A betting method determines rate of return on a bet by employing supply and demand forces. The bet can be made on any uncertain future event that has at least two outcomes (e.g. sporting events, financial market fluctuations, and elections). Investors that place a bet on a particular outcome provide money to a betting machine and receive shares (specific to the chosen outcome) in return. For each possible outcome there is a share type. Shares that correspond with the winning bet have a certain guaranteed value when the outcome is determined; losing share types are normally defined as worthless. Before the winning bet is determined, share values are calculated following a supply and demand model according to the following equation: ##EQU00001## where Q.sub.1 is the share value for shares corresponding to a first outcome, B.sub.1 is the amount bet upon the first outcome, and B.sub.Tot is the total amount bet on all outcomes. Analogous equations determine share values for all other outcomes. In the present method, share value calculations can be reiterated so that new bets can be placed, and shares can be redeemed for money before the event occurs. In subsequent iterations, the machine exchanges shares for money from new investors and exchanges money for shares redeemed by investors from a previous iteration. The machine calculates revised share values for each outcome based on the amounts of money and shares exchanged. The calculation of the new share values generally involves the solution of a polynomial of order n+1, where n is the number of different outcomes.