An important research problem in designing an open virtual world is how to enable virtual currency exchange between multiple virtual worlds and guarantee the exchange fairness when multiple virtual currencies are adopted as virtual payment instruments in virtual trades between virtual worlds. While an existing VMX theory solved the fairness problem in a VERA algorithm based on a Pareto exchange point, a new expectation problem has been found such that exchange requesters might submit minimum acceptable rates (MAR) to determine whether to accept VMX systems-generated virtual currency exchange rates. When exchange requesters think the systems-generated rates are lower than MAR, they select not to accept the systems-generated rates. The withdrawal of systems-generated rates creates the expectation problem such that the fairness has been lost due to Pareto exchange point no longer exists. To solve the expectation problem, this thesis has developed a new VERA-RS algorithm by extending the existing VERA algorithm based on a newly developed formal expectancy model and a novel m-stage and n-phase three-level computing framework. VERA-RS algorithm has solved expectation problem by achieving a set of satisfied virtual money exchange rates (SERs). Experiments that simulate to find a set of satisfied virtual money exchange rates are done in a specially-designed and implemented simulator. This simulator applies both an existing VERA algorithm and the newly-developed VERA-RS algorithm. The simulation results show that VERA-RS has solved the exchange requestor's expectation problem and provided less fluctuation in exchange rate generation than the existing VERA algorithm.