Babilonia - probabilistic coinjoin and covert betting

The recent update to version 1.1 of the paper has successfully addressed issues with protocol message ordering, paving the way for further discussions on proposed frameworks. Specifically, there are two potential approaches outlined for game or bet executions related to offchain settlements. The first approach involves a straightforward two-party setup where multiple game or bet executions can occur offchain before settlement. The second, more complex approach allows for the extension of the game across multiple channels, which significantly raises the ambition level due to the necessity of Point Time Locked Contracts (PTLCs).

Adding mechanisms such as Poon-Dryja style penalties and persistent states introduces considerable complexity but also opens up practical benefits. For instance, players seeking fair odds without relying on a dealer, and who wish to engage repeatedly while minimizing costs through amortization, would find this setup advantageous. This is despite the complexities surrounding timeout management.

The discussion also touches on broader implications for the Lightning Network (LN), particularly in relation to probabilistic payments. Insights from comments suggest that using $t^2$ type Zero-Knowledge Proofs (ZKPs), which are based on $\Sigma-$ protocols, could lead to high performance in implementation. However, this might not be feasible for extremely small win-probabilities ($p$). The overall utility of these innovations seems most promising in scenarios involving private coinswaps with no amount correlation, or payments between channel counterparts in the LN, including off-onchain swaps.

While initial thoughts on emulating OP_RAND for minuscule probabilistic payments were considered, the underpinning technology appears to be taproot-specific. The concept of combining coinjoin with betting—termed "joinbet"—is intriguing, though the conversation leans towards exploring variants of private coinswaps and related payment structures within the LN as potentially more valuable areas of development. This pursuit might necessitate further advancements like GTT 26 to effectively manage the challenges associated with tiny probability values.