A key point in this post is Las Vegas. A place to gamble, and where gaming equipment is made. The required randomness is determined by the application. Gambling needs a very high level of randomness. The game will not be approved if it cheats. It will not sell if it pays out more than the odds.
The was a case where a programmer got hold of the code for a game. Since pseudo-random patterns repeat, he was able to collect some data point, figure where in the pattern the number generator was, then know the future numbers.
There are tests for all the qualities of randomness. If it matter that much, then that aspect of the project should get the proper attention.
Note that Windows has a flaw in the random number generator used for encryption. This reduces the effectiveness of the encryption.