I suppose anything goes for apps and offshore gambling nowadays, but all these other answers are incomplete, at least for Nevada Gaming Control Board licensed machines, which I believe the question is originally about.
The technical specifications for RNGs licensed in Nevada for gaming purposes are laid out in Regulation 14.040(2).
As of May 24, 2012, here is a summary of the rules a RNG must follow:
- Static seeds cannot be used. You have to seed the RNG using a millisecond time source or other true entropy source which has no external readout anywhere on the machine. (This helps to reduce the incidence of "magic number" attacks)
- The RNG must continue generating numbers in its sequence at least 100 times per second when the game is not being played. (This helps to avoid timing attacks)
- RNG outputs cannot be reused; they must be used exactly once if at all and then thrown away.
- Multi-system cabinets must use a separate RNG and separate seed for each game.
- Games that use RNGs for helping to choose numbers on behalf of the player (such as Lotto Quick Pick) must use a separate RNG for that process.
- Games must not roll RNGs until they are actually needed in a game. (i.e. you need to wait until the player chooses to deal or spin before generating RNGs)
- The RNG must pass a 95% confidence chi-squared test based on 10,000 trials as apart of a system test. It must display a warning if this test fails, and it must disable play if it fails twice in a row.
- It must remember, and be able to report on, the last 10 test results as described in 7.
- Every possible game outcome must be generatable by the RNG. As a pessimal example, linear congruential generators don't actually generate every possible output in their range, so they're not very useful for gaming.
Additionally, your machine design has to be submitted to the gaming commission and it has to be approved, which is expensive and takes lots of time. There are a few third-party companies that specialize in auditing your new RNG to make sure it's random. Gaming Laboratories publishes an even stricter set of standards than Nevada does. They go into much greater detail about the limitations of hardware RNGs, and Nevada in particular likes to see core RNGs that it's previously approved. This can all get very expensive, which is why many developers prefer to license an existing previously-approved RNG for new game projects.
Here is a fun list of random number generator attacks to keep you up late at night.
For super-nerds only: the source for most USB hardware RNGs is typically an avalanche diode. However, the thermal noise produced by this type of diode is not quantum-random, and it is possible to influence the randomness of an avalanche diode by significantly lowering the temperature.
As a final note, someone above recommended just using a Mersenne Twister for random number generation. This is a Bad Idea unless you are taking additional entropy from some other source. The plain vanilla Mersenne Twister is highly inappropriate for gaming and cryptographic applications, as described by its creator.
