It’s actually 1.3%, not 1.6%.
And the math doesn’t work quite the way you’re describing, because that’s not how probability works.
This might help:
Or: How many summons are needed to get a HOTM?
Special thanks to @Garanwyn for assistance on summoning odds and proofreading for this section.
It’s important to remember that HOTM have very low summoning odds. No amount of summoning will guarantee a HOTM.
On average, in a 10-pull, you have a 12.3% chance of summoning the HOTM.
But that statistic can lead our minds astray in exactly how our odds play out as we continue summoning.
Some useful insights:
73 times out of 100, you’ll get a HOTM by pull 100
95 times out of 100, you’ll get a HOTM by pull 229
99 times out of 100, you’ll get a HOTM by pull 352
Putting that in Perspective
27 out of every 100 people won’t
If 1 Million players each summoned 100 times, 270,000 of those players wouldn’t get the HOTM
5 out of every 100 people won’t
If 1 Million players each summoned 229 times, 50,000 of those players wouldn’t get the HOTM
More Insights & Reading
I highly recommend reading these two threads for more information and context on summoning odds:
If you’ve read them a million times before, you may consider reading them again before deciding on your budget for summoning. A little time spent deciding on how much money you want to risk on summoning goes a long way to avoiding disappointment, frustration, and regret later.
And as @Infinite said, you can get more than one copy of the HOTM in a 10 pull — you can actually even get a bonus roll second HOTM off a first HOTM, but obviously it’s quite uncommon.
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