assuming.

Still, you won't bet heads in that case. If the coin maybe biased, it's most likely biased towards tails. Gambler's fallacy has no basis in the real world.

Time for a Diablo3 example: if you go one hour without a single leg drop, you should not expect to find one the next hour just because of this. What you can say is “after 100 hours I should expect X legs” based on previous calculations.

I strongly disagree, there is nothing wrong with adding up events in the past and predicting a better outcome in the future. It's quite simple, if you play twice the time then your chance to get a leganderie is twice as high. If i played for an hour finding no legendary then it is perfectly fine for me to expect to find a legendary in the next hour.

Why?

I'am looking at a timeframe of twice the size than yours. Obviously my chances are better.

I'm sorry but what you write is wrong. Go and read Kilo55555's coin flip example again, and try to understand it.

I'm sorry but what you write is wrong. Go and read Kilo55555's coin flip example again, and try to understand it.

Let him be ignorant. His ignorance on how independent events work keeps me employed.

He's the kind of guy who strolls up to the roulette wheel and says "So, black has hit seven times in a row?" and then drops $100 on red because he KNOWS that since black is on a streak red is "due." Then, when black (or 0/00) hits, he curses at the dealer, throws a shitfit, and claims the game is rigged.

He's the kind of guy who sees five straight "low cards" at a blackjack game, then bursts a vein in his forehead when the dealer pulls a small card and not the ten he needed to break because there's no way that a sixth small card could possibly come out. Even though it's very possible and he's making that statement not based on fact, but based on being very poorly informed.

Probability of finding a legendary increases the more you play. This is simple to understand, everyone knows this. You may say, "Yes, but the chances don't change!" I disagree.

Let's say the chance to find a legendary is 0.02% per monster kill. This is theoretical for demonstration only.

The chance to not find a legendary is 99.98% per monster kill. Let's see how this changes after killing 500 white monsters.

1 - (0.9998)^{500} = 0.9048283
So the chance to NOT find a legendary after 500 kills is 90.48283%. The chance to find a legendary is 9.52827%.

However that only tells us the chance for finding legendaries from normal white monsters. What if we wanted to include elite packs?

Let's assume that elite packs have a 0.5% chance to drop a legendary per kill. In a rift, we can assume that there are at least 20 elite packs.

1 - (0.9998)^{500}(0.995)^{20} = 0.8587234
So the chance to not find a legendary after 500 white kills and 20 elite packs is 85.87234%. The chance to find a legendary is 14.23876%.

As you can see, even though they are independent events we can increase our chances by simply playing more.

This thread is for people who want to understand probability better. Please feel free to add your own calculations/knowledge.My experience as an online poker player (it was my only income for over a year) has thought me a few things that made me understand randomness and probability a lot better than before.

Before we go any further I would like to state: I’m no math-wiz, nor do I claim to be one but a basic understanding how statistics work is necessary for anyone who wants to get this.

EDIT: This calculation (based on 100 rifts) (NOT MY OWN) states that from T4 rifts you will probably find 0,86 legs/person/rift - with 10 min rift time - roughly 5 legs/hour.

Plans and kadela is not included. Rifts were only cleared to guardian.

A person flipping the coin the 6th time has a 50% chance of getting tales. However, him getting to this specific outcome (6 tales) is 1,56%. Another fact is that getting to either 6-coin flip combination is 1,56%.

This may not have much to do with probability, but "hours" is a horrible indicator. Unless you are running so badly that the safety net kicks in, drops are based on kills, so things like "number of rift completed" or "number of malthaels killed" is much more sound.

Random does not mean streakless. Take a coin and toss it 100 times. The chance you get a streak of 7 is at least 1/2.

Law of truly large numbers: Just because something is extremely improbable does not mean it is impossible. In fact, with enough samples, the probability of it happening approaches 1. For example, the chance of anyone winning the lottery is very small. However, with so many people playing the lottery, the chance of someone winning the lottery is pretty large.

With my current build and gear one rift on T2 takes me about 20mins, including repairs/selling stuff/whatever. I play 2h every night. The first half hour I'm doing bounties, then the rifting starts. I do roughly five rifts a night. 7*5=35 rifts each week, that is my goal. How many legs that will net me is not important, as long as I put in the time and am focused my goal is reached.

I strongly disagree, there is nothing wrong with adding up events in the past and predicting a better outcome in the future. It's quite simple, if you play twice the time then your chance to get a leganderie is twice as high. If i played for an hour finding no legendary then it is perfectly fine for me to expect to find a legendary in the next hour.

Why?

I'am looking at a timeframe of twice the size than yours. Obviously my chances are better.

