Hitting the Flop In Omaha: 5678

We know that a gapless rundown is the type of hand that hit flops very well, but it is harder to come with precise numbers given the lack of tools such as Flopzilla for Omaha. I tried to enumerate these flops in a spreadsheet and calculate the odds of each flop, and here are the results.

The left column lists the different flops, with our hand (5-6-7-8) on the top. A line with “3 4″ means a 3-4-x flop. In order to avoid counting some flops several times, we excluded some cards, which are represented by a dot. Thus, for our 3-4-x flop, we excluded deuces, and fives to nines; they’ll be accounted for later.

The odds of each flops are broken down into four parts: all flops (paired board included), flops giving us trips if paired, flops with no pair, and flops without three cards of the same suit. Note that the 5-5-x type of boards exclude the trips that were already counted above (for the “no pair” column, it would count them all, then). That’s why the sum of the “only trips” and “no pair” are identical, modulo rounding. We see that our rundown hits a draw or trips/full house on about 30% of flops. If we exclude 3flush flops, it is 28%. The second total line excludes OESD.

Now let’s count the flopped straights (that were previously excluded): It is about 5% of flops, or 3% if we only count nut straights.

When we sum it all, we found that our hand hits 36% of flops, and 33% if we exclude 3flush boards. The second total line excludes OESD and non-nut straights.

5678 hits a draw or better on 33% of flops,
and 50% if adding pair+kickers.

Finally, 23% of flops give us a pair+kickers, and 16% if we exclude ace-high boards (in case we’re against aces, notably). That makes for a 50% grand total if we add these flops. That’s how well the gapless rundown flop!

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