I agree with everything here so far, also check out Threes, You Must Build A Boat, and Dandy Dungeon. I’ve got plenty more where that came from! There’s a lot of classics that I’m sure others will suggest.
Roller Coaster Tycoon Classic is great It’s RCT 1&2 with touch controls. It’s more expensive than most phone games and they do charge extra if you want to get all the expansions but it is so worth it!
Though I typically have a penchant for gacha games (both English and Japanese android games such as Final Fantasy: Brave Exvius and School Idol Festival), I can recommend something along the likes of Plague, Inc. and Pandemic. I do happen to like Plague, Inc. more out of the two I suggested since it’s a bit dastardly in that you are not trying to save the world but actually trying to destroy it.
EDIT: With that said, here is a link to another forum thread that has loads of suggestions already in it for mobile games though may not be android specific:
My favorite mobile game happens to play excellently one handed
Down well is great I’ve heard and I think you can play it with one hand.
Ridiculous Fishing’s still a lot of fun, and you can definitely play it with one hand. (Tho the motion controls can be a little funky if you’re laying down, for example.)
Polytopia is quite fun if you’re into the Civlization-style game. No ads, either, which is always nice.
Various genre’s here but I have enjoyed the following this year:
Spaceplan - A clicker with decent writing that doesn’t really require you to click.
Crazy Taxi Gazillionaire - A clicker that does need clicking, but is bonkers and a lot of fun
Gems of War - Sort of a card collectable game but you can progress fine without having to spend any money
Saber’s Edge - Pirates!
Puzzles and Empires - Standard base-building, troop-levelling fare but again I find myself progressing fine without spending and can play for five minutes here and there.
Monument Valley - Old now I guess but a great puzzle game. Think the sequel should be out for Android soon-ish.
Oceanhorn - I actually got this on the Switch but it’s a port from the Mobile version. It’s Zelda-lite but I am really enjoying it after an average start so would assume the Android version is good as well.
Solitairica - Brilliant card game
I’d also recommend Hoplite.
Simple and addictive game, I’M ALMOST UNLOCKING THE LLAMA WHOOOOOOO!
Also, can’t go wrong with Tetris, or better yet Tetrios which IMO is the best version. Simple touch controls that don’t get in your way, offline, no ads, no complex rules (sadly no MP). Unfortunately, the author website vanished and no updates where released so if you are interested, give me a shout out and I’ll share my backup.
Simon Tatham’s Puzzles is a great set of classic puzzle games if you can get past the late 90s Java desktop applet aesthetics.
I’ve also been slowly working my way through the paid puzzles in Alcazar. Scratches a similar itch as Slitherlink puzzles, though it’s getting a little heavy on proof-by-contradiction for my tastes.
Zoo Keeper DX is one of my favorite match-3 games, built around quick play sessions and the intentional design choice to never punish you when the tile replacement algorithm generates a field without any possible matches.
Jeff Minter released a few Android ports of some of Llamasoft’s iOS arcade games as donationware.
And in the same vein, Forget-Me-Not is a rad little Pac-Man riff that’s deeper than it first appears.
Downwell is definitely a two-handed game, but it’s also one of the few mobile games I feel comfortable recommending. It’s a “videogame-ass video game” through and through. It is a run-based game centered around precise controls and development of skill and strategy. I don’t know how well it’s suited for playing while holding a child, but perhaps you can set him in your lap so you can focus on the true miracle of life that is Downwell.
Hungry Cat Picross. It’s just Picross. It really is.
And it’s great.
Mini Metro! Great little puzzle game about transit with some very lovely procedural music. The kid might actually like the music, I find it to be very soothing.
King of Dragon Pass, aka the best game ever, is available on Android but tbh I think I wouldn’t play it on a phone, only on a tablet.
The Rebuild series are really compelling post-apoc citybuilders.
I love all the Kairosoft games, typically little shop/studio management games filled with cute pixel art and eccentric humour. They did the original Game Dev Story game years ago where you run a studio to make your own video games, then eventually consoles… I followed them since then, as their games have gradually become more complex and inventive.
They have games for everything from running a restaurant to a manga studio to a space colony to a pyramid… My fave is the one where you slowly build up a fantastic round-the-world cruise ship.
Girl’s Frontline is such a good gacha game.
The gacha p2w mechanic is (mostly) cosmetic items and I’ve had almost no issues running out of resources that are used to produce characters. You’re even incentivized to level low-rarity characters, since a lot of them can more than hold their own until the endgame, when you have more than enough resources to level some of the rarer ones. Not to mention all the character designs are all great and full of personality.
i think hungry cats is the best
Oh yeah, those guys! They also helped inspire Greenheart Games to make Gave Dev Tycoon, which might be one of my most played games on PC ever. The Android port is apparently very good.
I also fell that we can bring up a few short games while we’re here. On that page, I can recommend One Night, Hot Springs, a short queer VN about a Japanese transwoman visiting a hot springs.
Implosion: Never Lose Hope is pretty good if you’re looking for some fun action and storytelling but I never got really far. Opus Rocket of Whispers has beautiful visuals and story if you’re interested in that