That would absolutely be out of control. Assuming 24 core machines (which I would think is an underestimate), that'd be 10M cores, or ~1 core per 15-30 DAU. That seems like it's 3-4 orders of magnitude more than necessary.
1 of your orders of magnitude is you're forgetting that 50-75% of traffic is signed-out, and that 30-50% of resources go to logging & analysis vs the core product.
Another order of magnitude is you're forgetting the cost of 3x storage & buffer for 99.99% uptime.
Another order of magnitude is that data transfer is REALLY expensive. They're not paying just for compute & storage.
3x2x3 = 18x, which is still only ~1 order of magnitude (and I had actually already doubled the number of DAU I thought they had for that 30 number, but apparently it's more like 250M now, not 150M. I don't know whether that includes logged out users). I'm not sure how the data transfer or storage are relevant to how many blade servers are reasonable. My point was just that 400k blade servers would be insane. 400 seems like it'd be excessive, including triple redundancy.
Right, they have other expenses. I was commenting only on the "only 400k blades" part. That's a staggering amount of computing power. I'm sure their analytics and advertising stuff requires a lot of compute, but the core functionality from the user perspective should doable on something closer to 4 dozen.