 Bets 1 and 2 together amount to a conditional bet on \(A\), which is called off if \(E\) is false. In the event that \(E\) is true, this bet is bought back at the lower price of \(\pr_{2}(A)\). Bet 3 spreads the expected winnings of that exchange in order to assure a profit in the case that \(E\) is false. Thus, if \(E\) is true the agent suffers a net loss of [ \(\pr_{1}(A\mid E) - \pr_{2}(A)\)] \(\pr_{1}(E)\). If \(\pr_{2}(A) \gt \pr_{1}(A\mid E)\), then the strategy involves reversing the direction of the above bets. Where dollars are taken as measures of utility, each bet is fair given the agent’s beliefs at the time offered.  There is also a converse Dutch Book theorem that shows that adhering to conditionalization avoids Dutch Book vulnerability Skyrms (1987b).