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I think both AMD and Nvidia use alternate frame tech for their multiple card setups.
So card one does one frame, then card two does the other. This means the data is more or less mirrored between the two cards.
The reason why they don't combine into one 6Gb setup is most likely bandwidth restrictions.
What OptimaLnrg said, the latency of shuffling data over that distance would cause too much of a performance hit - theres a reason the VRAM is usually sitting around the core at equal distance - rather than parked in a nice neat block somewhere further back.
Wait so, if one card processes one frame, then the other card process the next, rinse and repeat. Does this mean that, the textures for frame one are stored on card one, and textures for frame two are stored on card two, meaning effectively 6GB?
actually, it's game dependent, some methods of SLI/crossfire involve one card drawing the top half of the frame and the other card drawing the bottom half
in any case, as mentioned above, both cards need to store all of the textures being used because those textures can be needed by either card at any time - cards will even deliberately not clear out used textures (if they have the space) in case they are needed again a few seconds later
a bridge allows the 2 cards to communicate with out needing to rely entirely on the PCIe bandwidth, which is part of the reason why pcie speed and type (e.g. x16 vs. x8 and v2 and v3) doesn't make a big difference until you get to 3 or even 4 card setups