Re: What are the chances of you getting an heirloom in Apex Legends?

@damsonwhufndthis Fully explained above.  Over 2 flips.  I've explained it several times now.  If you can't grasp it I can't help you, sorry.

You are focusing on individual events.  Not a collection of independent events.

- DR

@RockDokRockwhere did you learn this "math"?

@damsonwhufndthis  Thanks for asking.

Actually I've taught this subject before as part of a class.  I hold a PhD in a mathematical discipline and am a University Lecturer.

You?

@RockDokRockoh my bad, I searched little bit online

Can I ask you why you use on a 0,4% chance scenerio, a coinflip formula?

@damsonwhufndthis I used 0.5% chance as per @DarthValtrex scenario posted originally.  I didn't choose it.  

Truth of the matter is we don't know what the odds are really, they must be much less than that though.

- DR

@RockDokRockI'm just tryina say that your 71% chance of heirloom after 250 packs sounds way too optimistic, considering no matter how many you open it's still 0.5% chance.

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@damsonwhufndthis wrote:

@RockDokRockI'm just tryina say that your 71% chance of heirloom after 250 packs sounds way too optimistic, considering no matter how many you open it's still 0.5% chance.

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It is each time individually.  If you have 250 packs to open though, do you really think it's still 0.5% overall?

This is why the coin flip example is relevant to drive home this point.

Individual coin flips give you a 50/50 heads or tails.  Totally true.

Would you expect to get at least one heads after 10 flips?  Do you think your chance of seeing at least one heads after 10 flips is only 50%?

Can you see the difference?

- DR

@RockDokRockI'll say it again, you can either have heads, or tails

Not how lootboxes work, you have like 60% chance to get one of 1000+ commons, 30% chance for like one out of 500+ rares, 10% chance to get one out of 500+ epics, like 5% chance to get one out of 200+ legendaries, and finally 0.5% chance for heirloom shards.

Just because you opened 10 packs and got 3 commons 10 times in a row that suddenly mathematicaly you deserve to get a rare, you can still get 3 commons.

The chance is still same, the chance for common is still high the chance of heirloom is still extremely low.

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@damsonwhufndthis wrote:

@RockDokRockI'll say it again, you can either have heads, or tails

Not how lootboxes work, you have like 60% chance to get one of 1000+ commons, 30% chance for like one out of 500+ rares, 10% chance to get one out of 500+ epics, like 5% chance to get one out of 200+ legendaries, and finally 0.5% chance for heirloom shards.

Just because you opened 10 packs and got 3 commons 10 times in a row that suddenly mathematicaly you deserve to get a rare, you can still get 3 commons.

The chance is still same, the chance for common is still high the chance of heirloom is still extremely low.

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That's not what I am saying at all.  Nothing "suddenly" changes.  I've illustrated this several times.  Opening a loot box is no different than a roll of the dice or flip of a coin conceptually.

Answer the simple question... again.  One more time.  Just answer it.

Q:  If you flip a coin 10 times do you think you will have a better than 50/50 chance of seeing a heads.  Yes or no?

- DR

@RockDokRockto answer you, I'll make another post 🙂

@damsonwhufndthis You don't have to.  We can take this to PM or not bother or continue here.  I'm not fussed either way. 

- DR

I'm gonna ask everyone

@damsonwhufndthis But you've not answered my question.  That's fundamental to this problem.

The question you asked just now doesn't address it at all.  The chance of getting an Heirloom is so small it's inconsequential.  

- DR

@DarthValtrex What is "Probable Cause"? in Math.  Never heard that one.

I used basic probability theory.  That's how it works.  In real life it's never really 50/50 or whatever but it's close enough that what I'm saying works.

Sorry, facts don't care about your feelings.

It is not .5% chance at an heirloom with every pack.  I've clearly demonstrated this.  Again, it's not my fault you don't understand probability and modelling independent events (you keep saying every single time there is the same chance - that is *literally* what modelling independent events means, each invent is independent and its chance is not affected by others, you clearly don't understand probability).

