How do you ensure that the 500 concurrent keep-alives land on different Lambda functions? I.e. requests 220 and onwards might hit lambda functions which were warmed up by requests 0-219. I just made the above numbers up of course.

That's why I mentioned 'with maybe some overhead'. You can also have the keep-alive handling take a second or 2 extra to complete, to have the lambda blocked for this time, so the burst calls get more spread. It's not going to be a precise solution, but still, paying 2-3 seconds every minute instead of paying the whole minute is still a lot cheaper.

Ok, I quickly did the math for 500 lambdas (1Gb):

Provisioned: 500 * 86400 (sec/day) * 0.000004167 ~= $180

Keep-alive: 500 * 1440 (min/day) * 2 (sec. runtime) * 0.000016667 (100ms price) * 10 ~= $240

Invocation costs on the provisioned ones would be a lot cheaper too cheaper too. Roughly $45 provisioned vs $80 for 50M calls.

So depending on the demands, provisioning can be more performant, and cheaper at the same time.