Opening ranges, family by family

Module 21: Five-card Omaha. One extra card, and the thresholds it moves.

Every lesson so far in this module has said that the five-card game re-ranks hands rather than simply tightening them. This is the re-ranking, written out, and it is the page to come back to.

One thing has to be said before the table, because it is the difference between a useful chart and a misleading one. The four-card opening frequencies in Module 13 come from a published solver set: under the gun opens about 17.6% of hands, the hijack 22.3%, the cutoff 30.5%, the button 48.6%. Those numbers are set by position, stack depth and rake, and not one of them knows how many cards you were dealt. So the share you open does not change when you sit in a five-card game. Which hands make up that share does, and that is the only thing this table measures.

1. Each family was measured against a random hand of the same size. Five cards against five cards, 12,000 deals per family. Comparing a five-card hand with a four-card field would flatter it; comparing it with a field that also got an extra card is the only comparison that means anything.
2. That equity was turned into a percentile. 2,500 random five-card hands were measured the same way, which gives the distribution each family sits inside. "58% against a random hand" becomes "the top 5% of hands", and a percentile is the thing a seat table can actually use.
3. The percentile was mapped onto the seat frequencies. A seat that opens the top 17.6% opens the families inside it. That last step is a judgement rather than a measurement, and it is the part to argue with.

Three families in that table are worth stopping on, and they are the ones that fall furthest. Each is shown with four cards and then with the same shape plus a natural fifth.

1. Four cards: King of clubs, King of diamonds, Queen of clubs, Queen of diamonds

   Five cards: King of diamonds, King of spades, Queen of diamonds, Queen of spades, Jack of diamonds

   Two pair, double-suited. Top 0.5% of four-card hands, top 3.9% of five-card ones, and losing 8.4 points of equity against a random hand of the same size.

2. Four cards: Ace of diamonds, Ace of spades, King of diamonds, King of spades

   Five cards: Ace of diamonds, Ace of hearts, King of diamonds, King of hearts, Queen of diamonds

   Aces and kings, double-suited. The strongest family measured with four cards, and the top 1.3% with five, losing 8.2 points of equity against a random hand of the same size.

3. Four cards: Queen of hearts, Queen of spades, Jack of spades, Ten of hearts

   Five cards: Queen of diamonds, Queen of hearts, Jack of hearts, Ten of diamonds, 9 of hearts

   Queens with connectors, double-suited. Top 1.9% of four-card hands, top 6.4% of five-card ones, and losing 6.8 points of equity against a random hand of the same size.

And the other side of it. These barely moved, which in a game where the hands above them dropped several points is the same thing as rising.

1. Four cards: Jack of hearts, Ten of clubs, 9 of spades, 8 of diamonds

   Five cards: Jack of spades, Ten of diamonds, 9 of clubs, 8 of hearts, 7 of spades

   Middle rundown, rainbow. Top 53.1% of four-card hands, top 38.9% of five-card ones, and gaining 2.3 points of equity against a random hand of the same size.

2. Four cards: Ace of diamonds, King of hearts, Queen of diamonds, Jack of hearts

   Five cards: Ace of hearts, King of diamonds, Queen of hearts, Jack of diamonds, Ten of hearts

   Broadway rundown, double-suited. Top 6.6% of four-card hands, top 5.5% of five-card ones, giving up only 1.7 points of equity against a random hand of the same size.

3. Four cards: Ace of clubs, Ace of spades, Jack of spades, Ten of clubs

   Five cards: Ace of clubs, Ace of spades, Jack of spades, Ten of clubs, 9 of spades

   Aces with connectors, double-suited. Top 0.1% of four-card hands, top 0.3% of five-card ones. It gave up 4.9 points of equity against a random hand of the same size.

If you remember one line. Open the same share of hands from each seat as you would in four-card Omaha, and change which hands they are. Pairs out, nut potential in. The seat still decides more than the cards do.

One warning about reading any equity table, and it is the warning Module 19 spends six lessons on. An equity figure counts how often a hand holds the best cards at showdown. It cannot count how much of that equity you will actually collect, and the hands that collect least are exactly the ones that make second-best versions of good hands. Treat every row above as an upper bound.

Check your understanding

Aces and kings, double-suited, in five-card Omaha. Where does it sit?

Answer: The top 1.3% of hands. Right. 62.7% against one random five-card hand, which is the third-best family measured and a hand to put in as many raises as the table will allow.

What does NOT change when you move from four-card to five-card Omaha?

Answer: The share of hands each seat opens. Right. Position, stack depth and rake set the frequency, and none of them knows how many cards you hold.

Two low pair, double-suited. What happened to it?

Answer: It fell about 28 percentile places, the largest drop measured. Right. Its whole value is sets and full houses, and that is the value the extra card devalues fastest.

The last two columns of the table are kept separate from the seat columns. Why?

Answer: Opening is a different decision from responding to a raise. Right. An unopened pot offers open or fold. Once somebody has raised, the question is whether the hand plays well in a bigger pot, which is not the same question.