If the first roll in a game of craps is neither a natural nor craps, the player can make an additional bet, equal to his original one, that he will make his point before a seven turns up. If his point is four or ten he is paid off at 2 : 1 odds; if it is a five or nine he is paid off at odds 3 : 2; and if it is a six or eight he is paid off at odds 6 : 5. Find the player's expected winnings if he makes this additional bet when he has the opportunity.