So far I get the same results under Mac OS X, Windows, and Linux
(Google App Engine).  I'm particularly interested in getting the same
results under the Google App Engine even as Google upgrades its
servers over time.

I just had a look into the python source - and I was wrong, it appears random is implemented as part of the python c modules itself.

So chances are good that unless this module changes, you get a stable behaviour.

But I'd not advise to rely on that. Why do you want that anyway?

Diez
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