open-ended str8 draws

In working with the probability theory vs the standard theory, the differences are there, but the greatest difference is between flush draws and open ended straight draws. Now I don't know about you, but I have never been comfortable with open ended str8 draws even though using the standard theory they are not that much apart from the flush draw...1.86/1 vs 2.17/1 at the flop and 4.11/1 vs 4.75/1 at the turn....with the probability theory I come up with a 1.26/1 vs 2.47/1 at the flop and 2.88/1 vs 5.29 at the turn and to me it stands to reason.

With the flush there are 13 suited cards making it one out of 4 cards dealt will be of the same suit...with the open ended there are only 8 cards that can help, making it one out of 6.5 cards dealt will be one of the cards that can help...since we are dealing to 9 players 18 cards and 3 cards to the flop, means that we have dealt 5.25 suited cards for the flush draw and 3.2 cards for the open-ended draw on the average. Now with the standard theory, since you did not receive nor did the flop lay down any of the open-ended cards it is assumed that they are still in the remainder of the deck...in the probability theory it does not assume that just because you nor the flop were dealt any, that none of the 16 cards dealt to the other 8 players did not receive any...in fact a 3.2 card average means that you nor the flop got any, but between the other 8 players and 16 cards they still got the 3.2 cards....so now there is a big difference in outs...8 vs 4.77 between the 2 theory's.

Filling an open-ended str8 is the same as hitting one of two unpaired pocket cards that did not flop, in both cases you are looking for one of the 8 cards…it is just that in the case of the unpaired pocket cards, you received 2 of the 3.2 dealt and in the case of the open-ended the 3.2 cards were in the 16 cards dealt to the remaining 8 players.