Provably Fair Algorithms

When a new game of Russian Roulette begins, the location of the bullet in the revolver's chamber is randomly determined. Each time a player pulls the trigger, the system checks if the bullet is in the next chamber to be fired.

To ensure fairness, the number determining the bullet's position must be publicly known at the start of the game. However, simply publishing this number would give away the bullet's location, rendering the game meaningless.

The solution is to encrypt the random number and publish it at the start of the game. Then, the decryption key is revealed at the end. This way, the randomness of the bullet's position can be verified, but the players don't know its exact location until the game is over.

The challenge lies in proving that the initial random number was not manipulated by the system operator to influence the outcome. This can be addressed by using a verifiable random function (VRF) to generate the random number cryptographically securely. By publishing the VRF proof alongside the decryption key, players can verify that the number was truly random and not subject to tampering.

This approach balances the need for randomness, verifiability, and game integrity. The initial encrypted number ensures the bullet's location is unknown, while the final VRF proof demonstrates the number's fairness without revealing sensitive information during gameplay.