There's no two ways about it: the Arc A770 was a really big chip. 406 mm2 is a lot of die area - it's a few percent larger than its contemporary from Nvidia, the GA104 chip that came in at 392 mm2. That would seem fair enough, were it not for the fact that GA104 actually went into graphics cards like the RTX 3070 Ti and the Laptop RTX 3080, with dramatically better performance than anything in the Alchemist line-up.
So what's the end result? If you compared the top end A770 and A750 cards to their contemporaries in terms of how much silicon and power gets used, they turned out to be far slower than the RTX 3070 and RX 6750 XT. If you compare instead to their performance competitors, the RTX 3060 and RX 6650 XT both used little over half the transistors. Either way, Intel's offering falls far short.
That's where the story normally ends in mainstream discourse, maybe with an epilogue saying "...but they're good now that they're so cheap!". But the question has to be asked where that price cut comes from. With how much more silicon they used, maybe Alchemist graphics cards had to make do with an MSRP that had effectively zero margin - but then there's the fact that Alchemist was fabricated using TSMC's N6 process, a more advanced and expensive option than the cheaper 8N from Samsung that Nvidia used for the RTX 3000 series.
And then there's the fact that the high-end Alchemist cards have taken a price tumble even from that initial list pricing, in order to remain competitive; the number at the end of all of these sums is going to be very, very red.
At the end of the day, Alchemist was a huge money sink for Intel. Even disregarding R&D expenses, each individual GPU cost more and did less compared to the competition. So as its second-generation Arc products inch closer, fanciful projections of Battlemage's price-to-performance ratio based on GPUs that have to be sold at a major loss is just setting gamers up for disappointment. The competition has moved on since Alchemist, too; despite having just half the memory bus, the RX 7600 chases down the Arc A770's performance while being priced close to the cheaper A750 on Amazon.
Of course a new generation should have significant performance improvements. Of course it'll have two years of driver improvements to have learned from. But unless Battlemage can stand on its own two feet against the competition, Alchemist's only achievement will have been to waste precious TSMC capacity during the worst of the chip shortages - because Intel can't afford to do fire sales like this forever.
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