Visualizing Hand Groups in Hold ‘Em

In the last few years I’ve developed a huge interest in Poker, and after reading a number of poker theory books, I’ve started experimenting with alternate (and hopefully better) ways of illustrating common poker theory. In this case, the lists which rank the strength of starting hands in the game of Hold ‘Em.

In Hold ‘Em, every hand starts with two cards dealt face down to each player. This is the point, before any bets are made, where a player decides whether a hand is worth pursuing, or should just be mucked. Because there are only 169 unique two-card combinations that a player may be dealt, this is also the stage of the game with the fewest variables and one where strong guidelines are written about what hands should be played and how.

HAND GROUPINGS

In 1988, David Sklansky created a Group-based ranking system to illustrate the relative strengths of starting hands in his book Hold’Em Poker for Advanced Players. Group 1 consisted of the strongest starting hands (AA, KK, QQ, JJ, AKs) while Group 8 hands were the weakest — or at least the weakest hands worthy of rank. The eight Groups only cover a total of 86 hands, the remaining 83 possible combinations aren’t recommended as playable cards, ever.

The Groups are frequently referenced online and in other poker manuals and are typically displayed as a simple list of hands or in table format to allow for easy on-the-fly reference. Below are two pages from Sklansky’s Hold ’Em Poker for Advanced Players showing how he displays them in his own book.

Though there is always debate as to the relative strength of specific hands or how and when to play certain combinations, on the whole the Groups are well respected as an excellent starting guide especially for beginning players.

What frustrated me about the Groups and what initiated this project was that I could memorize the information, but I didn’t feel that the lists and tables were showing me the larger picture. I don’t know if Sklansky developed the original groups based on intuition and experience honed over millions of hands, or whether mathematical calculations were used (which have certainly been applied to the Groups since then) – but my guess was that the hands included in each group were not accidental and that given the right perspective, patterns could be seen. Along those lines I sat down with the information and tried to make some sense out of it.

The result was the following chart.

The chart itself is a simple triangle, with rows and columns of card values, representing every possible combination. When displaying a Group, the combinations are hi-lit in either black or blue. The version of the chart below displays only the Group 1 hands (AA, KK, QQ, JJ, AKs)

The version of the chart below shows what combinations you would play if you were only playing hands from Groups 1 through 4.

The black combinations represent cards that you would play suited or not, the blue combinations are cards you would only play if they were suited. So in the Group 1 through 4 diagram, you’d play any AJ, but you’d only play AT if it was suited. KJ is always a tempting hand to play but according to the chart, if you’ve decided that you’re sticking to Group 4 hands or better, than you should only be playing KJ if they’re suited.
Ultimately, the chart on its own serves as a good reference tool, superior in some ways to the table listings and useful for the same at-a-glance comparisons.

REVEALED RELATIONSHIPS

The chart goes beyond serving as a basic reference tool. When the hands are lined up in this triangular formation relationships start to develop between the rows as you can see from the diagram below.

The outermost diagonal are all pairs. The next diagonal are all Connectors (AK, QJ, 34… cards which immediately follow one another). The next diagonal row are Split Connectors (cards with a gap between them). Two rows past that are the Inside Straight Draws (the farthest cards which could still be connected to form a straight – AT (AKQJT) or 84 (87654). There are a few exceptions that pop up down at the bottom of the Aces column. A5 gives you an inside straight draw since an Ace can be used to complete a low (or “wheel”) straight (A2345) and for the same reason A2 is a connector and A3 a split connector.

Once you see the relationships, when you look at the progression of each group you can start to see what hands increase in value at each stage. Compare Group 4 and 5 where there’s a huge jump in the number of hands you can play.

Group 5 opens up pairs down to 77, it also significantly expands the Suited Connectors you can play, from 98 down to 65. Split Connectors expand from J9 down to 97, not to mention that any suited Ace combination is fair game. What hasn’t increased at all are the Inside Straight draws. You’ve been able to play a ATs since Group 3, but it isn’t until Group 6 that you’d ever play AT (unsuited). Group 6 is also the first level that the K9s Inside Straight Draw is an option.

CONCLUSION

I think these charts are a great success in presenting group information in a new and revealing way. Also, I just love the way the Black and Blue designations slowly climb their way down the chart as the Groups progress. I’ve included a link to a .pdf of the charts (850k) listing all 8 groups for perusal at a greater resolution. Feel free to use them and hopefully they’ll improve your game! Good Luck!

*CLOSING NOTES

First, I should note that I’ve been describing these as what hands “can” or “cannot” be played. These Groups are of course just guidelines and the actual cards you play obviously depend on who you’re playing with, how the other people at the table are playing, what your position is at the table, how deep your stack is, etc… The purpose of my redesigned charts are to simply wring as much information as possible from the Groups; to go beyond understanding which cards fall in each group, to understanding why cards fall in each group.

I have also created individual diagrams, showing ONLY the cards in each Group (not a cumulative progression). They can be used to see how many combinations and specifically which ones are added in each Group, but as a reference tool, I don’t find them to be very useful.

Finally, while I think these reveal a lot more information than the original listing, there is one bit of information that they lose, and that is the relative rank of hands within each group. In Sklansky’s listing for Group 4 you would technically consider a T9s as a stronger hand than KTs – he lists the T9s first. However, he also points that “in reality, it’s usually only necessary to know in which group a starting hand belongs” and I agree.

Tagged as: charts, diagrams, infographics, poker