Emulating OP_RAND in Bitcoin

This paper proposes a method of emulation of \verb|OP_RAND| opcode on Bitcoin through a trustless interactive game between transaction counterparties. The game result is probabilistic and doesn’t allow any party to cheat, increasing their chance of winning on any protocol step. The protocol can be organized in a way unrecognizable to any external party and doesn’t require some specific scripts or Bitcoin protocol updates. We will show how the protocol works on the simple $\mathbf{\text{Thimbles}}\mathbf{\text{Game}}$ and provide some initial thoughts about approaches and applications that can use the mentioned approach.