Categories: First Five, Odds, Cannibals


*See full-size charts below

After you set your first five cards OOP in Open Face Chinese Poker, there are 47 unknown cards remaining in the deck, or what we call the 'array of unknown cards'. This is where your individual sub-hand (row) improvement draws originate. You can visualize the array in a neatly ordered way, as a jumble of alphabet soup, or not at all.

HU 1st to act

You are first to act in a heads up match and you have been dealt the above hand. Before considering how to set it, let's refresh ourselves on HU strategy. Goals for any HU hand are threefold:

1) Create a vertically and horizontally strong hand
2) Scoop + Score
3) Get to Fantasyland

It looks as if this particular starting hand will provide challenges in all 3 areas. Setting a relatively weak-looking hand out of position (OOP) is one of the toughest plays in Open Face. Setting any hand OOP is dicey because you are always acting in a vacuum with no information on your opponents' hand. Additionally, your opponent has the luxury of seeing your cards and your set before making a decision on what to do, giving them the advantage of being able to adjust their play to counter yours.

When you are out of position, you'd love to wake up to a hand like 999AK or 4-to-a-flush, hands that are a strong start to meeting the above criteria. What you have here, however, are rainbow cards containing one small pair at the bottom of the deck, whose best immediate royalty draw is a gutshot to a low straight that is easily countered. Adding to the awkwardness is the fact that these cards are what we consider to be "Cannibals" -- cards that require a difficult split decision before setting and whose improvement draws and value ranges are merged within the array. [In set theory this would be called an intersection of sets; for OFC purposes we will use the terminology 'merging' of 'draw ranges']. For more on Cannibals and starting hand theory, see OFO's article Classification of Starting Hands.

Well, what about Fantasyland? As QQ+ in front is generally the requirement to get there, we will be separating all QQQQ, KKKK, and AAAA from the rest of the array of unknown cards, and reserving them for middle and front row draws. Q's will targeted as the primary draw for the front, and K's and A's in the middle. Got it? Okay, done. Let's get this party started, unlock the luckbox, Ace me dealer! I'm pretty sure I can boat or straighten in the back, and I could catch a couple of Kings and Queens, right?

Errrr, not so fast. Unfortunately here is where we must temper our ambition, take off our Fantasy-colored glasses, and acknowledge the uncomfortable fact that there is, indeed, an elephant in the room. It's been sitting there inside the array the whole time -- actually it's 16 elephants, to be precise:

[8888 9999 10101010 JJJJ]

Together this group forms a large chunk of the array of unknown cards, they are almost completely unrelated to your starting five's improvement draws, and you'd better believe they're coming. In fact, there's a 57% likelihood that one of these cards will find their way to you as soon as 6th or 7th street. So with 35667 weighted heavily to the 'tiny' side of the deck, you need to plan for when the elephants do appear. You certainly can't ignore them and just look to your babies while dreaming of the high broadway binkage that's going to transport you to Fantasyland. After all, it would be unrealistic to suppose that somehow only cards that complete your draws and give you FL are the ones that will hit you from 6th street forward. To become a more complete OFC player, you must plan for unwanted and/or unexpected cards, and develop a strategy to deal with them as they arrive. And, the better the quality of the plan, the better your chances are to avoid fouling pitfalls, and perhaps even to turn an unfortunate pull into something positive.

This type of planning is the beginning of organizing and sorting the array into separate draw ranges for our separate rows. Complicated, we know! But so is Open Face Chinese.

To illustrate this line of thinking, we will consider several sets of the 35667, sorting the array differently for each set. Primary and secondary draws will be established for each row, as well as merged draw ranges split between rows where relevant. The 'elephants' are used differently in each set.

The goal in Part I is not to justify any one play over another, but to illustrate unique array organization for each different set. Familiarize yourself with the concepts here, and in Part II, we will go into more math and strategy behind each set. It should be pointed out that none of the draw ranges are absolutely set in stone; rather, they are meant to be adjusted throughout the hand if necessary.

SET A: x / 73 / 566

SET B: x / 53 / 766

SET C: x / 6 / 3567

Part II - Some Elephant Mathemantics

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