This method involves issuing subsequent transactions where each new transaction (denoted as (s_{i+1})) covers more recipients than the previous one ((s_i)), despite the fact that earlier transactions might appear to be more cost-effective due to the lack of increment in the minimum relay fee. The primary advantage highlighted is the potential for cost savings, even when a batcher has to reissue a transaction. This could happen if someone else pays for the inclusion of an earlier state, thereby reducing the overall expense for the batcher.

A specific scenario is used to illustrate a situation where the rolling batch technique may not seem advantageous but actually is. In this example, the first version of a batch transaction pays an individual named Bob 1BTC, and a subsequent version increases the payment to 2BTC. The initial assumption might be that executing these payments through two separate transactions would be more cost-effective. However, the email points out that having the second batch version mined, with just a single payout of 2BTC, is cheaper than processing two separate transactions. This effectively challenges the common misunderstanding regarding the inefficiency of later versions of batch transactions over their predecessors, underlining the necessity of a deeper understanding of Bitcoin's operational mechanics.

The narrative essentially debunks a misconception about the Bitcoin network's operation, specifically within the context of transaction batching and fee optimization. It emphasizes that the dissatisfaction with transitioning from an initial transaction state ((s_0)) to a subsequent one ((s_1)) stems from incorrect assumptions about Bitcoin's functionality. Through the given example, it clarifies how strategic use of batch transactions can lead to significant savings and efficiency improvements, contrary to the belief that earlier transactions are inherently better because of lower fees.