You are running the chi-square against the claimed distribution of the RNG, not against another RNG. Which is just about enough to use the RNG for simulating di

You are running the chi-square against the claimed distribution of the RNG, not against another RNG. Which is just about enough to use the RNG for simulating dice rolls ( sometimes, if the players are not too passionate). RNG can have a lot more subtile flaws, for example the RNGs from the ANSI C rand() with the suggested parameters lie in just a few thousand planes, if you construct points in some vector space out of the random numbers. ( That is bad, if you want to run Monte Carlo integration, because your error estimate improves, but not the accuracy of the result.) So even for simulation you can have rather subtle effects, even though there you get bitten just by bad luck. The task for cryptographically secure random number generators is actually quite a bit harder, because a attacker tries to exploit any weakness in your RNG, but your tests do only tell you which specific attacks do not work.