It's supposed to be unlimited, but a few summers ago some kid found out the limit is really 100 a day. He wasn't happy, and even less happy when everyone laughed at him in the forums.
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Thanks for that. A 100 a day is plenty! 
At the main site I use I only get 100 every 30 days. 
Apparently they changed this, or maybe I was just wrong. 
It's 100 a week. My bad.
Tht's okay, I've been tracking it myself.
I seem to be getting 300 a week.
One of the beauties of running out of analyses is that it when you try to request another it gives you a list (on a red background of the last 300 requests - with the time they were requested).
By geting a print out I know when I'm going to be able to request my next analysis - 168 hours from the time of the last one on the list I haven't crossed out.
How many (post game) computer analyses does one get as a Diamond member?