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I`ve been searching it for a quite long time as well:
Sadly, no.
There is no similar game yet, considering the seriousness + depth + complexity + historical meta data + etc...Which means, there is no any GRAND-Strategy game on iOS yet.
But there does exist something close, in some aspect. If you just need some nice game to help you kill some time during outdoor...Here are some:
Starbase Orioin (classical Master of Orion 2 like game, a deep 4X space game)
-----It offers a well-balanced multiplayer as well (and also plus a healthy and happy community) ---- But it`s sci-fi, based on fiction. No historical background at all. It`s kinda a sandbox-competitive game in terms of its system.
Personal rank: 5/5 for replayability, 3.5/5 for fun part, 0/5 for historical meta-gaming, 4/5 for sandbox level, 5/5 strategy level ---- totally it will be 17.5 /25
Civilization Revolution for iPad (classical game, lots of historical depth but the mobile version does skip a lot compared to the original)
-----It`s more like a fast-food light-weighted game than heavy bomb HOI, but anyway, the game is still fun.
4/5 for replayability, 4/5 for fun part, 3/5 for historical meta-gaming, 3/5 for sandbox level, , 2/5 strategy level ---- totally 16 /25
World at War
----- A Risk style game at WWII, has lots of historical campaign such as Sand-fox, Blitz attack, USSR anti German invasion, Poland anti USSR invation, USA vs German, USA vs Japan etc...I`ve played this for quite a lot, imo this game is great. It`s much more fun in the tactically view even than HOI, if you like the WWII, and also feel comfortable with the risk-style gaming system you must give it a try. Trust me, you won`t regret.
3/5 for replayability, 4.5/5 for fun part, 5/5 for historical meta-gaming, 3/5 for sandbox level, , 4/5 strategy level ---- totally 19.5 /25
Great Big war (newest generation of the classical STG Little Great War/ Great little war)
Outstanding graphic, classic STG Eco->Build->Deploy->Find Counter->Learn-to-Fight game. You will like it if you like the graphic, and it`s modern based. It`s a tactical level game instead of grand strategy.
3.5/5 for replayability, 4/5 for fun part, 0/5 for historical meta-gaming, 2/5 for sandbox level, , 3.5/5 strategy level ---- totally 13 /25
Sadly, no.
There is no similar game yet, considering the seriousness + depth + complexity + historical meta data + etc...Which means, there is no any GRAND-Strategy game on iOS yet.
But there does exist something close, in some aspect. If you just need some nice game to help you kill some time during outdoor...Here are some:
Starbase Orioin (classical Master of Orion 2 like game, a deep 4X space game)
-----It offers a well-balanced multiplayer as well (and also plus a healthy and happy community) ---- But it`s sci-fi, based on fiction. No historical background at all. It`s kinda a sandbox-competitive game in terms of its system.
Personal rank: 5/5 for replayability, 3.5/5 for fun part, 0/5 for historical meta-gaming, 4/5 for sandbox level, 5/5 strategy level ---- totally it will be 17.5 /25
Civilization Revolution for iPad (classical game, lots of historical depth but the mobile version does skip a lot compared to the original)
-----It`s more like a fast-food light-weighted game than heavy bomb HOI, but anyway, the game is still fun.
4/5 for replayability, 4/5 for fun part, 3/5 for historical meta-gaming, 3/5 for sandbox level, , 2/5 strategy level ---- totally 16 /25
World at War
----- A Risk style game at WWII, has lots of historical campaign such as Sand-fox, Blitz attack, USSR anti German invasion, Poland anti USSR invation, USA vs German, USA vs Japan etc...I`ve played this for quite a lot, imo this game is great. It`s much more fun in the tactically view even than HOI, if you like the WWII, and also feel comfortable with the risk-style gaming system you must give it a try. Trust me, you won`t regret.
3/5 for replayability, 4.5/5 for fun part, 5/5 for historical meta-gaming, 3/5 for sandbox level, , 4/5 strategy level ---- totally 19.5 /25
Great Big war (newest generation of the classical STG Little Great War/ Great little war)
Outstanding graphic, classic STG Eco->Build->Deploy->Find Counter->Learn-to-Fight game. You will like it if you like the graphic, and it`s modern based. It`s a tactical level game instead of grand strategy.
3.5/5 for replayability, 4/5 for fun part, 0/5 for historical meta-gaming, 2/5 for sandbox level, , 3.5/5 strategy level ---- totally 13 /25
Well damn. I've been searching too 
Just wanted something to play on the bus for iPhone since bus journeys can be damned boring..
I'll check that Starbase Orion out and World at War too, thanks
Just wanted something to play on the bus for iPhone since bus journeys can be damned boring..
I'll check that Starbase Orion out and World at War too, thanks
You should also add Realpolitiks Mobile (iOS, Android) by Jujubee studio. It's a modern time grand strategy where player becomes a leader of any contemporary country. The game was recently released for Android and iOS and it' really fun to play.
https://play.google.com/store/apps/details?id=pl.jujubee.realpolitiks
https://itunes.apple.com/app/realpolitiks-mobile/id1238141350?mt=8
https://play.google.com/store/apps/details?id=pl.jujubee.realpolitiks
https://itunes.apple.com/app/realpolitiks-mobile/id1238141350?mt=8
The Gary Grigsby games are fairly similar, but I don't know if they're available for IoS at all.
Smart phones are as of yet too weak in computing power to run a grand strategy game like HoI III, EU III, CK II, etc. Although games such as EU I or HoI I, etc., might be portable. But I doubt PDX would do such a thing.