Dual vs Nexus Crystal (5*)

So after a heated 24hrs, thought we focus on something a bit lighthearted.

I was wondering if any of our fellow players are mathematician, I was just wondering which crystal would give a better percentage/chance of getting a champion you want.

Dual crystals - cut the option down to about 1/3, depending on which duel class you looking for.

Nexus crystals - give 3 options from the whole pool.

I can imagine Nexus crystals would be more special because we get to choice, but does it actually give better chance (higher percentage).

Of course this is just a fun question, because we don't get to choose, and usually just happy to have any 🤣🤣🤣.

Comments

odishika123

Forgive me little one
Dual*

Fryday

Many thanks, I have amended it 🤣

odishika123

Nexus crystals can both be a good and a bad thing
Good news you might get a champ you have been looking for
Bad news: you might have to pick 1 champ BTW 2-3 very good champs

Scarcity27

So I'm no @DNA3000 , but let's think about this practically.
Let's say there are 300 champions, 50 per class (there are 200-odd, but this is for simplicity's sake)

So, from a dual, you would theoretically have a 1/100 chance of getting your champ.
From a nexus, you have 3 choices from the basic pool. So 3/300, which is 1/100 again.

A nexus gives you 3 choices to be able to select your champion if they appear, but at the same time, decreases the chance that they would appear by 3.
A dual gives you 1 choice (not really a choice, but for comparison's sake it is) but at the same time, increases the chance that your champion will be that one choice by 3.

So it really comes down to Choice or Chance.

I would probably take the nexus, just cause there may be many champs I'm hunting, and while they may not all be in the same dual, I'll have a better chance of one of them appearing in the nexus.

Duals, however, are more accessible. And you don't have to make any difficult decisions there.

TyEdge

They are roughly the same in a vacuum. Situations where they aren’t the same:

You want champs from smaller dual class pools (iirc science/mystic is smallest by a not-insignificant number)

The champs you want are clustered in a dual class crystal. (3 of the 4 I want right now are in Mutant/Skill)

You have a fair number of max sig champs. (The odds of getting who you want off a short list are pretty long in both cases. If the rest of the pulls are relatively meaningless to your roster, the nexus gives you a better chance to opt for a max sig crystal when you don’t get one of the pulls you need.)

Malreck04

I'll be working with rough numbers but any reader can alter them according to needs.

Suppose a nexus crystal has a pool of 200 champs. We want to calculate the probability of pulling any particular champ from a single nexus, which will be equal to the number of outcomes in which you pull the champ(n(E) suppose) divided by the total number of outcomes you could get from the nexus(n(S)).

Using some basic counting techniques, n(E)= 200C2 (the number of ways we can get two other champs considering the third champ to be who we want), similarly n(S)=200C3

Dividing we get the probability as 1/66, which almost exactly what you would get considering a third of the champs to be in the dual.

SandeepS

I think the answer is dual class nexus Crystal's until the wish crystals come out

Malreck04

I'll be working with rough numbers but any reader can alter them according to needs.

Suppose a nexus crystal has a pool of 200 champs. We want to calculate the probability of pulling any particular champ from a single nexus, which will be equal to the number of outcomes in which you pull the champ(n(E) suppose) divided by the total number of outcomes you could get from the nexus(n(S)).

Using some basic counting techniques, n(E)= 200C2 (the number of ways we can get two other champs considering the third champ to be who we want), similarly n(S)=200C3

Dividing we get the probability as 1/66, which almost exactly what you would get considering a third of the champs to be in the dual.

Ok small mistake, n(E) will actually be 199C2 because the other two champs will be from the rest of the pool.

This changes the probability to 3/200, still arbitrarily close to the first result.

DNA3000

I was wondering if any of our fellow players are mathematician, I was just wondering which crystal would give a better percentage/chance of getting a champion you want.

That is the key to the question. Most people are approaching this starting with the assumption you are trying to target a specific champion, and calculating the odds of pulling that champion from dual class or nexus crystals. But in practice, most people want a number of different champions. In the general case, the way you would decide which crystal option was better would be to do this:

1. List all the champs you want.
2. Figure out how many are in each dual class crystal
3. Calculate the ratio of the champs you want vs the number of champs in each crystal.
4. Calculate the ratio of all the champs you want vs the total number of champs in the basic crystal, times three
5. Pick whichever one is higher.

