This app was mentioned in 25 comments, with an average of 2.32 upvotes
Have you guys tried Tower of Hero? That's where I ended up in my search for a soda dungeon alternative. It's pretty damn good, actually, supports both active and idle play styles, has a fairly unique system of prestige, wherein you don't get anything for the prestige itself, but for every so many floors, you get a chest that contains one or more items that enhance various game attributes, and these items stack, and carry over through prestige. There's a pretty good size list of them, and it always seems like, just when you thought you had all the items, you get a brand new one with a super cool effect (The Genie Lamps are my favorite. They give you chests at the beginning of a run depending on your progress through the previous playthrough!) Also, seemingly endless amount of recruits to buy and upgrade, in a similar, though pointedly different (and, IMO, better) system as Clicker Heroes.
Okay...I could go on and on about it, or you could go download it. It's free, and it's awesometastic!
This dev is also behind the excellent Inflation RPG and a cookie incremental (click on his name in the app store to see the other apps).
I believe Tower of Hero Link! is fairly battery friendly. Maybe not amazing, but definitely not a huge hog.
EDIT: /u/Cicmile98 made a good point, apparently it eats battery for some/many.
An incremental game where you tap to create soldiers that will attack mobs, each floor has enemies, when you kill them all you unlock the next floor, with more powerful mobs, tons of stuff to drop and improve your dmg etc...
https://play.google.com/store/apps/details?id=com.Tatsuki.Tower&hl=en
You can try to install it outside of your phone. ie using the above link to install it and select your phone as the device.
I personally think that Tower of Hero had a great prestige system. Also, Soda Dungeon.
Tower of Heroes is a great one that I've absolutely fallen in love with. Last update was a few months ago, though. (Not that it seems to matter to me, since I still haven't reached end game. That said, I've been pretty slow with these games lately.)
https://play.google.com/store/apps/details?id=com.Tatsuki.Tower
Its also on android :)
https://play.google.com/store/apps/details?id=com.Tatsuki.Tower&hl=en_GB
Link for android users
I'm looking for games like Infiroad: http://www.houmotsuko.net/_webgl/infiroad/
I've seen similar games before like Tower of Hero on Android: https://play.google.com/store/apps/details?id=com.Tatsuki.Tower
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I would prefer web-based browser playable.
Please keep in mind that mobile games aren't as good as their PC counterparts. The mobile incrementals I've listed all have some aspect of grinding / looting and have been the ones to keep my attention.
Tower of Hero is one of my favorites, but its very active and the offline progress is pretty much 0. It has the best loot system in my opinion though. If you get bad items the change to get a good item increases, and if you get a good item only the chance to get that specific item decreases.
Zen Idle is one of my currently played games. Its also very active, but the offline is much better than Tower of Hero
Adventure Communist Its good if you like offline progress, but its not extremely active.
Please keep in mind that mobile games aren't as good as their PC counterparts. The mobile incrementals I've listed all have some aspect of grinding / looting and have been the ones to keep my attention.
Tower of Hero is one of my favorites, but its very active and the offline progress is pretty much 0. It has the best loot system in my opinion though. If you get bad items the change to get a good item increases, and if you get a good item only the chance to get that specific item decreases.
Zen Idle is one of my currently played games. Its also very active, but the offline is much better than Tower of Hero
Adventure Communist Its good if you like offline progress, but its not extremely active.
On Android there's this one : https://play.google.com/store/apps/details?id=com.Tatsuki.Tower&hl=en
On PC there's this one : https://www.houmotsuko.net/en/game/infiroad/index
was it tower of hero?
link : https://play.google.com/store/apps/details?id=com.Tatsuki.Tower&hl=en_US
It's for Android, but I think it's what you're asking for otherwise.
https://play.google.com/store/apps/details?id=com.Tatsuki.Tower
Same dev as Inflation RPG.
Can I point out that you're asking for a contradiction? Your topic name is asking for mobile games, but your description seems to be asking for browser games, which... is kinda strange, if you ask me...
But anyway! If you're looking for phone, like the topic seems to be asking, I really, really like Tower of Hero for the Android. It has a mild idle, but it definitely rewards active play more than idle, and fairly fast prestiging, especially once you get the hat that gives you rewards for getting as high in the tower as you can get in x minutes (I've seen 8, 9, 10, and 11).