Using frequency distributions of daily closing price time series of several financial market indexes, we investigate whether the bias away from an equiprobable sequence distribution found in the data, predicted by algorithmic information theory, may account for some of the deviation of financial markets from log-normal, and if so for how much of said deviation and over what sequence lengths. We do so by comparing the distributions of binary sequences from actual time series of financial markets and series built up from purely algorithmic means. Our discussion is a starting point for a further investigation of the market as a rule-based system with an algorithmic component, despite its apparent randomness, and the use of the theory of algorithmic probability with new tools that can be applied to the study of the market price phenomenon. The main discussion is cast in terms of as- sumptions common to areas of economics in agreement with an algorithmic view of the market.