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There's a big thread about this - game crash on ranged attacks - a bit further down the page.

Always during a ranged attack?
I assume you play on Dx9, correct? If so, then please try DX11, and see if it happens again.
Please check if Steam or Civ5 have been installed in Vista compatibility mode.
How? Make a right click on the .exe file -> properties -> compatibility tab. There should somewhere be a checkbox, which is in your case most likely marked and set to Vista compatibility mode. Please uncheck that box, hit ok, and try if you can now play under DX11.
(my what?!?)?[....]
THANK YOU SO MUCH !! it was unchecked for some weird reason 0.0 but i got it working however i dont know if the games crashes are completely fixed.
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every thing is up to date and it just crashs at a bombardment or ranged attack and will not get past the first move on dx 11 .i played again to day and it did not freeze at first ranged attack but started blurring in the resource section at the top of the page and soon locked up totally .i used bombardment prior to that and it froze instantly .
my drivers are all above recommended specs i believe and up to date . i just installed the game for the first time a day or so ago and with out ranged attacks it is inhospitable to play


Hey J, im still following this thread cause im intrested in the final solution. You're doing a good job helping people here
Please dont think I wanted to troll or something, im realy just intrested when I ask: Did updating the drivers fix it for someone?
I know, its allways a good idea to keep them up to date, so telling people to update is never a bad thing. I just think this is more like a 'known bug' right now, something people have to accept
I'd say the only thing to tell people is: Play with Dx11 and if you cant try to minimize the problem by using windowed mode and save all the time.
Hope this didnt sound too trollish now, cause its not ment that way.![]()
After being directed to this thread, i tried to find a workaround for running in DX11(I'm runnin windows 7 sp1, so the option is greyed out intially), and found one pretty quickly. I right-clicked the DX menu and created a shortcut for the DX11 startup on my desktop. Doubled-clicked the icon and it started right up. Game plays on max settings flawlessly now
Thanks to all the help in this thread and especially the guy who redirected me here!

Please dont think I wanted to troll or something, im realy just intrested when I ask: Did updating the drivers fix it for someone?
good question, and apparently not, since nobody reported anything like that.