For additive smoothing, simply add a small amount to all counts. Adding one is called **add-1 smoothing**. Remember to rescale the denominator in probability estimates to ensure the distributions still sum to 1. This can have a very large impact especially on the most frequent observations. For this reason, typically add-1 smoothing is not used unless the skew is unusually low. The inspiration for add-1 smoothing arose from biology, where rare species have low detection probabilities. (What is the probability of encountering a rare fish having encountered a number of co-occurring species but not the rare fish?)