In the specific example you gave above, here is how I would derive what I would consider the correct count of possible Omaha starting hands that contained at least one king and at least one jack, given that Ks, Jh, and 7d are dead (not possible to appear in my hand).
Count(1K,1J) = C(3,1)*C(3,1)*C(43,2) = 8,127
Count(2K,1J) = C(3,2)*C(3,1)*C(43,1) = 387
Count(3K,1J) = C(3,3)*C(3,1)*C(43,0) = 3
Count(1K,2J) = C(3,1)*C(3,2)*C(43,1) = 387
Count(1K,3J) = C(3,1)*C(3,3)*C(43,0) = 3
Count(2K,2J) = C(3,2)*C(3,2)*C(43,0) = 9
TOTAL = 8,916
If there are no dead cards, then you have:
Count(1K,1J) = C(4,1)*C(4,1)*C(44,2) = 15,136
Count(2K,1J) = C(4,2)*C(4,1)*C(44,1) = 1,056
Count(3K,1J) = C(4,3)*C(4,1)*C(44,0) = 16
Count(1K,2J) = C(4,1)*C(4,2)*C(44,1) = 1,056
Count(1K,3J) = C(4,1)*C(4,3)*C(44,0) = 16
Count(2K,2J) = C(4,2)*C(4,2)*C(44,0) = 36
TOTAL = 17,316
It seems that both percentages that are displayed in the PPT output table are in relation to the total number of Omaha starting hands = C(52,4) = 270,725.
That may or may not be the "correct" thing to show in the case of dead cards. An argument could be made that the "correct" denominator in the first calculation (accounting for dead cards) should be C(49,4) = 211,876 which would make the relative percentage 8,916/211,876 = 4.21% rather than the 3.29% that is displayed.
For confirmation/clarity on these issues, I suggest contacting ProPokerTools directly.
Last edited by whosnext; 05-21-2018 at 08:44 PM.