In the Mr X sample, the people passing by is random, the sequence of the prizes obviously isnt. Now luckily multiplying a random with a non-random gives a random .. so answer . .still random from the people's point of view as long as they are unaware of the rules and cant count the nr of people that went before them (unpredictability).
In the Mr DCM sample, the sequence of the machine would not be random, and if he doesnt know which player is gonna hit it, then it'll still go to a 'random' player. However. Looking at just the machine, its not random, and thus not fair.
Keep in mind that something can be totally random if you miss bits of information, and get to be totally predetermined if you have the information. This is actually the case with a computer based RNG, if you have the algorithm, the seed, the internal state, it's predictable. But since good RNG's use stuff like the nr of interrupts, the number of cache misses, network bytes etc, it gets to be impossible to tell the internal state of the RNG. This is why it is called a pseudo random.
The existance of 'random' in the real physical universe is a big question. (one of the _Big_ ones). There's a general agreement on the fact that most randoms out there are pseudo-randoms (random because of too complex to predict). This actually boils down to a classic sample in filosophy, where in order to 'predict' the next state of everything in the universe, you need a computer that actually stores all the information on all the elementary elements, this computer would be so big however that it requires ALL the elementary elements in the universe to build it. In other words its impossible .. that doesnt mean it is factual random, it may still be that everything happens for a logical cause .. just impossible to predict because of the complexity.
Luckily, for gaming purposes, all you need is unpredictability..
