THE QUANTUM INTELLIGENCER

Emulating Randomness in Bitcoin: A Trustless Game-Theoretic Approach to OP_RAND In Plain English: Bitcoin doesn’t have a built-in way to generate fair randomness, which makes it hard to run games or lotteries where no one can cheat. This paper proposes a clever game between two people that creates a random result without either side being able to rig it. The game works in a way that looks like regular Bitcoin activity, so outsiders can’t even tell it’s happening, and it doesn’t require changing Bitcoin itself. This means people could build fair gambling systems or other apps on Bitcoin without needing new software or trusting third parties. It’s a smart workaround that makes Bitcoin more useful for everyday applications. Summary: This paper introduces a method to emulate the functionality of a hypothetical OP_RAND opcode in Bitcoin’s scripting system, which currently lacks native support for randomness. The authors propose a trustless, interactive protocol modeled as a probabilistic game between transaction counterparties, where outcomes are determined in a way that prevents either party from increasing their chance of winning through deception. The protocol relies on cryptographic commitments and interactive verification steps, ensuring fairness without requiring changes to the Bitcoin protocol or the introduction of trusted third parties. It can be implemented using existing Bitcoin script capabilities and potentially disguised to appear as ordinary transactions, enhancing privacy and censorship resistance. The “Thimbles Game” is presented as a concrete example—a shell game where one party hides an item and the other guesses its location—demonstrating how such protocols can simulate randomness through game mechanics. The authors suggest this approach opens new possibilities for decentralized applications on Bitcoin that require verifiable randomness, such as gambling, lotteries, or fair dispute resolution, all while maintaining Bitcoin’s core principles of decentralization and security. Key Points: - Bitcoin currently lacks a native opcode for generating verifiable randomness (OP_RAND). - The paper proposes a trustless, interactive protocol between transaction parties to emulate such functionality. - The protocol is probabilistic and designed so that no participant can cheat or bias the outcome. - It requires no changes to Bitcoin’s consensus rules or script system. - The protocol can be hidden within standard-looking transactions, making it indistinguishable to outside observers. - The “Thimbles Game” is used as a demonstrative example of how the protocol works. - Applications include decentralized gambling, lotteries, and fair decision-making mechanisms on Bitcoin. Notable Quotes: - "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." Data Points: - No specific numerical data, metrics, or experimental results are provided in the abstract. - The paper references a conceptual demonstration via the “Thimbles Game,” but no implementation details, success rates, or performance benchmarks are given. - The work is presented as theoretical and proposal-based, with no cited dates for implementation or testing. Controversial Claims: - The assertion that the protocol is entirely cheat-proof and that no party can increase their winning probability on any step may be speculative without formal security proofs or adversarial modeling. - The claim that the protocol can be made completely unrecognizable to external observers raises questions about potential detectability through transaction graph analysis or timing patterns, especially at scale. - The feasibility of implementing complex interactive games on Bitcoin without incurring high fees or usability barriers may be overstated, given Bitcoin’s limited interactivity compared to more programmable blockchains. Technical Terms: - OP_RAND (hypothetical Bitcoin opcode for randomness) - Trustless protocol - Interactive game - Cryptographic commitment - Bitcoin Script - Probabilistic outcome - Transaction counterparty - Taproot (implied context for advanced scripting) - Commit-reveal scheme (inferred) - Game-theoretic fairness —Ada H. Pemberley Dispatch from The Prepared E0