Breakdown of an Omaha Preflop Range

We previously examined some PLO starting hands, but it would also be interesting to put a weight on them using combinatorics. This would enable us to make more educated guesses against our opponents’ ranges, and later on we will be able to study how likely it is for them to hit various flops.

The following charts list several hands and give the probability of being dealt one of these hands from a 52-card deck. In each case, the whole type is considered; for instance, the (gapless) rundowns are represented by 2-3-4-5, but the probabilities include all rundowns up to J-Q-K-A. When a rank is excluded (to avoid counting the same hands multiple times), it is marked with a dot. This is the case for 2-3-4-A big suited ace, where the jack, queen and king are excluded since the hand would then fall into the gapped rundown category.

The “(any)” column makes no assumption about suits; the “(no 4flush)” one excludes hands with four cards of the same suit; the “(1+ suit)” one also excludes hands without a suit (rainbow hands); and eventually, the “(2 suits)” column gives probabilities for double-suited hands. When a column is not relevant to the type of hand (for instance, the “(any)” and “(no 4flush)” do not really apply to the “big suited card” type of hand, since it must be suited by definition), then the correct probabilities are taken from the relevant column, and put in gray/italics.

The respective sums of each column are 10.58%, 10.44%, 9.60% and 2.13%. So, overall, we have a 10% chance to be dealt one of these hands. Naturally, these hands are not all equal, and some of them are pretty marginal, but they should account for some other marginal hands that are not listed here but some players will occasionally play.

Now let’s consider paired hands:

The sums are now 13.57%, 13.57% (same, since a paired hand will never be all of the same suit), 10.59% and 1.83%. So it is about 11-13%.

Roughly speaking, there are as many rundown hands as paired ones, and most of the paired hands are big pairs. The grand sums for each column (after rounding) respectively are 24%, 24%, 20% and 4%. This is consistent with our previous recommendations regarding VPIP; you can add a few more marginal, suited hands if this is your style, and you will still be in the 20-35 VPIP “standard” range.

In the next articles, we will study how these hands connect with several kind of flops.
Stay tuned !

Nb.: I double-checked the numbers, but errors frequently creep in for these kinds of analyses — feel free to ask or point them out.