Kolmogorov-Chaitin complexity has long been believed to be impossible to approximate when it comes to short sequences (e.g. of length 5-50). However, with the newly developed coding theorem method the complexity of strings of length 2-11 can now be numerically estimated. We present the theoretical basis of algorithmic complexity for short strings (ACSS) and describe an R-package providing functions based on ACSS that will cover psychologists' needs and improve upon previous methods in three ways: (1) ACSS is now available not only for binary strings, but for strings based on up to 9 different symbols, (2) ACSS no longer requires time-consuming computing, and (3) a new approach based on ACSS gives access to an estimation of the complexity of strings of any length. Finally, three illustrative examples show how these tools can be applied to psychology. Keywords Algorithmic complexity · Randomness · Subjective probability · Coding theorem method Randomness and complexity are two concepts which are intimately related and are both central to numerous recent developments in various fields, including finance (Taufemback et al., 2011, Brandouy et al., 2012, linguistics (Gruber, 2010;Naranan, 2011), neuropsychology (Machado et al., 2010;Fernández et al., 2011Fernández et al., , 2012, psychiatry (Yang and Tsai, 2012;Takahashi 2013), genetics (Yagil, 2009;Ryabko et al. 2013), sociology (Elzinga, 2010 and the behavioral sciences (Watanabe et al., 2003;Scafetta et al., 2009). In psychology, randomness and complexity have recently attracted interest, following the realization that they could shed light on a diversity of previously undeciphered behaviors and mental processes. It has been found, for instance, that the subjective difficulty of a concept is directly related to its "boolean complexity", defined as the shortest logical description of a concept (Feldman, 2000(Feldman, , 2003(Feldman, , 2006. In the same vein, visual detection of shapes has been shown to be related to contour complexity (Wilder et al., 2011).More generally, perceptual organization itself has been described as based on simplicity or, equivalently, likelihood (Chater, 1996;Chater and Vitányi, 2003), in a model reconciling the complexity approach (perception is organized to minimize complexity) and a probability approach (perception is organized to maximize likelihood), very much in line with our view in this paper. Even the perception of similarity may be viewed through the lens of (conditional) complexity (Hahn et al., 2003).Randomness and complexity also play an important role in modern approaches to selecting the "best" among a set of candidate models (i.e., model selection; e.g., Myung et Behav Res (2016) 48:314-329 315 al., 2006Kellen et al., 2013), as discussed in more detail below in the section called "Relationship to complexity based model selection".Complexity can also shed light on short term memory storage and recall, more specifically, on the process underlying chunking. It is well known that the short term memory span lies b...