In general, no. If legendary drops are independent events, just because you haven't found a legendary in the past hour does not increase your chance of finding one in the next. Whatever bad luck happened in the past already happened, and there will be no "good luck" to compensate for it. Once you have that hour of bad luck, that's it. It's in the past, and will not affect the future (see caveat below). That hour is gone, poof, disappeared, and all you get is gold and XP to show for it. It will no longer be in your time frame. Any thinking otherwise is the gambler's fallacy, and is responsible for leading many men and women's lives to ruin.

There is however a caveat. The safety net in D3 means that the chance of legendaries dropping will increase if you haven't find one in hours, which means that the events are no longer completely independent, should your luck be so bad that you haven't find a legendary in hours.

Actually, you should. Blizz has a timer in there to account for cold streaks.

Read carefully the entire post that I wrote. Anyways, most people should not see the caveat. It does not kick in until after many hours, not a mere 1 or 2. For all intents and purposes, we can assume them to be independent.

Lets say you have done 100 hours of rifting. and you have been taking notes along the way.

Lets say in those 100 hours of rifting you have done 600 rift

That means you on average have done a rift every 10min sometimes longer other times shorter.

Lets also say you have gotten 150 legendarys from those 600 rift

That means using my awesome calculation you have around 25% chance of getting a legendary everytime you finish a rift.

Since you take around 10m per rift you can say that after 2 hours of rifting I have a chance of getting 3 legendary's I allso have a chance of getting more than that and less that.

If you go in with this mindset then you won't get dissapointed.

Now I have not done 600 rift in 100 hours this is arbetary numbers.

My experience so far is:

17 legendary's

13 legendary plans

After 81 rift

That means on average:

21% chance of legendar's per rift

16% chance of plan per rift

Since I take around 15min per rift

I have on average a chance of getting 4 legendary's every 5 hours.

That means when I do rifting I do not expect to get 1 every hour but I do expect to get 1 within 5 hours since the chance to get on is within than time span on average is 4 times higher

It's my impression from blizzards comments that the leg drop rate doesn't even *start* increasing until a decent dry spell has occurred. But again, I'm reading between the lines of what Blizzard is saying.

That's misleading at best because you're implying that the "falisafe" mechanism grants you a legendary, automatically, after a certain timeframe. I'm pretty sure that the blues described it as scaling up your chance to find a legendary based on how lucky you are, and never as a guaranteed legendary after X hours.

So the idea that you could make a statement that after 100 hours you should have X legendaries because of the failsafe is..... misleading at best.

EDIT

Why are quotes all jacked up? This new forum software leaves a lot to be desired.

No, the hour isn't gone, didn't poof nor disappear. It is still in the system and effects it. In fact you do need the time, or more precisely the amount of rolls and their outcome to determine your prediction for the future.

The only effect on the system is the safety net, which is usually inconsequential. Other than that, it is gone. Read up on gambler's fallacy.

Unless, of course, the reason that you flipped ten tails in a row is that the coin is biased. There is a point when you need to start considering that maybe the chances

aren'tthe 50/50 that you were assuming.Not meaning to endorse any of the crazier tinfoil hat theories we seen thrown around here, but it's something to bear in mind. As you said in your first point, though, you need a lot of data before making such claims.

Still, you won't bet heads in that case. If the coin maybe biased, it's most likely biased towards tails. Gambler's fallacy has no basis in the real world.

I'm sorry but what you write is wrong. Go and read Kilo55555's coin flip example again, and try to understand it.

Let him be ignorant. His ignorance on how independent events work keeps me employed.

He's the kind of guy who strolls up to the roulette wheel and says "So, black has hit seven times in a row?" and then drops $100 on red because he KNOWS that since black is on a streak red is "due." Then, when black (or 0/00) hits, he curses at the dealer, throws a shitfit, and claims the game is rigged.

He's the kind of guy who sees five straight "low cards" at a blackjack game, then bursts a vein in his forehead when the dealer pulls a small card and not the ten he needed to break because there's no way that a sixth small card could possibly come out. Even though it's very possible and he's making that statement not based on fact, but based on being very poorly informed.

Let's say the chance to find a legendary is 0.02% per monster kill. This is theoretical for demonstration only.

The chance to not find a legendary is 99.98% per monster kill. Let's see how this changes after killing 500 white monsters.

1 - (0.9998)

^{500}= 0.9048283So the chance to NOT find a legendary after 500 kills is 90.48283%. The chance to find a legendary is 9.52827%.

However that only tells us the chance for finding legendaries from normal white monsters. What if we wanted to include elite packs?

Let's assume that elite packs have a 0.5% chance to drop a legendary per kill. In a rift, we can assume that there are at least 20 elite packs.

1 - (0.9998)

^{500}(0.995)^{20}= 0.8587234So the chance to not find a legendary after 500 white kills and 20 elite packs is 85.87234%. The chance to find a legendary is 14.23876%.

As you can see, even though they are independent events we can increase our chances by simply playing more.