Just to make things simple, lets assume there are 60 champs in the sci/mystic crystal, 65 champs in the tech/cosmic crystal, and 70 champs in the skill/mutant crystal (I don't know what the actual numbers are off the top of my head). And let's say you want just one champ. If that champ is a sci/mystic champ, then the ratio of that crystal is 1/60. The odds of the other two are zero - because you don't want any of them. And the ratio of the basic crystal is 1/195. Times three is 3/195. 1/60 is approximately 0.01667. 3/195 is approximately 0.01538. 1/60 is bigger, so that crystal is better.

If your one and only was skill/mutant, then that ratio would have been 1/70 ~= 0.01429. Now, the basic ratio is better, so the Nexus would be better.

If you want more than one champ, the process is the same.

This math is simpler than most "what are the odds" calculations because in the dual class case you're only dealing with one draw, and in the case of the Nexus all of the draws are unique - meaning no possibility for duplicates. That simplifies the math a lot.

In general, the Nexus cannot do better than (all of) the dual class crystals, because the odds of pulling what you want from a Nexus crystal is identical to what the odds would be for an imaginary "average dual class crystal." Imagine a dual class crystal that contained exactly one third of all the champions in the basic. This hypothetical crystal contains the average amount of champions that the real dual class crystals contain. Now also imagine that of all the champions you want, exactly one third happen to be in this crystal. So this crystal also contains the average amount of champions you want from each of the real dual class crystals. This hypothetical crystal has the average number you want and the average number of total champs. The Nexus crystal has exactly the same odds as this imaginary crystal - because the Nexus pulls from a crystal with three times the number of options, and is looking for three times the number of wanted champions, and it has three tries to hit them.

Since the Nexus crystal has the same odds as this imaginary "average dual class crystal" there's only two possibilities. Either a) all of the real dual class crystals have exactly the same odds, and their average is therefore identical to any one of them, and thus the Nexus is also identical to all of them, or b) at least one dual class crystal must be above average (because they can't all be below average). Therefore, either the Nexus odds are identical to all of the dual class crystals, or at least one dual class crystal must outperform the Nexus. You just have to calculate which one.

TrashyPanda

I think the answer is dual class nexus Crystal's until the wish crystals come out

I don't think Wish Crystals are gonna be what people hope they are.

Ercarret

I suspect that Nexus crystals are better if you don't care what class you get a champion in, while dual crystals are better if you're targeting those specific classes.

For example, I desperately need a good science 6* because I don't have one. For me, I'd probably prefer a Science/Mystic dual crystal rather than a nexus because the dual crystals limit the pool down to the class I'm after (plus mystics). The nexus would just give me three choices out of every possible choice in the game.

However, if all you want is a good champion regardless of class, then a nexus is a better bet because you get more options. While it opens up the pool for a lot of rubbish champions, it opens it up for a lot of A-listers as well.

Stebo_79

Yeah that's how I see it. If you're hunting a particular champ (that's in the basic pool) then get a dual.
If you want to increase your chances of getting someone good, then a nexus will normally do that.

Fryday

It is pretty much a hypothetical question, specifically since it isn't really a choice we get to have between a dual and nexus crystal, and for someone like myself, just happy to get any of these crystals. Mainly just bit of fun discussion in the community, away from the many heated issues out there.

Really appreciate everyone involved, specially the legendary @DNA3000 (your fame precedes you by about 5 posts 😆).

I'm no mathematician, so only assume that the probability between dual and nexus crystals is roughly the same. I just randomly thought about it because seeing a lot of members taking about Nexus crystals in a special light, but I guess it is really more about the psychological concept of having choice (even if it isn't always a good selection of choice like
@odishika123 said) and it rarity that make us more intrigued in the Nexus crystal, rather the daily available dual crystals.

Unitman

i didn't know so many people did crystal math

Bugmat78

i didn't know so many people did crystal math

A lot of mathheads around here #addiction

Reference

i didn't know so many people did crystal math

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“quad long shot grande in a venti cup half calf double cupped no sleeve salted caramel mocha latte with 2 pumps of vanilla substitute 2 pumps of white chocolate mocha for mocha and substitute 2 pumps of hazelnut for toffee nut half whole milk and half breve with no whipped cream extra hot extra foam extra caramel drizzle extra salt add a scoop of vanilla bean powder with light ice well stirred.... oh by the way, I have a free reward.”

Malreck04

i didn't know so many people did crystal math

I mean, you would know, being unitman and all

Corkscrew

I don't think Wish Crystals are gonna be what people hope they are.

So you're saying you don't think Wish Crystals are gonna be what people wish they are?

Irony Level 100.