Re: What are the chances of you getting an heirloom in Apex Legends?
@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
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.
You replied to an ancient thread. I'll leave your reply here as the math you shared is relevant to this discussion, but I'll close the thread to prevent further replies!
