The formatting you’ve copied across is a bit of a disaster. I have coped by following the link to the original post, but it has been tiresome. If you could tidy it up that would be really helpful. Maybe it’s not possible?
Yes. The more times you summon, the better your chances of pulling any particular hero, just as the more times you toss a coin (or the more coins you toss) the better your chances are of getting heads at least once. (One toss: 50%; two tosses: 75%; three tosses: 87.5%; four tosses: 93.75%.)
At the same time, of course, your chance of pulling that hero does not change from one summons to the next, just as your chances of tossing heads are 50% for every toss (or coin). This often seems to confuse people. I don’t know why.
The actual chance is not quite 100%, but it so close as not to matter. (Spoiler: I’ll tell you what it is later.)
If players want to increase their chances of pulling a hero they want, then yes, they should summon more heroes. But whether they summon them one by one or in groups will not affect their chances (nor does the summary data suggest that it would).
If someone did 1500 pulls and didn’t get a single legendary hero then my response would be as follows:
If you are telling the truth and you can prove it, then get yourself a lawyer and sue because you have compelling evidence that the odds are not as stated. It is IMPOSSIBLE, in any practical sense of the word, to summon 1500 times and receive no 5 heroes.
(I just tried to calculate the odds and gave up halfway. I’ll finish, for the sake of it:
The probability of getting only HOTM as your 5* heroes from 1500 summons is 0.975^1500 = 0.000000000000000003 (to 1 s.f.)
And the probability of getting no HOTM from your 1500 summons is 0.987^1500 = 0.00000003 (to 1 s.f.)
So the probability of you getting no legendary heroes at all from your 1500 summons is:
0.000000000000000003 x 0.000000003
= 0.00000000000000000000000001 (to 1 s.f.)
If I have my large numbers correct, that means the chances are 10 septillion to one against this ever happening.
For reference, 10 septillion is about one million times the number of grains of sand on earth.
I’m very happy to call that impossible.)
I think you might be getting yourself a little bit mixed up.
Okay, but based on your earlier comments I’m now concerned that you might not actually understand this. Yes, the odds for each individual pull with a 10x summons package are the same as the odds for a single pull. But the cumulative probability of you pulling a 5* hero is much higher if you summon 10 times (whether one by one or all at once - it doesn’t matter) than if you summon once.