There are a lot of great suggestions here already, so I will just share Mini Review with you as a discovery tool. I like to use them because they have a lot of filters to help you find a mobile game. For example, here's their list for free, single-player, offline games with no ads or in app purchases, sorted by highest user score. They also have an app for both Android and iOS with the same info and filtering as the site.

Neko Atsume: Kitty Collector. You put down furniture. Cats sleep on the furniture. You get gold to buy more funiture, and the cycle repeats.

Not sure if it fits your criteria but the only mobile game I play is pinball deluxe. If you like real pinball, then you'll love it, it tries to stay as true to real pinball as possible on some/most tables, it does have small transaction stuff you can buy but I still haven't bought any including all the additional tables etc after playing it 6 months + and if you did, then it's just an 8€ one time buy to get all the content and remove the ads, I'm gonna get that once I actually get bored of the "free" tables.

"0h h1" is a fun, easy logic puzzle game that I find myself going back to when I have a minute to kill.

A couple that I like:

• 80 Days - it's not free but I think it's worth it. It's a sort of steampunk version of Around the World in 80 Days where you have to plan your routes, and buy and sell things in different cities to make money. The main gameplay is sort of choose-your-own-adventure events that happen during travel and in different cities.

• Card Thief - I just started playing this recently. It does technically have a microtransaction but it's more like, they let you play for free if you don't mind waiting for chests to unlock, or you can buy the game to bypass this. The main gameplay is sneaking through dungeons represented by a 3x3 grid of cards randomly drawn from the deck; collecting treasures and avoiding getting caught.

Slice and dice

Solitaire, straight out of classic Windows (pre-advertising death throes):

https://play.google.com/store/apps/details?id=com.potatojam.classic.solitaire.klondike

Hoplite, classic turn based dungeon/puzzle:

https://play.google.com/store/apps/details?id=com.magmafortress.hoplite

I'm not sure it fits 100% with what you're looking for, but I'll take chance and recommend Slice & Dice (Google Play, Apple App Store). Free demo, no ads, single in-app purchase to unlock the full version. This game is easily the best value-for-dollar mobile game I've ever purchased.

Polytropia

You should download Mini Review

It is a currated version of the Play Store with many filters including paid/free, IAP, genres, ...

The reviews are very thorough and always include a paragraph about the "presatoriness" of IAP if any

Shattered pixel dungeon has been a mainstay on my phone for what feels like a decade now

I have clocked a lot of hours in Slice & Dice both on mobile and on PC well worth the 8 bucks even though I've paid it three times now I think. Honorable mention to Suika(Watermelon game) about 3 bucks on the Play store.

Rodent Rush, it’s similar to Chips Challenge from back in the day but a bit different, and imho it’s a better game.

It’s only on iOS though as far as I can tell.

desert golf and its follow up golf on mars are big hits at my house

Old school RuneScape, it has free "demo" version which you can easily put a 100+ hours in. And if you really love there is a subscription model that's kinda expensive if you bill monthly, but no other micro transactions.

2048

I really liked Lara Croft GO. It's better than Hitman GO or other GO games.

Some good games I recommend are Alto's Adventure / Odyssey, any bejeweled game, Cell to Singularity, Idle Slayer, Monument Valley, Reigns, Sky Force Reloaded, and Stick Fight Shadow Warrior. Hopefully that's enough!

Vector pinball

Grand prix story and game dev tycoon.

Both good games, low stress, clear progression

Beleentoro Pro might be something for you. Basically a chill factory game, which I enjoyed for a long time. Other games by the developer Yiotro might be worth a look too.
There are also free versions of most of their games available, with ads iirc (not sure, has been a while). But if you don't want the ads: the pro versions are really cheap. One time purchase for everything.

Another idea I have a puzzle game called: Mekorama by Martin Magni. The last time I played you got an option to pay what you think the game is worth at the end of the game. But you don't have to.

Mini Metro by Dinosaur Polo Club is also really good, but comes with a purchase.

If you like tower defense, Bloons TD 6 by Ninja Kiwi is a must have. Comes with a purchase and has the option of microtransactions for cosmetics, but you can get those by playing as well. More importantly, it's tons of fun.

In case you've got a Netflix subscription, check out their games. They have lots of games in their repertoire which you would have to buy if you went through the App/Play stores. (Bloons TD 6 should be included there for example.)

Edit: corrected Bloons TD 5 to Bloons TD 6.

Anti-mine: foss minesweeper Blockinger: foss tetris Puzzles: foss app with 40 ish mini games Lexica: foss boogle Lichess: foss chess

Johngbac: gba emulator L game: one of the simplest game which will make you rage. Underhand: light card game.

Assuming that you have Netflix, open it, scroll to games and open the section. There are tons of great games without any microtransactions or ads. They're overwhelmingly commercial games licensed by Netflix.

Flow is a fun puzzle game with a hint of nostalgia

Neopets still exists and is going strong! The community is wholesome and so amazing, You can play it on your phone's internet browser, it's wonderful nostalgic break from everything else, and they have a TON of free games built in... Solitaire, Pyramids, Bullshit, Battleship, Minesweeper, Brick Breaker, Mahjong, Blackjack, Poker, Keno, etc.

I still play every day and have a BUNCH of goodies for new players, if you do check it out!

I used to play Unblock Me. Made it maybe 1000 levels in various difficulties before stopping.

It doesn't quite fit, but there are a lot of boardgame phone adaptions, and they rarely have microtransactions. Cat lady, carcassonne, ghanz schoan clever, doppelt so clever, hex roller, rail road ink and roll player are some of my favorites

I don't think there's any meta progression as far as I'm aware, but I find Shattered Pixel Dungeon (available on both android and ios) to be a low stress enough game. I suck at it, so I've never gotten much further than the first boss fight, but the game is about running through randomly generated dungeons, going down floor by floor as one of 4 different characters.

Andor's Trail, it's barely recogniseable as a "phone" game, other than that it does indeed run on phones. I don't remember if it had ads or anything, been taking it from phone to phone for over 10 years now. I don't think it had ads or anything. It's open source, but has a pretty consistent feel despite having like 50+ contributors so far.

It's an adventure RPG. The low level experience might be best with a bit of grinding, but.... casual grinding... lol. I kind of just wander around collecting "meat" until I feel strong enough to leave the areas near town and set out on the rest of the adventure. But there has been alot more work around town since the last time I started a new character. So it might feel more natural now.

I have a 2048 clone from F-Droid and a Solitaire-like games collection from F-Droid that keep me busy on flights, etc. No stress, easy, entertaining.