This app was mentioned in 17 comments, with an average of 1.94 upvotes
It's called Free Heroes 2, basically an emulated instance of the game. The same dev also ported Commander Keen if you feel extra retro
Shit, I sunk a TON of hours into Heroes of Might and Magic II on my phone when I found out there was an Android version ~~you could sideload~~ Edit: Hey! It's on Google Play!
Once I switched from a Galaxy Note 2 to a Sony Z1 Compact I stopped playing as much though. I feel like smaller screen made RTSes less playable. I've got a slightly bigger phone now though (Sony ZXP) so maybe it'll work a little better for gaming. Thanks for the tip!
For anyone interested there is a mobile port of HOMM 2! It works really well actually! Takes a little getting used to but great for long commutes or roadtrips.
https://play.google.com/store/apps/details?id=net.sourceforge.fheroes2
Looks like it's still in the store: https://play.google.com/store/apps/details?id=net.sourceforge.fheroes2&hl=en_US&gl=US
I've tried the following options on Android, with ExaGear being the only one I still have installed:
Free Heroes 2 - A direct port of Heroes 2 to Android. You'll need the original game files to play a full game, but otherwise this is the simplest option. I personally haven't experienced any bugs, but be aware the app hasn't been updated in a long time.
ExaGear Strategies - The best way to play real Heroes 3 on Android, including HotA. However, it's the most complicated to set up. The app is no longer available, so you'll need to find an APK. It's also picky about where the game files are, and how they're named. But, if you set it up right, you can play Heroes 3 using the exact same files as you would on a computer, meaning it's the full experience.
VCMI - The simplest option for Heroes 3 on Android. It also needs the original game files, but is much easier to configure, with a still-available APK and proper instructions. However, I stopped using VCMI because the AI was very poor. VCMI is a new engine for the game, so it's not quite identical to playing on a computer.
ExaGear Strategies will let you play Heroes 3, including HotA, on an Android device. The app is defunct, so you'll need to sideload an APK of the full (paid) version. However, it's the only real way to play the full game on your phone. I don't fire it up often, but this is what I use.
VCMI is somewhat more straightforward to install (instructions here), but because it's recreating the game engine, the experience isn't yet complete. Last I checked, development of the project has slowed to a crawl, so it likely won't improve for a while. I used to run VCMI, but I'll wait to revisit it until development progresses.
Someone also ported Heroes 2 to Android a long while ago, if you'd like to give that a try. All you need are the game files, but otherwise it runs fine out of the box.
There is a free ported version of HOMM2 available - link. I've downloaded it but haven't tried it outside of starting up a game so can't comment on how well it performs unfortunately
There is also a clone of the games called Palm Kingdom 2 thats paid but fun - I've played a bit of it and enjoyed it for the price
If you're on Android, Heroes II was ported a long while ago. And it's free:
https://play.google.com/store/apps/details?id=net.sourceforge.fheroes2
Be aware that it's not completely without potential compatibility issues and that you should probably try running it on a tablet for the increased screen size as the UI wasn't exactly designed with tiny phones in mind.
Yeah, there's way more tactics in it. You can also try fheroes2, an open source implementation of HoMM II (not sure about playability and stability though), or VCMI, an open source implementation of HoMM III (it was terribly broken some time ago because the maintainer of this port disappeared somewhere, but now it seems to be fixed).
Heroes V has this as a game mode (duel mode), where you can choose from a number of heroes with preset armies and skills. This is probably your best option if you want something ready to go and reasonably balanced.
For mobile devices specifically, Free Heroes 2 will let you create custom battles from scratch. For Heroes 3, you can try this, but it's online play only.
VCMI is still an option. I don't use it often, but it's a quick way to play on the road: https://wiki.vcmi.eu/Installation_on_Android. Do note that it's not a perfect implementation of the game yet. For example, the AI doesn't know how to properly defend a town.
ExaGear Strategies is another option, but I've never used it myself. It was removed from the store, so you'll need to grab the APK elsewhere. Since I've never used it, I can't speak to how functional it might be today.
And for a third choice, Heroes 2 was ported over a long while ago and still works perfectly: https://play.google.com/store/apps/details?id=net.sourceforge.fheroes2. Similar to the other options, you'll need the game files to play.
It's pretty easy really, you just enable 3rd part apps on your phone, and you can download various APKs (like EXEs for windows) and install them directly to your phone. Just be careful about what you install, some APKs can have viruses. This can let you install a wide variety of emulators that let you play older console games on your phone.
If you're asking specifically about HOMM2, you'll need to have your copy of the game because the APK just launches it but does not contain the game data. You copy the HOMM2 client you bought (If you don't have one Good Old Games has it available, DRM free). If you're curious about it, here's a decent article about the game running on Android: https://www.androidpolice.com/2011/05/07/review-videos-nerdgasm-fully-working-heroes-of-might-and-magic-2-homm-2-on-android-and-boy-is-it-good/
Actually, it doesn't even look like you need to sideload it anymore: https://play.google.com/store/apps/details?id=net.sourceforge.fheroes2&hl=en_US
It's available right there in the store now.
If you're still interested in sideloading APKs, here's a list of various sources:
https://medium.com/pen-bold-kiln-press/best-google-play-store-alternatives-30c759de1c26