Simple genetic algorithms on populations of l-binary words usually become iterative systems on 2l dimensional spaces when populations have size infinite. However, in a particular model (BCCG model) previously introduced, it has been shown that the iterative system works in a l-dimensional space. In this paper we propose a simplification of the BCCG model and we analyze it in the case of large but finite-size populations. In particular: We exhibit a Markov chain with states in ℝl that approximates the system behavior. We estimate the steady state distribution of the Markov chain.