Since all splits must be successful for the original payment to be successful, the higher the number of payments into which an original payment is split, the lower the probability of success. This is because the success probability of the original payment is determined by multiplying the success probabilities of each “child” payment. This creates a kind of paradox, because theoretically, the lower the payment, the higher the chances of success. Therefore, an optimization challenge arises in finding the correct pitch.

Pickhardt Payments attempts to increase the probability of success of the original payment by seeking this optimization, which is achieved by reducing the cost of uncertainty. To achieve this, it uses Operations Research (OR).

More specifically, Pickhardt Payments uses Minimum Cost Flows, a well-studied OR tool, to model and execute the optimal multi-part Lightning paymentâ€”improving the decision-making process for splitting and delivering payments on Lightning. In short, the premise is that uncertainty about each channel’s liquidity information comes with an inherent cost.

Uncertainty cost, not to be confused with fee cost, can be thought of as the opportunity cost of trying a particular path. In theory, the higher the uncertainty cost, the higher the opportunity cost, since the payment is less likely to be successful. By quantifying this uncertainty, Pickhardt Payments can minimize opportunity costs and choose the path that maximizes the chances of success.

Finally these tweaks enable Pickhardt payments to Send large Lightning payments that were previously not possible on the internet.

Pickhardt’s design differs from current practices at Lightning because split payments are typically prioritized based on fees, just like single payments. On the other hand, Pickhardt Payments prioritizes lowering the cost of uncertainty as it seeks to increase the probability of payment delivery, which means fees can often get relatively high compared to fees typically paid at Lightning.

However, Pickhardt told Bitcoin Magazine that his algorithm could also provide an opportunity to optimize fees, although he argues that given the existence of Lightning’s base fee, this is currently computationally intensive. In this case, the challenge would be finding an optimal balance between the two options – which he calls “features” – while letting users grapple with what they ultimately want to prioritize.

How to use Pickhardt payments today
Pickhardt Payments can now be used via LND manageJ by Carsten Otto. Alternatively, Pickhardt is developing a library that currently enables simulation and production testing. Pickhardt told Bitcoin Magazine that he will eventually ship the library with bindings for implementations, but that’s not as high a priority as technical correctness, security, and runtime right now. While there isn’t yet an easy way for a regular user to use Pickhardt Payments, availability should increase as the developers continue to work on the algorithm and library to boast of its robustness and security.

Thanks to Rene Pickhardt for information and feedback.

Further details on Pickhardt Payments can be found under the relevant research paper and mailing list post . Additional resources are also available at Pickhardt’s website .