We discuss a set of purely sequential strategies to estimate an unknown negative binomial mean $\mu$ under different forms of loss functions. We develop point estimation techniques where the thatch parameter $\tau$ may be known or unknown. Both asymptotic first-order efficiency and risk efficiency properties will be elaborated. The results will be supported by an extensive set of data analysis carried out via computer simulations for a wide variety of sample sizes. We observe that all of our purely sequential estimation strategies perform remarkably well under different situations. We also illustrate the implementation of these methodologies using real datasets from ecology, namely, weed count data and data on migrating woodlarks. (This is a Skype talk.)