# Nexus Crystal Synthetic Drop Odds

The drop odds for the Nexus PHC are the same, per selection, as the normal PHC - 3% 4*, 20% 3*, 77% 2*. But what are the odds of getting each tier from the Nexus, given the triple choice?

If we assume that a player will always select the highest star rating champion (or from the highest if there are multiple), then we can simplify this a bit. The odds of pulling three 2* champs (and thus forcing you to pick a 2*) is (0.77)^3 ~ 0.4565, or about 45.65%. The odds of pulling

So basically, the odds of "effectively pulling" the different tiers in the Nexus PHC are:

45.65% 2*

45.62% 3*

8.73% 4*

Given that it costs 50% more than the base PHC, that's a substantial increase in value.

Just for giggles, what would the synthetic drop odds be for a hypothetical Cavalier crystal? Glad you asked. The standard Cav has drop odds of: 1%/11%/38%/50%. So the odds of getting stuck with three 3* champs in a Nexus Cav would be (0.5)^3 = 0.125, or 12.5%. The odds of getting at least one 4* but no 5* or 6* champs would be about 55.65%. The odds of getting at least one 5* but no 6* would be about 28.88%. And the odds of getting at least one 6* champ would be about 2.97%.

So the synthetic drop odds of getting at least a certain tier would be about 3%/28.9%/55.7%/12.5% (rounded to one decimal place). The odds of getting a 5* or 6* champ would be almost one in three.

If we assume that a player will always select the highest star rating champion (or from the highest if there are multiple), then we can simplify this a bit. The odds of pulling three 2* champs (and thus forcing you to pick a 2*) is (0.77)^3 ~ 0.4565, or about 45.65%. The odds of pulling

*at least one*4* champ is a bit more complicated to calculate, but it comes out to be ~ 0.08733 or about 8.73%. That means the odds of getting at least one 3* but no 4* is 100-45.65-8.73 = 45.62%.So basically, the odds of "effectively pulling" the different tiers in the Nexus PHC are:

45.65% 2*

45.62% 3*

8.73% 4*

Given that it costs 50% more than the base PHC, that's a substantial increase in value.

Just for giggles, what would the synthetic drop odds be for a hypothetical Cavalier crystal? Glad you asked. The standard Cav has drop odds of: 1%/11%/38%/50%. So the odds of getting stuck with three 3* champs in a Nexus Cav would be (0.5)^3 = 0.125, or 12.5%. The odds of getting at least one 4* but no 5* or 6* champs would be about 55.65%. The odds of getting at least one 5* but no 6* would be about 28.88%. And the odds of getting at least one 6* champ would be about 2.97%.

So the synthetic drop odds of getting at least a certain tier would be about 3%/28.9%/55.7%/12.5% (rounded to one decimal place). The odds of getting a 5* or 6* champ would be almost one in three.

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## Comments

813★★★12,172Guardian104★7,346★★★★★6,065GuardianI would assume how this crystal works is that it Random picks which Star Rank you get, and THEN would randomly choose which of the 3 champs to offer you “of that already determined Star Level”.

So that Drop Rates are still identical to the base Drop Rates.

7,346★★★★★12,172Guardian6,065GuardianGuess it’s better at least from the point that it’s really better odds then for at least some type of 4*. But still...

12,172Guardian12,172GuardianThe Nexus is better. It rerolls for you twice and lets you pick any of the results: the original, or any of the two "rerolls." That's better than being able to reroll, because you can pick an earlier option if the later ones are not as good.

7,346★★★★★3,604★★★★★12,172GuardianAlso, the way you're describing it is not the way I would do it. You end up with all sorts of potential fencepost and round off errors, and this requires a lot of extra state. The proper way to do this is probably to use collision bitmaps. If you're crazy, you can also do offset rolls, but that just seems to be asking for trouble unless you were under some sort of efficiency gun.

And this bears repeating: the time to write the code fragment to make this work is 0.1% of the total resource burn doing this would eat up in any game development group, or for that matter probably most anything development groups.

2,608★★★★Like the probability of any star except 4 happening 3 times

12,172Guardian12,172Guardian