I sufferred so that 10 000 of you don't have to

This is just a fun post, don't take it seriously.

So, since the start of this event, I have opened 10 cavs. The chance to have sth else than a 3* is this:

(3* drop chance is 40%, so 60% chance for NOT getting a 3*)

The chances of pulling at least one champ other than 3* are 99.98951%. That means only 1.05 people outta 10000 should get 10 3*s in a row.

I am not complaining, I have big enough roster and take the game casually, so it is no big deal since I didn't pay for them with real life money. But ngl, I need ISO pretty bad and I definitely could have used some 4* duppes. Well, next time.

And why I post this? Because the odds are pretty low imo and there have been a lot of posts featuring the best pulls from cavs. I feel like the other part of the spectrum should be represented too.

I expect DNA3000 to correct where I am wrong in this post so pretty please, tell me how to count the chances propperly. I love math but I just can't grasp statistics. I can count derivations and integrals, but probability is just impossible for me. Thank you.

Comments

NastyPhish

The problem is better solved through geometric distribution. Check Simula67 channel for videos about. Called “how I decide on featured crystals” but the same math applies to any % crystals. But it will explain to how you could get a “clump” of 3*.

That being said there should be some system in place to keep spending money from feeling punishing. Like maybe you earn shards relative to your level regardless of what you roll

Colinwhitworth69

If you opened 1000 crystals, would it be as odd that there were 10 3 stars in a row somewhere in those pulls?

DNA3000

I expect DNA3000 to correct where I am wrong in this post so pretty please, tell me how to count the chances propperly. I love math but I just can't grasp statistics. I can count derivations and integrals, but probability is just impossible for me. Thank you.

The calculator you're using seems correct on the surface. If the odds of pulling a 3* champ are 40% the odds of not pulling a 3* champ is 60%, and the odds of pulling all 3* champs is (0.4)^10 = 0.0001049 or 0.01049%. The odds of getting at least one pull that is not 3* is thus the inverse of that, or 1 - 0.0001049 = 0.9998951 or about 99.98951%. The odds of doing this are about one in 1/0.0001049 or about one in 9537. That verifies at least the simpler values the calculator is generating.

This might sound rare, and it is, but there are a lot of opportunities for players to see something like this, because they collectively open a lot of crystals, so the odds of seeing something like this, as opposed to exactly this, are much higher. When we say something is a rare occurrence, it is important to keep context in mind. Rare can become uncommon, then likely, then inevitable if you take enough swings at it.

I'd say the odds of any one person seeing this in any one month are very low, but the odds of this happening to a player across, say, a year of similar opportunities starts getting closer to one in 800, and now we're talking about probably hundreds of players that see this every year. An event can be both rare, and also happen to a very large number of people collectively.