Low Power Mode on, brightness down: these three still play clean without turning into a squinty mess.
Polytopia is my airplane-mode fallback

My favorite time to start The Battle of Polytopia is right when a flight hits that dead zone after takeoff and the little Wi-Fi icon goes from hopeful to useless. No login tantrum, no spinning wheel, no "reconnecting" banner parked on top of the screen. It just drops you onto that chunky, toy-like map and asks what kind of ruler you feel like being for the next 15 minutes.
It also happens to be kind to a phone that's hanging on for dear life. When I'm at 1% battery, I'm already doing the whole ritual: Low Power Mode, brightness dragged down until the screen looks like a haunted Kindle, and every background app swiped away like I'm exorcising demons. Polytopia still reads clearly in that state. The units are big enough to tap without surgical precision, the colors are high-contrast, and you're never punished for playing slow. Turn-based strategy is basically the opposite of "my phone is dying" panic.
The way I keep it fun (and not a long tutorial vibe) is to set a tiny entertainment goal before I even place my first city: "I'm going to make boats this time" or "I want one ridiculous border". If you've ever watched someone get bored with a strategy game because it feels like homework, that little goal fixes it. Two other practical notes from doing this too many times: play a small map if you're truly on fumes, and turn off the music if you're already listening to a podcast in your earbuds. The sound is fine, but the game is at its best as a quiet, pocket-sized board game that doesn't demand your whole phone.
Hoplite: five minutes of clean, mean tactics

Hoplite is what I open when I want my brain to snap into focus without committing to anything that looks like a "session." It's a little tactics roguelike on a hex grid, and it wastes zero time trying to charm you. You hop, enemies move, lava threatens, and every mistake has a sharp little sound that says, yes, that was your fault.
Entertainment-wise, it hits the same nerve as a good arcade cabinet: short rounds, immediate feedback, and that quiet itch to try again because you can see the exact moment you blew it. There's no plot to keep in your head. No inventory anxiety. The fun is in the rhythm of planning one move ahead, then two, then realizing you're cornered and trying to do something clever with a bomb or a spear throw.
It's also a great "my phone is overheating" game. The screen is mostly simple shapes and clear icons, and it doesn't feel like it's constantly waking the device up with animations. I can play it one-handed while standing in a line, and the taps are deliberate instead of frantic. That's a weirdly important distinction when you're in public and trying not to look like you're defusing something.
If you bounce off it at first, here's the trick I wish someone had told me: treat the early levels like a rehearsal space. Don't rush to go down stairs just because you can. Lure a few enemies into clean positions and practice the push-and-punish dance. Once it clicks, the game becomes this tight little stress ball for your thumbs. And when you die (you will), it doesn't guilt-trip you with a bunch of menus. You're back in instantly, which is exactly what I want from casual gaming when the clock is ticking.
Alto's Odyssey (and the volume-off vibe)

There's a specific kind of low-battery boredom where you want something pretty, but you can't afford a game that turns your phone into a space heater. Alto's Odyssey lives in that sweet spot. It's an endless runner, sure, but it's more like a moving wallpaper you can influence with a thumb. One tap to jump, hold to flip, and the rest is this smooth glide across dunes and canyons that still reads well even when your brightness is cranked down to "movie theater."
The reason I keep coming back is the vibe is the entertainment. The landscape changes in a way that feels authored, not random, and the little set pieces land: the first time you ride a wall for a long stretch, the moment a sandstorm eats the horizon, the quiet satisfaction of threading through rock arches without thinking too hard about it. It's one of the few mobile games I can play with volume off and not feel like I'm missing the point. (Helpful when you're on a couch with someone watching Netflix, or you're pretending you're not killing time in a waiting room.)
On 1% battery, I also want games that don't punish me for bailing mid-run. Alto's is forgiving. You can play for 45 seconds, wipe out, and still feel like you got a little hit of something. If you have a minute, chase a simple goal like "three backflips in one jump" or "don't touch the ground on the next slope". If you have ten minutes, go hunting for a specific biome and try to ride it clean.
One practical, hands-on note: wipe your screen first. This game is basically a smear detector. A slightly greasy screen turns precise jumps into "why didn't it tap?" drama, and that is not the energy you need when your battery indicator is already red and judgmental.