"Increased chance for Legendary Hero"

I’ll try my best:

Probability of landing heads when tossing a coin = 50%

Probability of landing heads when tossing a coin on the 3rd attempt = 50%

You got that part right, well done! But let’s go even deeper! :slight_smile:

Probability of landing heads when tossing a coin in 3 attempts (i.e. getting heads in any of the 3 attempts) = 100% - (50% * 50% * 50%) = 87.5%

But anyway, that’s completely unrelated to the issue. SG clearly states there’s a 2.5% probability of getting Legendary on EACH attempt, and in the normal summon it’s only a 1.5%, so it’s an increased chance. Nothing shady there.


Hi guys! Interesting discussion. Let’s please keep it respectful and constructive. Thanks!


Good outline, Neko. You’ve summarized the key points beautifully.

No, it’s a 1:72 chance accompanied by a 1:48 chance. 2.5 percent is 1:28.8.

All I know is that the chance of agreement on this thread is less than that of pulling an individual event Legendary Hero, which is about 1/3%. I can’t believe I went over that many statements back and forth talking past each other. The participants should realize when things are fruitless but none can back down. This is not math, it is semantics and that is where each side can be right in a sense. The thread should be locked.

P.S. A lot of we outsiders understand the math too. It helps taking the position that the other person does understand something rather than they are ignorant.

Ducking into a trench…

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It’s clear there is a difference of opinion. Do y’all want to keep painting the column, or wait for @Petri to clarify?

I don’t think there’s something for Petri to clarify here… :wink:

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It definitely IS math.

Assuming we believe the figures provided by SG (and, if we don’t, none of this matters), there’s either a mathematically greater chance of getting a legendary in the event portals or there isn’t.

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That would be opinion, yes? :wink:

Ugh - just so wrong.

We agree that the chance of rolling 1 through 3 in one roll is 3%, right? And we agree that the chance of rolling 1 in one roll is 1%, right?

Surely, surely you can understand that if you have a 1% chance of an outcome, then repeating the event multiple times improves that chance? (If you do not understand that then you are beyond redemption.) So please explain how you would calculate the cumulative chance of success if you have multiple events with each having 1% chance of success?

(Spoiler: the actual answer is that the cumulative probability of success is 1 - 0.99^n, where n is the number of events.)

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@Rook if Petri clarifies that the odds of 5 star are indeed 1:28 rather than the two separate lower odds then I will stand corrected.

Ok I will code for you in ruby.

odds = { rare: 710, epic: 265, legendary: 15, event_legendary: 10 }

def single_pull(odds)
	odds.flat_map { |choice,num| [choice] * num  }.sample

10.times { puts single_pull(odds) }

Results what I got from 10 pull


Like you see I got 1 standard 5* hero, 2 4* heroes and 7 3* heroes. Course I can go further and make a list of all possible heroes but I think it is clear enough.


The chance is always the same. This is why casinos are always successful.

Rook, I’m new here, and I completely understand if you want to shut down this thread. I agree that we’re not getting anywhere.

But this is not a question of opinion. Either I’m correct about the math or I’m wrong. No opinion involved.

I was gently joking with you Orynn, that your comment that Petri would add nothing was mere opinion.

Sorry, I tease.

The thread hasn’t violated any rules yet, and it’s a vibrant discussion about math. I’m all for it. If, however, both sides are at an impasse, you might want an official SG voice to clarify (if they will).


Fair enough, and I can certainly appreciate that. I’m still trying to figure out the culture here-- thanks for clarifying! :slight_smile:

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Do you disagree with the way it is stated on the portal there is a 1:72 odds chance and a 1:48 odds chance at a legendary? That is what is being questioned whether it is as I say or a 1:28.8 odds chance with a 66% chance attached to that odd.

In the name of all things holy:
1:72 + 1:48 = 1:28.8
You are now explaining in clear maths exactly how you are wrong.

That’s two separate odds, not one odd. Nowhere in the portal are the two odds grouped together giving no reason to believe those odds are connected.

Your odds apart: On a summon, you don’t have 5 chances, but 1 chance. To pull a hero, that is. So how is this one chance distributed within your pool of 5 different possibilities?