I don't know what to make of this. When you look up the help for optimized count, ppt tells you this is the probability after removing dead cards. IN OMAHA, when I run kj on a board of KsJh7d I get a count of 8916 or 3.29%.

I have two problems with this:
1. Dividing 8916 by .0329, you get 271003.xxx. This is a rounding error for the number 270725 or 52C4. The problem is that this is not taking into consideration dead cards. It should be doing 8916/211876, or 49C4. Of course, this gives us a significantly bigger %, and it does meet the definition of optimized count given by ppt

2. I go to double check the math with combinations and I get 9729, not 8916, and I don't see what the error is. First, I choose the K and J (3c1*3c1=9), then since I don't care about choosing extra Kings or Jacks, I choose the last 2 cards as 47C2. ((47*46)/2)*9=9729.

Any combinatorics folks who can straighten this quarrel out?

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.

Thanks for clearing up my error. That makes perfect sense for issue #1. Now, #2 is really a steaming pile and I should contact ppt to fix that. You can say "its only 1% error", but this compounds as you put this into a range as well as add other 2 card combos to a range.

of course an explanation can only come from propokertools, so in no way should my post discourage you from making contact.

propokertools is more than the 'simulation' page, it is also PQL which allows you to write queries for simulation, below is the query that arrives at the answer you wish they'd give as the optimized count.

select
count(inrange(p1,'kj'))
from game='omahahi',
board='ksjh7d',
p1='*'

Results:
Trials COUNT 1
600000 25074 (4.18%)

Maybe I am misunderstanding what you are saying, but I don't think anyone wants to "simulate" counts.

Counts are counts. If you have a button for counts it should give you the correct counts.

And then if you supplement the counts with percents, it is not asking too much to get those correct as well.

In short, nobody should have to simulate frequencies (not equities but frequencies).