Yes, you can flip a coin on its head and get 100 heads in a row... try it and post again when that happens for you.

Not really sure what to say. 

- DR

@DarthValtrex Sure thing.  I've described, done the calculations and shown what I am doing.  All I am getting from you is assertions and claims.  What are the odds then?  If someone opens 250 packs what are the expected odds that they will end up with at least one heirloom after?  Show me - Answer that and we can have a real discussion.  Show your work, don't just arm wave and assert.

Incidentally, if 1000 people opened apex packs with a .5% chance of an heirloom there is more than a 99% chance at least one heirloom would be unpacked.

The reason many people have not gotten an heirloom is because the odds are much lower than .5%.  That's ok, that's how it's supposed to work.  It's supposed to be very rare.

- DR

I just saw this:

https://www.sportskeeda.com/esports/apex-legends-chances-getting-heirloom-shards#:~:text=Like%20the%20Heirloom%20gear%20before,in%20500%20chance%20to%20drop. 

Apparantly it's a 1 in 500 chance (so that's .2%).  I don't know if this is true, they may be assuming that as you get one after 500 this is how it works (It's not an EA source webpage).

Less than .5% but higher than I thought.

Anyone have any actual hard evidence on the odds?  I've seen claims but not where people are getting these values from.

- DR

@RockDokRock As I was reading this thread, the first thought that came to my mind was "With so many people participating in this thread, you'd think that probability would favor that at least one person, other than RockDockRock, would understand how basic probability works."

My second thought was the realization that most people who would bother to be on an ea.com thread are probably children.

My third thought, though, was remembering that basic probability was taught to us in like... 3rd grade... so, yeah, this is kinda crazy... I was so baffled that I just had to weigh in.

You tried, multiple times to explain it, but no one even acknowledged you: Calculating the probability of an outcome in one event, where the odds are known, is not the same as calculating the probability of one outcome over the course of multiple events, where the outcome odds are known for each event.

Your coin flip example hit it dead on the money. I think, perhaps, that the thing people are failing to understand is that the probably changes over time, as each event [in a series] is executed (i.e. each coin is flipped). Who knows, maybe someone will read this and get it:

Suppose we're going to flip a coin two times and me and you are making bets about whether or not heads will be flipped at least once. From that moment, there are exactly four possible outcomes across the two coin flips:

TT
TH
HH
HT

The result *will* be among those four possible outcomes and it is no more likely to be one than any other. There are no other, possible, outcomes, and, you can observe that of the 4 possible outcomes, 3 of them include at least one "heads" result. Thus, 3/4 of the results include heads, thus 75% of the results include heads, thus there is a 75% chance that heads will come up in two flips.

That does not mean that heads will "definitely" come up. It just means that if I tell everyone on Earth that "heads is a sure bet!" then approximately 3 out of 4 of those people will think that I give sound financial advice and about 1 out of each 4 people will think I'm a scammer.

However, if, the first flip is "tails" and we stop to calculate what the probability of the _next_ flip will be, then we would realize that _now_ the odds of heads coming up both in the next flip and across the series has reduced to 50% (made evident by the fact that "H" only exists as the last character on 2/4 of the possible outcomes; i.e. with the first event now known, 2/4 of the total possible results have been eliminated because they're no longer possible).

That really is basic probability theory and people have been building wealth on top of that since money was invented. It's as sound as anything that has ever been realized in all of human history; it is no longer open to debate here on the round Earth.

Yes, obviously the coin flip is an over-simplification and the calculation that EA is running is more sophisticated, but that does not make it any less subject to basic probability math. If the odds of any possible outcome from a single event are known, then you can calculate the probability of that event occurring in any series, of any size, using the same formula.

