[Vex]

Where do you draw the line? You could in theory create a precise computer simulation of a bingo cage that could predict the results from that cage. If the simulation is accurate enough, this would work, because the physics of the balls tumbling around inside is a solvable math problem. Therefore, you could say that the outcome of the Bingo game is not subject to chance but is rather a function of the starting positions and orientations of all the balls in it, the amount of rotation given to the cage before drawing the ball, and whatever other variables you can quantify.

In the computer world, you can do two things to generate chance: you can use pseudorandom number generation, or you can use a hardware random number generator. Pseudorandom numbers use large other numbers as seeds to produce output that is the result of a fixed function. For example, a hand number might be used as a seed to generate a random sequence for a deck of cards. Good pseudorandom number generators can produce all possible card sequences with equal probability of each out of any arbitrary selection of seed values, and can also be so tough to reverse-engineer that it would take a supercomputer hundreds of years to discover the cipher that translates seed to output.

At least some online sites use hardware random number generators, which sample quantum noise in order to create true randomness. Basically, they measure something that fluctuates in an impossible-to-predict way, like temperature or vibrations, using lots and lots of precistion. Then, you discard the most significant digits and keep the least significant ones -- the ones that vary the most wildly and unpredictably. The output from that then becomes a perfectly arbitrary seed for a pseudorandom number generator, and nobody has any way to know the seed used for any event unless they have a direct tap into the hardware random number generator.

A hardware random number generator is in fact more truly random than a bingo cage, because the hardware device is influenced strongly by quantum fluctuations. Even if quantum effects are not truly random, it is generally believed that we'd never be able to gain enough knowledge about a quantum system to model it accurately -- so it's as random as the universe-as-we-know-it can be!