We study the decision theory of a maximally risk averse investor - one whose objective, in the
face of stochastic uncertainties, is to minimize the probability of ever going broke. With a view to
developing the mathematical basics of such theory, we start with a very simple model and obtain the
following results: a characterization of best play by investors; an explanation of why poor and rich
players may have different best strategies; an explanation of why expectation-maximization is not necessarily
the best strategy even for rich players. For computation of optimal play, we show how to apply the Value Iteration
method, and prove a bound on its convergence rate.