Hand Groups Formula

[YY] Yuri the Young Gun joins in the discussion on Hand Groups1, “Benny, that’s a great chart, but only the most informal poker games would let you look at it during hands, and it’s really hard to memorize.”

[JJ] Joey the Juvenile nodded loudly in agreement.

[BB] Benny the Book is taken aback, “But it’s so worth learning! I couldn’t imagine playing without it.”

[YY] “What if I told you there was a fairly simple formula to approximate your chart?”

[BB] “I may be an old curmudgeon, but I’m all ears.”

[JJ] “I can handle one simple formula better than that huge table.”

[YY] “When I was first learning Hold ‘Em forever ago in 2008, I didn’t feel like memorizing those 169 values, even if there are plenty of patterns to make it easier. So I Googled for a better way, and it turns out that Bill Chen worked out an excellent formula2. I tinkered with it to make the end result a Hand Group instead of a strength value, and so it3 works like this…

  • If your hole cards are paired:
    • Aces through Tens are Hand Group 1; Nines through Sixes are 11 minus the denomination (i.e., Group 2 through 5), and Fives and lower are Hand Group 6. [As a list, AA-TT:1, 99:2, 88:3, 77:4, 66:5, 55-22:6.]
  • If your hole cards are unpaired:
    1. If your higher card is an Ace, start with 1, King is 3, Queen is 4, Jack is 5, and otherwise 11 minus half the denomination rounded up; e.g., a Seven is 7 (11 – 4). [As a list, A:1, K:3, Q:4, J:5, T:6, 9:6, 8:7, 7:7, 6:8, 5:8, 4:9, 3:9.]
    2. Add 1 if the gap4 is 1; add 2 if the gap is 2; add 4 if the gap is 3; and add 5 if the gap is bigger (e.g., for QJ add nothing, for J9 add 1, for 74 add 2, for J7 add 4, and for A2 [gap of 11] add 5).
    3. Subtract 1 if the gap is 0 or 1 and the higher card is a Jack or lower.
    4. Subtract 2 if your cards are suited. Anything under 1 is Group 1, while anything over 10 is Group 105.

[YY] “For example, AA is Group 1, 44 is Group 6, AKo6 = 1 + 0 – 0 – 0 = Group 1, AQs = 1 + 1 – 0 – 2 = Group 1, KTo = 3 + 2 – 0 – 0 = Group 5, T9s = 6 + 0 – 1 – 2 = Group 3.”

[YY] “I’m working on a similar formula for heads-up play, and then a way to mash them together to handle any table size. Hopefully, I’ll have it done by the next time we play.”

[JJ] “Cool.”

Footnotes:

  1. Sunday’s blog post was about Pre-Flop Hand Groups.
  2. Here are a fuller explanation and calculator for the original Chen Formula and Bill’s original post to the rec.gambling.poker newsgroup back in 1999.
  3. If I may be so bold as to name this, the obvious name is the “Chen-Jen Hand Group Formula”.
  4. For no particularly good reason gaps include neither end card, so a 75 is a one-gapper, a QJ is a zero-gapper, and a pair would be a negative-one-gapper by logical extension (fortunately, nobody says that).
  5. Hand Groups often get cut off at Group 8, but for the sake of completeness, I always use ten (should have mentioned that on Sunday).
  6. While ‘s’ stands for “suited”, ‘o’ stands for “offsuit”. You will also sometimes see ‘u’ for “unsuited”, which is the same thing.

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