It's extremely hard for me to answer a lot of these card-specific questions because I lack the hardware to try it on and I can't really continually pester the devs with those questions either (they need time to actually do work) so...
Here are a few guesses but none of this should be treated as being in any way "official":
First off, those of you who are experiencing
graphic anomalies (artifacts, odd shadow behaviour, strange colours, etc.) but can otherwise launch and play the game should probably be fine with the release version since most of those card/driver-specific problems are being actively worked on (or may already be fixed). If they persist in the release version (or 1.1 when it's released), I am quite confident that they will still be addressed. There will be a special means of reporting such issues and getting them dealt with.
Further to this, I received a PM from one of the reviewers who received a full finished version (for testing for his review) but he also downloaded the demo, just to see what it looked like. He reported that the demo version had some weird graphic glitches on his card, but that the full version worked perfectly. I have no idea why this would be (the devs might) but it gives me some confidence in guessing that there we some issues introduced in preparing the stripped-down demo version that are probably not going to occur with the gold (1.0) version.
One last note on that subject...I installed the demo version on my Core2Duo with GeForce 7300LE and am having some odd graphic issues myself (Windows mouse pointer instead of the EU3 pointer, etc.) and yet my beta version runs perfectly on exactly the same system. I have no idea why there's a difference (though that doesn't mean that the devs don't). I don't have an older beta version archived to compare it to, but this same system has been flawless with EU3 betas since I got it in December. I also installed the demo on my older machine (an AMD 64 X2 Dual 3800 with GeForce6100 (same nVidia driver)) which I used for most of my betatesting and have roughly the same issues. Again, this is the system that has been flawless with all betas since early November, and I know that the demo build is later than that. This again makes me think that something happened with the demo build that shouldn't happen with the final release version. (Also a side note that for each system, the performance of current beta is a bit better than the demo's performance in spite of having more content -- though there are some optimizations that have been made since the demo build so that's probably the reason.)
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For people with nVidia 5xxx series cards, I have some serious reservations about the performance you'll get with the game, though I expect that the game will probably load and "work". This has been discussed in some detail in other threads so I won't rehash it here. The bottom line is that this series (particularly the very early ones) are only barely able to support the Dx9.0 library requirements and will probably only barely be acceptable on a 1024 x 768 monitor. Trying to drive higher resolution monitors with these cards is probably pushing them too far. Whether any sort of "fix" for this will be forthcoming from Paradox is hard to guess. I have no doubts that they'll look at it, but I don't know what would be involved in terms of code changes or whatever so I wouldn't even try to guess how long it might take (if ever) before the game will work well with them.
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People with somewhat high-end cards/integrated chipsets that (for whatever reason) aren't reporting 128MB v-RAM but use turbocaching (or equivalent) to share system RAM will probably be okay once Paradox releases a bypass for the v-RAM check. As I posted earlier in this thread, you may experience some (or no) performance reduction but I'm pretty confident that the game will run acceptably if your overall specs are good.
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As was pointed out in another thread, there are issues with a few Intel series that may not be resolvable and also seem to have a problem with a number of mainstream games (i.e. if the huge budget game designers can't make those cards work, I'm highly skeptical that Paradox will be able to). From what I gather (and I'm certainly no expert) with would require a fix directly from Intel, and Intel refuses to acknowledge that there's a problem at all (or rather, they dump it back on the game designers).
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People with business laptops (good/great sys specs but less-than-great integrated video chipsets) will probably be fine once Paradox releases the fix that removes the 128MB check,
provided that the laptop does have PS2.0 support -- i.e. full support for Dx9.0. (Obviously this excludes laptops with the aforementioned Intel series). You might not get quite as good a performance as you would on a similar-spec desktop with recent graphics card, but it shouldn't be too far off.
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People with graphics cards that are 4+ years old and don't support the full Dx9.0 library will almost certainly either need to get a new video card or stick with EU2. Sorry, but EU3 is far from unique in terms of games that won't run on what (for the computer industry in general and games industry in particular) is essentially an antiquated system. If your computer is the same vintage, you really might want to consider a whole new system.
No...I'm not saying you should buy a new computer or new card just to play EU3. There's no way I could possibly justify that kind of expense to play a $40 game. However, you should consider that any software released anytime in the near future is probably going to force you to do this anyway, so start planning and budgeting for it, and when you get the new system come and give EU3 another look.
My understanding of the issues involved in trying to make EU3 work on an older system like that leads me to believe that it's beyond the scope of the company's capabilities and development constraints (not to mention that it's like trying to part a 40-foot 18-wheeler in my one-car garage). I feel sorry for you, and am disappointed that you won't get to play the game (and it's also unfortunate that you won't generate sales revenue for a company I like), but I understand that we all have to make our own decisions about what's important to us. I spend my money on computers and beer, but I can't fault any of you who have different vices.
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For those of you who don't know whether your card or computer supports PS2.0, see
this post (which you really should already have seen since it's in a stickied thread entitled "EU3 Forum - PLEASE READ FIRST" but I know some people find the number of threads in the forum overwhelming so I'll cut you some slack) and proceed from there.
EDIT: if you really still can't figure it out, I'll try to help you but I have a huge volume of threads/posts on this forum to keep up with, and lots of other gameplay-related questions to answer, so perhaps a few computer-savy members could help the process along by looking up the cards and then helping out your fellow members. I'll try to assist when possible, but I can't continue to devote 90% of my time to it.