Texas Holdem has 169 unique starting hands which are easily ranked according to relative strength. When you hear someone talking about
"top ten hands" or "top 30% of his range", they are referring to the chart that starts with hand #1 (AA) and ends with hand #169
(2-7 offsuit). Among other uses, this chart can be helpful to a beginner trying to determine what a good starting hand is, or a tournament
player tanking on a call and trying to range an opponent's short stack shove.
How many starting hands are there in Open Face Chinese?
Including duplicate-value hands, such as the following,
the combinations are 2,598,960. Filtering out all duplicates distills the list to 7,462 hands of unique value.
Can these be sorted according to relative strength? The answer is probably not any time soon (as the reasons below will help to illustrate).
However, in this article a classification system will be established which can be a starting point for
first-five hand strength discussion. Before introducing the system, let's outline the difficulties in creating a starting-hand
A) There are 7,462 hands to rank.
Compared to only 169 in Holdem, that's a considerable jump. Even if a comparative strength chart could be created, how would you present
that much information? The "top 10" hands in Holdem becomes......."top 441" in Open Face?
B) The full Open Face set contains 13 cards,
nearly twice the number used in games like Omaha or
Stud. This creates mind-boggling combinatorials to deduce.
C) The architecture of the hand is vertical as well as horizontal. An Open Face Chinese hand is built in
three sub-hands (or rows), not just one. This differentiates it from NLHE,
Omaha, Stud, and all the other major poker variants, because their hand structures are horizontal only. The following
deal might look great in 5-card draw, but it's only a great start in Open Face. Hence it is much more complicated to begin to determine
expected value or win percentages.
D) Traditional starting-hand strength is variable in
a way that makes volatile in size and quality the array of (unknown) cards to be drawn upon to improve
the hand. For example, if you catch a pair of kings but you are last to act in a 4-handed game and kings are dead, a KK set will never improve against AA.
Thus a hand that has good relative strength in a vacuum loses value in the real-world situation, because the array of cards that contains
draws to improve the hand has now shrunk. Variables that affect the array include:
1. Traditional starting-hand quality
2. Variant of the game
3. Number of players
4. Position on the table
5. Live and dead draw cards
E) A gargantuan number of full-game simulations are needed
to determine draw completion and foul probabilities of 7,462 unique
starting hands in various sets as they progress from the deal to 13th street.
It's one thing to calculate probabilities in a single row at any given point in the hand (and this certainly can be useful while
making decisions during play),
but quite another entirely to predict the outcome of first-five dealt cards as they evolve into a fully set hand, not to mention
EV and win rate against 1-3 opponent hands.