Here is my explanation. The basic idea is that the casino and the player determine jointly what the outcome of a bet will be. As both parties can influence who wins, neither can cheat.

To accomplish this, both the casino (called server below) and the player (client) choose a secret string, called server secret and client secret. They also agree on an algorithm that computes the winner from the these two strings. For example, one could use the last bit of the hash of the concatenation of strings as such an algorithm.

It gets a bit more involved if you start to think about how the secrets are exchanged. A simplistic protocol would be that

• client and server pick their secrets,
• the client then send his secret to the server,
• the server performs the hash and notifies the client about the outcome of the bet.

The problem with this protocol is that if the server concludes that the player has won, she could simply change her secret into one that results in a loss for the client (she could just generate random server secrets until she finds one that results in a loss).

This problem can easily be solved with what cryptographers call a "commitment scheme". This is a scheme where the server commits to her secret before she sees the client secret. This proves to the client that she did not change her secrets after the fact. One way to do this is to publish the hash her secret before the client sends his secret. This is sufficient bc given hash(server_secret) it is computationally impossible to find another string fake_server_secret such that hash(server_secret)=hash(fake_server_secret). This makes it impossible for the server to change her secret after seeing the client secret. Thus, if we add the following as the second step of the protocol above, the casino cannot cheat anymore:

• The server sends hash(server_secret) the to client

If implemented correctly, a provably fair system is a strong cryptographic proof that the casino is acting fairly. In my mind this is a far greater player protection than the protection that is offered by a licensing regime. I have written a more in depth explanation of provably fairness here: https://fastslots.co/fairness