"Random" is hard to define. There is a vast literature out there on the topic.
For purposes of video poker, what is needed is a way to provide for any card to be "as probable" as any other card, to within some statistical criteria. That last phrase after the comma is "the best you can do."
"Pseudorandom" is an admission of imperfection, applied to any programmatic method of generating a random sequence. Some important person once called this "living in sin."
In the end, you have to realize that if a departure from pure randomness is hard to recognize, you need not spend more effort on improving it.
I understand that the RNG (random number generator) in a video poker machine runs constantly, even between the deal and the draw. The precise millisecond that the user hits a button is a natural randomness. So you have a random pick out of a pseudorandom sequence. That's possibly good enough for all practical purposes.
I'm personally inclined to trust the Nevada Gaming Commission's dominion over in-state casinos. Seems to me that, say, a 3% advantage for the house, averaged over a month for all the action on the floor, would provide a satisfactory house income.
I have no such trust for "Indian" machines outside Nevada. Biasing the RNG is programmatically trivial.
We folks here may play to better than 97% payback (on certain payoff schedules) but the unwashed multitudes play well below that, to the advantage of the house.
- - Norma