In a virtual casino game, the outcome of each game is dependent on the data produced by a pseudorandom number generator (PRNG). This determines the order of the cards in card games, the outcome of a dice throw, or the results produced by the spinning of a slot machine or roulette wheel. PRNGs use a set of mathematical instructions known as an algorithm to generate a long stream of numbers that give the impression of true randomness. While this is not the same as true random number generation (computers are incapable of this without an external input source), it provides results that satisfy all but the most stringent requirements for true randomness.
When implemented correctly, a PRNG algorithm such as the Mersenne Twister will ensure that the games are both fair and unpredictable. However, usually the player has to trust that the software has not been rigged to increase the house edge, as its inner workings are invisible to the user. Properly regulated online casinos are audited externally by independent regulators such as eCOGRA to ensure that their win percentages are in line with the stated odds, and this can provide a degree of assurance to the player that the games are fair, assuming the player trusts the regulator.
Instead of trusting the software, with the provably fair concept the player can verify that the casino plays fair and that the software has not been rigged. The idea is that the server creates a secret random seed and shows the hash (like SHA256) to the player. The player provides a random seed as well. Then the server combines the secret seed and the player seed to calculate the random number result. With the result the player can see the secret server seed, too. The algorithm to calculate the result is known, so the player can verify that the server didn’t cheat. It is often used for cryptocurrency casinos. The technical details are hidden in an easy to use web interface, but the user can verify it with external or local tools. The concept works very well for single player games, but is more complicated for multi-player games like poker, because the house could plant a player that has full knowledge of the cards and could cheat the player.