Hindman's theorem (HT) asserts that for every coloring of N by finitely many colors, there is an infinite set H⊆N such that the color of any non-empty finite sum of elements of H is the same. The reverse mathematical and computability-theoretic content of this principle has been the focus of much research. Recently, attention has turned to variants of HT where instead of arbitrary non-empty finite sums in the set H, one looks only for finite sums of length at most k, or equal to k, for some k≥1. I will discuss several recent investigations of these restrictions, and the somewhat surprising introduction to these investigations of probabilistic methods, specifically the Lov\'{a}sz local lemma. Among some other results, I will talk about joint work with Csima, Hirschfeldt, Solomon, and Westrick which uses this lemma to show that HT for sums of length exactly 2 is not computably true, and in fact, implies the rainbow Ramsey's theorem for pairs over RCA0.