# Zero-Collateral Lotteries in Bitcoin and Ethereum

arXiv: https://arxiv.org/abs/1612.05390 · HTML: https://mlsanity.com/paper/1612.05390/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Dec 2016.

## Built on by (most cited first, 1 of 1)

- [LLMs as verification oracles for Solidity](https://mlsanity.com/paper/2509.19153/) (2025)

## Abstract (arXiv)

We present cryptocurrency-based lottery protocols that do not require any collateral from the players. Previous protocols for this task required a security deposit that is O(N2) times larger than the bet amount, where N is the number of players. Our protocols are based on a tournament bracket construction, and require only O(log N) rounds. Our lottery protocols thus represent a significant improvement, both because they allow players with little money to participate, and because of the time value of money. The Ethereum-based implementation of our lottery is highly efficient. The Bitcoin implementation requires an O(2N) off-chain setup phase, which demonstrates that the expressive power of the scripting language can have important implications. We also describe a minimal modification to the Bitcoin protocol that would eliminate the exponential blowup.