Here is one that is quality and engaging if you like a good story:

80 Days

Downwell and Holedown are both fantastic games played in portrait. But I won't lie; lately I've fallen back into Marvel Snap and I live it. (Not love, live.) But never spent a dollar on it.

Big fan of Melvor Idle, Assembly Line 2, Mindustry, and Homequest. I've played all of these a couple of times and even redownloaded them all at one time or another.

Surprisingly, mindustry hasn't been mentioned yet! Great quality, well thought out, addictive combination of tower defence, RTS and factory building.

Backpack brawl is fun, township as well.

It’s an older game, but Downwell is fun. Just a little action/arcade game where you fall down a well and try to get combos by not touching the ground by bouncing off of enemies.

https://play.google.com/store/apps/details?id=com.devolver.downwell_rerelease

Dawncaster is a great deck builder that's vertical if you are into those!

Rogue Adventure is great. I recently switched to iOS but I miss playing this game.

Link

Downwell is one of the best mobile games of all-time

https://play.google.com/store/apps/details?id=com.devolver.downwell_rerelease&hl=en_US

Ingress

https://play.google.com/store/apps/details?id=com.nianticproject.ingress

Dungeon Tracer is a pretty decent remake of one of my favorites from back in the day, Dungeon Raid

I guess it's my turn to say it in a thread:

Shattered pixel dungeon

Best classic roguelike on mobile IMO

I was going to also suggest Downwell but it doesn't seem to be available any more

Sudoku by SecUSo

Deep rock galactic survivors is on mobile now and it works in both portrait and landscape mode

The different types of Gameboys and most of their games emulate really well on a smart phone. I prefer playing them in landscape orientation for the larger display, but portrait mode gives a more accurate recreation with the screen on top and buttons on bottom.

I'm out of touch with what the latest best options are for emulators and where to source your ROMs, but if you ask around in communities focusing on things like piracy, they'll point you in the right direction.

Recommended to use a VPN for any downloads.

I haven't played it in a million years but I remember Cut The Rope being really fun.

• Tessel
• Ricochlime
• Shattered Pixel Dungeon

‘Antiyoy’ is a simple strategy game, fit well for shortish sessions. Free and with minimal permissions. Iirc ‘Antiyoy Classic’ is offline-only, while the regular one has multiplayer.

‘Diplicity’ is a multiplayer-only (afaik) strategy like Risk, but with zero element of chance, only diplomacy. However the games can be rather slow, from what I've heard.

‘Fabularium’ is an app for running text-adventure games — one of many such apps, but I like it because it supports modern game formats. You'll need to download the games themselves elsewhere, mainly from ifdb.org — there are a lot of games, some of them with quite novel mechanics.

‘Hocus’ is a geometrical puzzle with impossible shapes. Iirc additional levels are paid.

I've heard that ‘Mindustry’ is a good open-source clone of ‘Factorio’, but idk how it plays on a phone screen.

This is a fun new puzzle game. Like a cross between Tetris and Ingenious

https://play.google.com/store/apps/details?id=com.xceler8games.triangles

Once Upon a Galaxy has been my default game since I first played it.

It's an asynchronous alternating activation autobattler (like Arcane Rush, or Storybook Brawl/Hearthstone Battlegrounds but you play against ghosts). Games take about 10-15 minutes.

It's largely public domain fantasy themed, but has been expanding into the "legally distinct" cultural references as they add content, basically every captain/unit/treasure is a reference.

The shop mechanic is simplified, there's no currency, you just get a set of choices, and can pick 1. You get two shops per round by default, lots of ways to get extra.

Asynchronous play means that you face challenging opponents that naturally evolve with the meta game but you can also take time to make thoughtful decisions.

The draft pool for the shop has a large base pool that you add to by selecting a custom sebset from a second large pool as your captain's deck. The progression is through unlocking cards for each captain's secondary pool, and unlocking new captains. You can naturally earn all cards through play, most captains are free, new captains are paywalled for a limited time.

Monetization is through 3 paths: cosmetics, acceleration of card unlocks, access to paywalled captains. I haven't found it to be particularly exploitative or negative feeling.

My only gripe is minor, that it doesn't have mid-run save/resume, but that is on their road map.

There is essentially no story, if that matters to you.

If it's not obvious, I'm really enthusiastic about this game. I'm not affiliated/sponsored in any way. Happy to answer any questions.

I am quite partial to Puzzles

https://play.google.com/store/apps/details?id=name.boyle.chris.sgtpuzzles

https://f-droid.org/packages/name.boyle.chris.sgtpuzzles

Currently playing Block Blast as my time killer and loving it.

I would highly recommend Monument Valley (1,2 and 3 is coming soon) as far as puzzle goes, for a quick arcade fix, I like Breakout 71 (with rogue-lite elements) and all games by Arnold Rauers (Card Crawl being my favorite, but by a small margin).

Here's a quick selection from the top of my head, if you want I can go throw my app history for a few more :)

Slay the spire!

Edit: nvm I'm an idiot and forgot about "vertical" in your request. Its not, but I still recommend it because its a good game

Tessel is a beautiful tile puzzle game

F-Droid

Goddess of Victory NIKKE fits what you are asking.

It is a high quality Free-to-Play mobile game played in portrait mode and completely playable with one hand (depending on how wide your device is). As long as your don't care about leaderboards, it also isn't Pay-to-Win. It is playable on PC as well, which is how I play these days. As a Day 1 Player, you don't need to spend any money to play, enjoy, or progress in the game.

In terms of negatives:

• Some people may not like the anime art style (game is playable in various language dubs, including Korean, Japanese, English, and depending on region, Chinese, which are optional downloads to reduce filesize) or the character designs, which have huge... personalities

• If you don't care about time limited events or being at the top of leaderboards, its not hostile to your playtime and mental health. Go at your own pace.

• It is a gacha game for characters and skins, but the game gives players a lot of options, so unless you're trying to be #1 on the leaderboards in your server, having every character max level isn't that important.

They recently added a "Story Mode" for the campaign, which significantly reduces the difficulty of all the missions in the 40+ campaign chapters so that players can enjoy the story without needing to have as powerful characters. I think you get reduced rewards as well, but its a nice addition. You can also get photo film rolls to unlock past time limited events (not licensed or collab ones though) so you can enjoy the stories of those as well. You don't get the rewards for them as they were running, but still can experience the stories and minigames. You get plenty of free currency for free character rolls, no money is needed. Unless you really want a skin or really like a licensed collab and want to buy an IP specific bundle or something.

Basically, for a free player, there is A LOT of story content available to keep your busy for a while. Play at your own pace, and don't worry about leaderboards and you'll be mostly fine. The biggest advice is to try to get 5 characters 4 times each. If you are playing the regular difficulty story, there is a point where it is required to progress, and is often referred to as the only "wall of progression" in the game.

magic survival

Anuto TD

I love puzzle games, either ones with an overaching story or standalone puzzles. I love the professor layton series Googke Play Store. I believe you should also check out Monument Valley Google Play link. If you're looking for a FOSS option, there's Simon Tatham's puzzle collection F-Droid Link