Omaha Preflop Range With ProPokerTools

It has been about three weeks that the new ProPokerTools syntax is out, and it enables users to define much more precise ranges, thanks to the intersection and grouping operators. The textfields have also been fixed, now allowing ranges of much greater length.

Another nice new feature is the count form (available in the beta site), showing how many hands a given range actually represents. This is a very useful tool when working with combinatorics, as we briefly did in this blog.

Let’s use it to check the numbers we calculated in the Breakdown of an Omaha Preflop Range article.

Rundowns

Gapless rundowns are: A234,2345,3456,4567,5678,6789,789T,89TJ,9TJQ,TJQK,JQKA

PropPokerTools results:

Fortunately, our numbers look right so far!

The other rundowns are (1-gap, double 1-gap and 2-gap, respectively):

A345,2456,3567,4678,5789,689T,79TJ,8TJQ,9JQK,TQKA
A245,2356,3467,4578,5689,679T,78TJ,89JQ,9TQK,TJKA
A235,2346,3457,4568,5679,678T,789J,89TQ,9TJK,TJQA

A356,2467,3578,4689,579T,68TJ,79JQ,8TQK,9JKA
A346,2457,3568,4679,578T,689J,79TQ,8TJK,9JQA
A246,2357,3468,4579,568T,679J,78TQ,89JK,9TQA

A456,2567,3678,4789,589T,69TJ,7TJQ,8JQK,9QKA
A256,2367,3478,4589,569T,67TJ,78JQ,89QK,9TKA
A236,2347,3458,4569,567T,678J,789Q,89TK,9TJA

Again, ProPokerTools confirms our previous results.

To count suited hands (ie. with at least one suit), we add the following condition: (A234,2345,3456,4567,5678,6789,789T,89TJ,9TJQ,TJQK,JQKA) ! *s*d*c*h

PropPokerTools results:

Big Suited Card + 3-Card Rundown

For the suited ace, the range is:

(234As,345As,456As,567As,678As,789As,89TAs) & (*s*s**)
(234Ac,345Ac,456Ac,567Ac,678Ac,789Ac,89TAc) & (*c*c**)
(234Ad,345Ad,456Ad,567Ad,678Ad,789Ad,89TAd) & (*d*d**)
(234Ah,345Ah,456Ah,567Ah,678Ah,789Ah,89TAh) & (*h*h**)

Ranges for suited king and suited queen are:

(234Ks,345Ks,456Ks,567Ks,678Ks,789Ks) & (*s*s**)
(234Kc,345Kc,456Kc,567Kc,678Kc,789Kc) & (*c*c**)
(234Kd,345Kd,456Kd,567Kd,678Kd,789Kd) & (*d*d**)
(234Kh,345Kh,456Kh,567Kh,678Kh,789Kh) & (*h*h**)

(234Qs,345Qs,456Qs,567Qs,678Qs) & (*s*s**)
(234Qc,345Qc,456Qc,567Qc,678Qc) & (*c*c**)
(234Qd,345Qd,456Qd,567Qd,678Qd) & (*d*d**)
(234Qh,345Qh,456Qh,567Qh,678Qh) & (*h*h**)

Results for the suited queen:

Our results are still good.

Double-Suited Ace + Two High Cards + Dangler

The best way to define this range is with the “N” wildcard. Leaving suits alone, we have:

((ANNL) ! (AA**,9***)), (AJ9L ! AA**)

Adding the double-suitedness, we have:

((ANNL) ! (AA**,9***)) & (*s*s*c*c,*s*s*d*d,*s*s*h*h,*c*c*d*d,*c*c*h*h,*d*d*h*h)
(AJ9L ! AA**) & (*s*s*c*c,*s*s*d*d,*s*s*h*h,*c*c*d*d,*c*c*h*h,*d*d*h*h)

There is a slight discrepancy with our previous results (we found 0.63 for this category); this can be due either to a calculation error, or the two ranges not being equal. Fortunately the difference is only 0.15%.

Big Pairs

The range for big pairs is:

(AA**,KK**,QQ**,JJ**) ! (AAA*,KKK*,QQQ*,JJJ*,AAKK,AAQQ,AAJJ,KKQQ,KKJJ,QQJJ)
(AAKK,AAQQ,AAJJ,KKQQ,KKJJ,QQJJ)

That is exactly the number we found.

Double Mid-Low Pairs

There is no other way than listing them all:

2233,2244,2255,2266,2277,2288,2299,22TT
3344,3355,3366,3377,3388,3399,33TT
4455,4466,4477,4488,4499,44TT
5566,5577,5588,5599,55TT
6677,6688,6699,66TT
7788,7799,77TT
8899,88TT
99TT

Again, same exact result.

Mid Pair + Connected Cards

Still no choice but listing all hands:

4566,5677,6788,7899,89TT
5667,6778,7889,899T,9TTJ
6678,7789,889T,99TJ,TTJQ

Good.

Mid-Low Pair + Suited Ace

The pairs must again be enumerated:

(22*As,33*As,44*As,55*As,66*As,77*As,88*As,99*As,TT*As) & (*s*s**)
(22*Ac,33*Ac,44*Ac,55*Ac,66*Ac,77*Ac,88*Ac,99*Ac,TT*Ac) & (*c*c**)
(22*Ad,33*Ad,44*Ad,55*Ad,66*Ad,77*Ad,88*Ad,99*Ad,TT*Ad) & (*d*d**)
(22*Ah,33*Ah,44*Ah,55*Ah,66*Ah,77*Ah,88*Ah,99*Ah,TT*Ah) & (*h*h**)
! (AA**,222*,333*,444*,555*,666*,777*,888*,999*,TTT*)

The list is now too large for the form textfield, so we split it in two:

For a total of 2.20%. Our calculated result was 2.63%, so we have a 0.43% difference. Edit: I actually already spotted the error (see the comments in the original article) and noted that 2.2% is the right number.

Summary

Our previous calculations turned out to be fairly accurate, with only a 0.58% difference. We also explored the new syntax of ProPokerTools, and the few lengthy ranges suggested that there is still room for some syntactic sugar, especially regarding suited and paired hands. The developer, bachfan, already let users know that suit parameters are on his to-do list — this will definitely be a great addition.

I think a handy new feature would be the range operator: [2-9] for cards from deuce to nine, and [22-99] for the according pairs. It might also deal with rundowns eg. [2345-789T], or [2345-T]. We could also imagine wildcards for rundowns eg. 2~~6, which would mean “any six-high rundown of four cards within a five-rank span (from deuce to six)”, and “2~6″ would be the equivalent three-card rundown. One might then fancy something like [2~~6-T], for the same rundown from six-high to ten-high.

Ok, time we stopped daydreaming.