As I noted in my previous post, in order to compare these two bets (which BTW I did assume were being made by different players, though I did not make that clear, and may even have implied otherwise :-S ) the P6 bet must be split into two parts, the initial $10 and the $30 added after a point, if any, is established, and these two components compared to their PL/FO counterparts: the initial $10 and the $30 odds added after a point, if any, is established. Furthermore, if 6 becomes the point (i.e. P6 wins on the comeout) then the initial $10 P6 bet is removed (because it has been resolved) and replaced only by the $30 that would have been added to it had some other number become the point, thereby keeping the total amounts at risk equal to $40 when a point is established. Comparing the initial $10 bets: HA(PL) = 1.41% HA(P6) = 1.52% Advantage PL. Comparing the $30 added: HA(FO) = 0.00% HA(P6) = 1.52% Advantage FO. QED And as I have shown, when the (equal) amounts at risk are compared to each other during the time each is at risk the PL/FO combination carries a lower HA than P6. Agreed. The typical P6 player would take the default of off on the comeout and would therefore not win if the point became 6, and if overriding that default would leave the initial $10 up to win again. Agreed again, which is why a true comparison must have the P6 player taking down the initial $10 when that happens so as not to have more action than the PL/FO player. And vice-versa. As I said before, if a betting strategy can win then a series of results can be composed to show that it does win.