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Nexus Cavalier crystal odds (for each rarity)

Based on what I've seen, the Nexus Cavalier randomly generates each pull independently (but I believe still does not generate duplicates). This means each "slot" has an independent chance to be 3*, 4*, 5* or 6*. So while the odds of pulling a 6* champ are 1.5%, the odds of at least one pull being a 6* are higher. Suppose we assume it is a given that a player will always select the highest rarity champ that appears (this isn't necessarily always true, but probably almost always true). In that case, what are the odds that a player will pull a 3*, 4*, 5*, or 6* champ from this crystal?

Short answer (rounded to 0.1%):
4.4% 6*
42.4% 5*
44.0% 4*
9.1% 3*

(Note: adds to 99.9% due to small round offs)

The math:

Odds of pulling 6* champ: 1.5%. Odds of not pulling a 6* champ in three tries: (1-0.015) ^ 3 = 0.956. Odds of pulling at least one 6* champ: 1 - 0.956 = 0.044 = 4.4%.

Odds of pulling a 5* or 6* champ: 17.5% + 1.5% = 19%. Odds of not pulling a 5* or 6* champ: (1 - 0.19)^3 ~ 0.5314. Odds of pulling at least one 5* or 6* champ: 1-0.5314 ~ 0.4686. Odds of pulling at least one 5* but not 6*: 0.4686-0.044 ~= 0.424 = 42.4%

Odds of pulling 3* champ: 45%. Odds of pulling only 3* champs: 0.45^3 = 0.091 = 9.1%.

Odds of pulling at least one 4* champ but no higher: 100% - 9.1% - 4.4% - 42.4% = 44.1% (round off causes this to be 0.1% higher than the directly calculated value above).

So the odds of pulling a 6* champ are almost three times higher, the odds of pulling a 5* champ are about 2.5x better, the odds of pulling a 4* are similar, and the odds of being stuck with a 3* champ are about 80% lower on a relative basis.


Bonus question: what are the odds of getting at least one 6* if you buy all seven Nexus Cavs: about 27.2%.

Odds of striking out with all 21 options of all seven Nexus crystals: (1-0.015)^21 = 0.728. Odds of getting at least one 6*: 1-0.728 = 0.272.

Comments

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    SquirrelguySquirrelguy Posts: 2,635 ★★★★★
    I appreciate the mathematical approach to a dilemma that I’m never gonna have until they release these into the game for F2P players in like 8 months.

    I assume it will happen though since the community seems to be pretty excited about them and I’m sure Kabam is raking in the dough.
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    DNA3000DNA3000 Posts: 18,660 Guardian
    Ebony_Naw said:

    Not to be that guy, but isn't the last one not a featured crystal? So the final question is only slightly off. So odds are 23.7% plus the 7th crystal

    You could be right on that score; I just assumed the featured odds would hold true for the entire week. It is all but guaranteed to be true for the first six days, but I'm not sure what Sunday will look like.
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    KDSuperFlash10KDSuperFlash10 Posts: 5,869 ★★★★★
    So does my bday money go to nexus cavs or new soccer cleats
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    KDSuperFlash10KDSuperFlash10 Posts: 5,869 ★★★★★
    Mcdonalds said:

    So does my bday money go to nexus cavs or new soccer cleats

    One is the opportunity of a life time other is a soccer shoe stuff
    Ok but what if I get SHAFTED

    At least I know I'm not getting shafted buying shoes
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