The only two things that remain open for debate are:

1. What are the odds that any given box will contain an heirloom (as many have cast doubt on the 0.5% figure)?

2. How similar each box opening is to real, random, chance; has it been biased?

Although we know that the probability does imbue biases, based on the fact that there is a 500 box guarantee (which is, itself a bias), we also know that it has not be biased beyond the possibility of statistical analysis and probability modeling, because a) Respawn, itself, provides probability models on the purchase screen and b) it's illegal to do that, virtually anywhere.

So yeah, there are things still worth debating but, what is not open to debate, is RockDockRock's logic. It's 100% accurate and anyone arguing with him _actually_ doesn't understand how probability works. Go watch a video if you still don't get it 🙂

@vmadman I'm so sorry, gonna have to disagree with you and Dok.

I know that the coin flip theorem might be correct in most cases, but it isn't in this one. You see, each pack has a 0.2% chance of an heirloom. You are guaranteed one at 500 packs. But, even if you are at pack 499, the odds are not 99% that you are going to get an heirloom; they are still 0.5%. The only number pack that does not have a 0.5% probability is pack number 500 itself.  

@DarthValtrex is correct, and @RockDokRock , though he makes a very compelling and usually accurate argument, is not. I hope this fully settles this and I don't have Mr. PHD arguing against me, fore I'm still in highschool

@vmadmanWell I'm 32 years old, still playing games, & as a Day 1 player, it took years before I got Heirloom shards.

I just got them last week for the first time.

I also have never paid for APEX packs, I only get them if they are part of a Store Bundle I want.

This is from three years ago, but reading this forum as a maths student just makes me want to reply to this.
RockDokRock​ and vmadman​ are correct, its basic probability - it's not the fact that the 499th apex pack has a 99% probability that it will have an heirloom, it's that by the time you've opened 499 apex packs, per se, there is a 99% probability that you'll have gotten an apex pack by then.

It's the exact same as a coin flip - except lets model it as a biased coin. Probabilities sum to 100% (or 1 if you're dealing with numbers) - so the probability of getting heirloom shards is, 0.045%, and therefore the probability of not getting heirloom shards is 100% - 0.045%, which is 99.955%, rather than a usual coin being 50% and 50%.

Let's open one apex pack - the outcomes are either H (heirloom shards) or N (No heirloom shards)

Outcomes:
H - 0.045%
N - 99.955%

Let's open two now.
Outcomes:
NN - 99.955% x 99.955% = roughly 99.91%
NH - 99.955 x 0.045% = roughly 0.04%
HN - Roughly 0.04%
HH - 0.00002025% (Two heirloom shards in a row - very rare!)

Now, as we can see the probability of getting at least 1 heirloom shard pack is based on the outcomes. there are three outcomes from two apex packs, and to find the probability of getting at least 1 heirloom, we can add the probabilities of the outcomes that have heirloom shards in them as a result - which would be NH + HN + HH - adding then up, we get roughly 0.0802025% - very low, obviously. This is the probability that we will have received heirloom shards after opening two apex packs - not the 'accumulative chance' of getting an apex pack on our second pack.

Let's scale this all the way up to 499 apex packs - I can't show all the outcomes as there are tons of them - 2^499 to be exact! (Which would be very large, and I'm not about to go here writing NNNNNNNNNNNNNNNNNNNNNNNNNNNNN..... HNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN.... and so on.) Using a calculator, the probability of AT LEAST getting 1 heirloom pack BY NOW, after opening our 499th apex pack, would have been... 20.116%! This doesn't mean that we have a roughly 20% chance of getting an heirloom on our 499th apex pack, it means that BY NOW, having opened all these packs, there will have been a 20% probability of us at least getting at least 1 apex pack with heirlooms in it.

Even chatgpt backs me up:

Hope this helps!

P.S. being in high school or having a PHD has nothing to do with this, I'm still in high school (the equivalent in the UK at least - year 12 or 11th grade I think), it's just a matter of understanding the concept of probability.