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

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

If you enjoy pinball, this one is decent: https://f-droid.org/packages/com.dozingcatsoftware.bouncy

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 :)

• Tessel
• Ricochlime
• Shattered Pixel Dungeon

Tessel is a beautiful tile puzzle game

F-Droid

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

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

Here are some FOSS games on Android that can be played on a portrait orientation.

Mental Math

Tessel - A tiling game

Flang - it's like chess, but not chess.

2048

BlastOff - endless runner

Chip Defense - it is a tower defence type of game, and is one of my favourites. You should try it.

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

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

Sudoku by SecUSo

Slice & Dice is a dice building rogue like, didn't originally have portrait mode, but they added it in at some point, I love the hell out of it

magic survival

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

I hope you like rogue-like deckbuilders... I think all of these are either paid or you can pay to remove ads.

• Night of the full moon
• Pawnbarian
• Card crawl
• Card crawl adventure
• Card thief
• Maze machina
• Lost 4 swords
• Enyo
• Void tyrant
• Solitairica
• Wordlike
• Cards of Terra
• LOK

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

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

https://play.google.com/store/apps/details?id=air.com.midjiwan.polytopia

I play this one more than I should

Here is a paid gem:

Idle of Arrows (Play Store)

Downwell

The original Shapez is vertical. I don't love how it plays on mobile in terms of controls but it works

Gonna go with the wildcard here and suggest Walkscape. It's still in beta, so access requires a one-time patron sub ($4.50, then cancel) or a free written application through their portal (may take like a week to approve)

It's a classic runescape-style RPG where all actions cost "steps" walking. It's designed to keep screen time to a minimum and walking time to a maximum.

Character management is generally pretty passive and 1-handed. Definitely much more casual by nature, but encourages much more active participation.

Square Valley

A Way Home

Dicey Elementalist

Perfect Grind

The Way Home

I don't play many Android games, and enjoy even fewer, but Hoplite is great. It's pretty simple to play but still requires some thinking, which is what I want out of a mobile game.

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

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

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.

For casual time wasters, Feudal Tactics and Shattered Pixel Dungeon are good games.

Anuto TD

https://play.google.com/store/apps/details?id=vo.threes.exclaim

https://play.google.com/store/apps/details?id=com.eightyeightgames.ymbab

I would say Umamusume but don't get into it if you don't really have much time.

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

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

80 Days

Nethack runs good in vertical. I use the version called Pathos. Good dungeon crawler.

I just finished Monument Valley 2 and adored it. Short little puzzle game where you kind of mix the background and foreground together to progress. There's 3 of them.

Not exactly an Android exclusive thing, but I like to play GameBoy ROMs vertical so it feels more like a gameboy color.

‘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

Idle Elemental (Play Store)

Oddly satisfying. And has an ending.

Ingress

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

Backpack brawl is fun, township as well.

Here is a paid gem:

Isle of Arrows (Play Store)

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.

Here's another: Paragon Pioneers 2. A simple Settlers clone.

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.

Pilgrims. Its a puzzle game, no dialogues but great story. Not FOSS.

https://amanita-design.net/games/pilgrims.html

It's a paid game, though. I got it for free from Epic Games.

You can play it on any device. On phones, it is played in portrait orientation.

A couple I enjoy:

• Tents and Trees
• OneBit Adventure

A 3DS emulator like Azahar or DS emulator like MelonDS both of which are on the Play store, and play a Pokemon game or anything turn based. Play it vertically. Different puzzle games

Hoplite

Try this FREE mystery horror puzzle text game where you are doing detective work... of sorts?

I got so hooked and absolutely loved it all the way.

Don't be fooled by the cover graphic or name.

https://william-rous.itch.io/type-help

Ps. It's playable on browser on any platform, you can save to disk, and did I say it' FREE?

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.