Below please find an Infographic comparing the current summoning portals, rates, stated odds and possible cumulative odds for certain summoning increments.
(update 2020-09-17:Ninja portal and Tavern portal v2)
(update 2020-12-03: Updated Tavern portal v3 odds and Atlantis v2)
(update 2021-05-24: Updated Challenge Event w. Trainers and Underwild Summons. Note skipped v4.0 public release but had internal copy)
Welp, I’m in that 3.3%
Good work!
Nice graphics @Dorkus. 
I’m not
I tryde to get a Miki. Conclusion 107 pulls
And i get nothing. Such a waste of money. The odds are too low. Tis was the point that i’m switching too Ftp. They only want more profit. But not from me any more. I did so many pulls whit atlantis. I never ever had a normal atlantis hero that’s not futured. I vind that very strange.
This is awesome - thank you for posting.
I understand chance and all, but so far I’ve had considerably better pull results with single pulls and 10 pulls. My 30 pull results are downright dismal (i.e., no 5 stars to date, not even S1). I know my results aren’t statistically relevant from a mathematical standpoint, but they are from a personal wallet standpoint. It makes sense to save/spend on 30 pulls, but if your 30 pulls are nigh always in the 3.3%? Even bonus chests don’t really make up for bad 30 pull results, IMO. I’m relatively new, but I’m quickly understanding why some P2P players stop maxing out their game budgets and just stick with lower pull rates. (My internal accountant is thrilled, but the rest of my psyche not so much).
So the best chance which you can get a 5* is in Event and Challenge combined with the money you spend … right?
Not wanting to turn this into a rant thread but I’m right there with you. My last 23 pulls were all 3* (0.1% chance).
I think you misread. 3.3% is all 3*stars
Ahhh oke 
but its still hurts 
For any 5*, they’re all about equal (except for Taverns and the normal Epic Hero Summon), with 3.8% chance of any 5*. If you don’t want a S1 hero, go for Atlantis or Valhalla (Valhalla seems to be best here).
Maybe I’m not good enough at math, but I don’t understand the numbers in “Bonus Draw” for Tavern.
While Myztero has a 0.1% chance being summoned as a bonus roll, at 10x it is at 1.0% (got that), 30x is at 3.0% (got that too) and 100x is at 9.5% (did not get that one). Shouldn’t it be 10%?
Edit: And thanks for the nice work btw 
Yeah, that’s where probability starts to hurt the brain. If a pull was 10% odds, 10 pulls won’t give you 100% chance, because there’s 90%^10 = 0.9^10 chance all the pulls fail.
For Myztero, there’s a 0.999^100 chance all of the pulls fail. That comes out to 90.48%, giving you the 9.52% chance in 100 pulls.
@nomadwolf beat me. It’s because the chart is rounding to the nearest tenth of a percent. 10x = 1 - (0.999)^10 = 0.995%. 30x = 1 - (0.999)^30 = 2.957%. 100x = 1 - (0.999)^100 = 9.521%.
Cumulative probabilities follow the Binomial Formula. Please see here for a better explanation than I could provide: Binomial Distribution
For those that would like to repeat this in M$ Excel with your own odds, or number of trials, here are the formulas I used:
For one success:
(CHANCE = cells with % odds to be considered, N = number of rolls)
=1-(1-SUM(CHANCE))^N
For more than one success: e.g. N_success = 2
=BINOM.DIST.RANGE(N,CHANCE,N_success,N)
@nomadwolf @TigerDevil Got it, thanks for the explanation.
It’s Very awesome and thanks!!
Hi @Dorkus!
I don’t understand the cumulative chance for getting 1x Non-Season 1 5* Hero in Costume Portal.
The table shows 32,1% - 68,7% - 97,9% for 10-30-100 summons.
Shouldn’t this be 0%?
Costumes are for Season 1 Heroes only.
Hey @Pois1 , thanks for your question.
The costume portal is a special event portal, so I categorize costumes as an “event” hero, even though they do apply to season 1 heroes only (right now…I think SGG‘S wording on costumes left this open in the future).
Dorkus can I ask whether the 5* rate all types percentage is correct when there a bonus summons? I think that’s two distinct events with 2.5% and 1.3% chance and therefore a combined chance of 3.7675% to get at least one 5*? You may just be rounding to one dp
