Do your summons odds get better as you progress through the game?
Nope, but you get smarter about where you pull.
Atlantis, events, seasonal, and elemental is you are early and looking for a specific element.
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With the right amount of money your chances will get, 1,3%, better.
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My chances to summon a dupe drastically increased with progression. 
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The per-summoning probabilities can be found by clicking the little question mark in the upper left corner of any summoning gate.
There is nothing you can do to change those probabilities. The devs have adjusted the probabilities for everyone from time to time (most recently, shifting a little probability in Atlantis toward Season 2 heroes). But nothing about your account affects the probabilities.
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Unless you stand in your bathtub and hop on one foot while you summon. Only works during a full moon, of course.
Sorry, had to 
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You’ll just pull Dawa with a sore leg, my friend 
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Sore leg? Nah, I’ll slip in the tub and crack my head open… the ambulance will come, I’ll desperately try and see my phone before I’m carted away… to see the lovely Dawa I just pulled.
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All jokes aside , I pulled Dawa earlier . Twice … two independent times, separate Atlantis pulls using tokens (which are exhausted now) and got the same hero twice !
Man I must be jinxed 
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RNG is like that. I did 2 30 pulls last Atlantis, hoping for Tarlak. No 5* at all. I did three summons this Atlantis: Elena(new to me), a 3*, and Drake Fong. I did literally 1/20th of the summons… RNG gonna RNG. And it will give me tomes of tactics non-stop… but nothing else 
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The 3* percentages are quite high. Atlantis 3* dupes are almost a certainty in any decent-sized pull. But yeah, you did get unlucky. Sorry 
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Do Atlantis coins give you a better opportunity?
100 of them give you a summon which has the same odds as a summon paid for with gems. So, no. The only benefit is that they are available for free… in very small quantities.
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Imo, not really. You will go through periods of droughts, and then you will go through periods of good pulls. You do get wiser about where you do your pulls at.
I wasn’t just wondering because I have been trying to get mitsuko for ages. I just did fifty summons and not a one was her
You also have a post where you claim that you lost her. I just read that and it seems like you fed her away.
No, my very first pulls (had a ice chests after one week playing with two ehts) have been Vivica and Gormekk.