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The underlying concept of provable fairness is that players have the ability to prove and verify that their results are fair and unmanipulated. This is achieved through the use of a commitment scheme , along with cryptographic hashing.
The commitment scheme is used to ensure that the player has an influence on all results generated. Cryptographic hashing is used to ensure that the casino also remains honest to this commitment scheme. Both concepts combined creates a trust-less environment when gambling online.
This is simplified in the following representation:
fair result = operators input (hashed) + players input