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Do you have any genre preferences or are you just looking for anything that's genuinely free? The thing is, real mobile games without pay-to-win stuff do exist but you gotta dig a bit, like on itch.io or in open source apps. Games like Mindustry or Two Dots charge you once and that's it, no weird microtransactions after. Otherwise "free" games from more legit publishers (like Nintendo or some indie devs) are usually honest about it, but yeah, you gotta check the reviews before downloading because a lot of free stuff gets annoying after a while.
Open-source games on F-Droid are really your best bet, because there's no way to monetize with microtransactions when the code is public and nobody's making money off it. Otherwise look for games that clearly say "truly free-to-play" rather than "free-to-start" - it's a distinction you don't see nearly often enough but it makes all the difference.
Check out indie games made by small devs, they often create really complete stuff for free just because they love making games, without the pressure from publishers to monetize at all costs. Yeah, F-Droid is a solid foundation, but even on regular app stores you can find gems if you avoid the top charts, which are almost always packed with pay-to-win garbage.
The problem is that "truly free without pay-to-win" barely exists on official stores, even games you think are innocent often have shady mechanics hidden in them! What nobody mentioned, is that you really need to read the reviews in detail and not just look at the overall rating - there are tons of people who explain exactly where the pay-to-win starts ruining your experience, that's your best indicator before downloading.
I tested quite a few things on my phone and I noticed a trap that nobody mentions: even games advertised as "free" can wreck your experience with invasive ads every thirty seconds. It's technically not pay-to-win, but it's gross anyway. So make sure you check the reviews that explain how the ads behave before downloading.
To actually find quality stuff, I'd start by digging around on itch.io - there are tons of indie creators releasing complete games for free, really polished stuff. After that, F-Droid is solid like others have said, but it's true the selection is more limited than the Play Store. Another approach: some "mainstream" publishers release games for free once they stop actively monetizing them - it's rare but it happens.
What also helps is reading the reviews carefully before launching a game, like asking the question on gamer forums rather than trusting the app store description. People are usually honest about the "it's free but you have to pay to progress" versus "it's actually free and complete" thing. Do you have a specific genre in mind or does nothing ring a bell?
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