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If you're the self-improving kinda person, I'd suggest looking up podcasts related to your line of work, hobbies, mind and health, psychology and that sort of stuff. Last time I went on a transatlantic trip, I stocked up on podcasts and took personal notes as well as notes for my private practice. Kept me engaged for a considerable part of it (total of ~22 hours), although without delays.

Makes you a bit more active even with passive media, and since you're working towards a goal, it also probably leaves you with a productive end result, be it for yourself or ideas for work, hobbies, etc. Couple of ones I like (as reference) are:

How to be a better human; Stuff you should know; Feel better, live more; Speaking of psychology; This jungian life

If I had that long of a layover I'd leave the airport and go check out the city I was in. I had an AWESOME 12 hour layover in London once.

does the airport have a bookstore? maybe a paper book?

Duolingo. Then start texting your family in the new language that you learned that you forgot how to speak normally because of the delay time warp.

Sleep, eat, sleep, watch/hear/read something, talk to random people (preferably other stranded people), visit the smoking lounge, walk though all the stores, maybe buy a magazine.

And all the people recommending mobile games... I've wasted hours on end playing tower defense games, bridge builder or something like that. Get up inbetween and mix things up. Everything will get boring in that situation.

I rarely play mobile games, but here's one that I quite like when I need to kill time or be active while media is in the background: Auralux 2.

I initially thought that the game wasn't properly weighted for difficulty, but then found that I just needed to adapt my strategy. I can complete most levels in 2-3 minutes, though some might take 4-7 depending on how it breaks (I play on the fastest setting after getting good at it on normal speed).

I pick it up when my partner pauses to get a snack, go to the bathroom, or take an important call. I can set it down as soon as she's ready because there's no real stakes; I'm really just competing with myself to score faster and faster "best" times. I also play it while listening to podcasts if I can't be physically active (or when I'm lazy).

I play on iOS. Not sure if it's on Android.

If you like DOS games, ScummVM has an android app for their emulator and then you could hit up abandonware sites for nostalgia games. Works for some Win95 games as well. Played Woodruff on my phone a few years ago, an ISO file inside ScummVM, and besides the aspect ratio being a bit off it was playable.

I tend to go back to mindless puzzle games on my phone and set weird challenges for myself. I like HexaMania and InBlock by AleksDev. I paid for no ads, iirc 99¢USD, and haven't regretted it. No freeminum b.s. in those two. (There is a HexaMania 2 by the same person, but even with paying for no ads it has a pay to keep playing mechanic that keeps me away from it.)

Flow Free is a great connect the dot series of games that you can get the full game through Google Play Pass. Hundreds of levels per game. And with it being on GPP, you get unlimited hints if you get stuck.

If you want an exploration sandbox game, there are always Minecraft and Terraria to enjoy.

Einstein Riddle by Rottz Games, also in GPP, is a good logic puzzle game.

If you’re an iPhone user and intrigued by mobile games, go subscribe to Apple Arcade for a month. There are a ton of fantastic games without the bs freemium shit. Monument Valley and Alto’s Adventure (and their respective alternative titles) are great starters. I’m also a big fan of Good Sudoku which will teach you techniques to get better at solving them.

I’m sure you can get a lot better recommendations on current Apple Arcade games from social media or hopefully here on lemmy.

If you're into metal/hardcore/etc at all, you should watch the documentaries Parkway Drive (Post-hardcore/metalcore band from Australia) has made, extraordinary stuff. This is the first one.

I also recommend chess.

Mini Reviews is an android app that has robust filtering features for games. You can download offline games so you don't have to worry about spotty connection. Pocket City 2 is pretty fun and a good time sink, only costs $5. You could also play a text based "choose your own adventure" type game. If.youre artistic, I'm sure you could find a paper and pen to doodle on as well. Maybe a take couple of hours to feel the gravity of your own mortality. A little existential dread never hurt anyone

Anything interesting like a museum in the area around the airport? I had an 8 hour layover once and I just left the airport and went to a nearby Air Force museum of some sort. It was nice to walk around instead of just sitting in the airport, and I got to see a B-24

Buy a pack of sticky notes and a pen and let your imagination go. Write weird facts and trivia, or just whatever you want and stick 'em in places where people are gonna look, like on maps, mirrors, napkin holders at the bar...
Then just wait and watch

Start a new factorio game on a handheld device. Don't forget to get out of the plane after 20 hours.

Or watch the extended cuts of Lord of the Rings plus The Hobbit. That is 1171 minutes (=20 hours).

On a more serious note: I would schedule multi-hour blocks of work time, off time and sleep. Watching movies and playing games is much more fun after work is finished, and you feel like you accomplished something. It's also a good opportunity to do the tedious things you always wanted to do but never had the time and/or motivation (finances, taxes, studying, sorting files, sorting mails, that kind of stuff). It's not like you had anything better to do or other places to be, and it might actually make you feel better. After three hours of working you will look forward to the movie, before going to sleep.

Just in the Android games thing, a couple of recommendations:

• Golf Blitz - very fun crazy golf game which does have IAPs but they're not at all necessary to progress a long way in the game (in the very upper levels, it gets a bit slow as you need to build XP, but I've been playing it more than a year and never felt tempted to buy my way up the ladder. It'll certainly provide entertainment for a few hours. Does need an online connection though.

• Antiyoy - very simple strategy game that starts easy and gets very tricky. It's fun and no connection needed. Over 170 official levels, plus a whole bunch of user levels of varying quality. No IAPs at all as far as I remember.

Buy books? 20 hours man, I could burn through at least two.

Sonic 1, 2, and CD have been ported to Android.

Try Dumb Ways to Climb. It's free without ads.

I would recommend eating. Try a few places. That always passes the time for me.

Maybe learn how to play chess?

For games, my suggestion is that you try a whole bunch of them; get Google Play Pass and, if you have a Netflix subscription, browse through the list of Neflix Games and try anything that looks remotely appealing. None of these are gambling or freemium - they have no way to make money from you except for your continued subscription - and there's something for pretty much every conceivable genre.

If you can give any guidance about the specific sorts of things you like from games (action, story, puzzles, building stuff) I'm sure people can recommend some specific titles.

Go exploring. Walk the airport and go to other wings if it's a large airport. You might be able to find a luggage locker so you can walk without carrying anything.

In the same line, there are a lot of games that gamify walking. One. Two. The goal here is to exhaust your body a bit better for the 13 hr flight.

Learn something. A new language, maybe. A skill. Learn braille and go around the airport decoding the braille signs.

Do an airport scavenger hunt. Can you find yarn and maybe practice finger knitting? Maybe a deck of cards and learn some card tricks?

Talk to people. Honestly I'm an introvert so I rarely do this but it can be fun.