Suppose that an investor has had a bet on a yet-to-be-contested event, and that the utility can now be improved; such that his confronting task is to bet on the complement of the earlier-backed outcome; to such an extent so as to maximize utility. Let the potential profit, ( as a proportion of capital, ) from the early bet, be symbolized " E ". Let the updated success probability of the late bet, be symbolized " P ". Let the available decimal dividend about the late bet, be symbolized " D ". Let the proportion of capital on the early bet, be symbolized " xi ". Let the proportion of capital to go on the late bet be symbolized " xii " ( - using the same capital figure as for xi & E. ) xii = P*( E + 1 ) - ( 1 - P )*( 1 - xi )/( D - 1 ). If xi + xii > 1, and credit is unavailable, set xii = 1 - xi.