delvingbitcoin

## Estimating Likelihood for Lightning Payments to be (in)feasible

### Posted on: June 26, 2024 14:33 UTC

The correspondence highlights a critical analysis of an innovative approach developed by Rene Pickhardt, specifically addressing the method's comparison between the minimum cost flow probability and the probability of payment feasibility across different models.

The critique emphasizes that these models operate within distinct probability spaces, making direct comparison somewhat misleading. In essence, the minimum cost flow model evaluates the likelihood of successful transactions based on the optimal distribution of channel balances, whereas the feasibility model considers the uniform probability of any suitable wealth distribution allowing for successful payments.

A specific example is used to illustrate this point: assessing the probability that a node in a network can simultaneously pay one coin to two other nodes under both models. According to the feasibility model, the arrangement is possible with a 3/8 probability, given three specific wealth distributions among the nodes. However, when analyzing the same scenario under the minimum cost flow model, the success probability increases to 5/12, as this model accounts for the most efficient transaction paths, which may include multiple considerations of a single state, thus artificially inflating the probability.

This detailed examination reveals a foundational discrepancy between the two models' underlying assumptions and calculations. It suggests that while both approaches aim to gauge the potential for successful transactions within a network, their methodologies and resulting probabilities should not be directly compared without acknowledging the distinct frameworks and probability spaces they each utilize. The critique serves to refine our understanding of these models, urging a more nuanced consideration of their respective merits and limitations in predicting network payment success rates.