I show you how to count poker hand combos to aid your mathematical understanding of the game and the ranges of your opponents.

In episode 78 I read an article by BlackRain79 about putting lesser-skilled opponents on tilt along with an additional insight not mentioned within the article.

Counting Poker Hand Combos

Podcast Mission (3:15)

My mission for today is to teach you how to count combos of hands in poker.

Take the time right now to answer these questions as a quick little test for yourself:

1. How many hole card hands can you possibly be dealt in NLHE?
2. How many ways can you be dealt JJ?
3. How many ways can you be dealt TJ?
4. The flop comes T92r, what hands have open-ended straight draws and how many combos of this draw are possible?

Total number of possible NLHE hands

52*51/2 = 1,326 (we divide by two to get rid of the double counts – AcAs is the same as the AsAc, order doesn't matter here)

10% range = 130 hands; 20% = 260, 30% = 400

Of the 1,326 total possile hands:

• Pocke Pairs = 6% of hands or 78 total hands
• Suited = 24% or 312 total
• Off-suit = 70% or 936 total

Seeing these %’s, it’s easy to see why pairs are more valuable than suited hands and these are more valuable than off-suit hands.  Scarcity = Value.

Individual hands – possible combos of each

Pocket Pairs = 6 combos of each

• JJ for example; there are 4 Jacks, 4×3/2 because you don’t double-count hands like JsJh and JhJs.
• If there's a Jack on the board, how many JJ could our opponent have?    There’s three remaining Jacks, so 3×2/2 = 3 combos.

Suited Hands = 4 combos of each

• AQ for example, AQc/AQd/AQh/AQs

Off-suit Hands = 12 combos os each

• 4×3 = 12; 4 of the first card, only 3 of the second of a different suit; AQo for example = AsQc/Qd/Qh, AcQd/Qh/Qs, AdQc/Qh/Qs, AhQc/Qd/Qs

Total combos for any non-paired hand like AQ = 16; the 4 suited + 12 off-suit, or just 4×4 = 16

Board Interaction

Let's look at an example flop.  We open AA and get one caller.  The flop comes T92r.  We’re likely ahead with AA, but let’s think about our opp’s range and what possible hands and draws he could’ve hit here and how many combos are possible:

• Set = 9 combos; 3+3+3 of possible pp’s T/9/2
• 2p = 9 combos; 3*3 remaining ranks of the T and the 9 (no T2 or 92 in his calling range)
  • Only 18 combos beat us (9 sets +9 two-pair hands)
• Oesd: QJ = 16 combos, J8s = 4, 78o = 16 >>> so 16+4+16 = 36 combos
• GS: KQ = 16 combos, KJ = 16, Q8s = 4, J7s = 4, 86s = 4, 76 = 16 >>> so 16+16+4+4+4+16 = 60 combos
  • 96 combos have draws that could beat us. Remember from before, every 10% of hands is 130 combos.  If they call 30% of hands, that’s 400 hand combos total in their range.  They have 96 combos of draws, which means 24% of their range could be drawing against you.
  • Knowing this, the larger their range pre-flop, the more drawing hands they could have. The tighter the range, the less drawing hands they could have.  Let's say you're up against a tight caller that wouldn’t call with some of those drawing hands just mentioned, namely J8s, 78o, Q8s, J7s, 86s and 76o.  That’s 40 total drawing hands we can remove from his range.  So he won’t be drawing as much and that knowledge can aid us in reading his hand through the streets.

Flush Draws

On any two-tone board (2 suits on the board) there are 55 total combos of hands that could have a flush draw.  Calculated as 11*10/2 (11 remaining suits in the deck if two are on the board).  But, that doesn’t mean you have to worry about your opp holding the full 55 possible combos.  You can probably remove weak suited hands like 92s and 53s from their range.  So, on average if your opponent has a fd, he’s likely got about 30 combos there, and that’s dependent on the two suited cards on the flop and the range your opponent plays post-flop.

Card Removal or Blockers

The concept of card removal is simply the idea that if you hold a card, it’s logical to say your opponent can’t hold it.  It’s a blocker for certain combos within his range.  Let’s look at the same flop as previously, T92r, but this time we raised pre JTo and got a caller:

• Set = 7 combos (9 before);  1+3+3 of possible pp’s
• 2p = 6 combos (9 before); 3*2 remaining ranks of the T and the 9 (no T2 or 92 in his calling range)
  • Only 13 combos beat us (18 before)
• Oesd: QJ = 12, J8s = 3, 78o = 16 combos >>> so 12+3+16 = 31 combos (36 before)
• GS: KQ = 16, KJ = 12, Q8s = 4, J7s = 3, 86s = 4, 76 = 16 combos >>> so 16+12+4+3+4+16 = 55 combos (60 before)
  • 86 combos (96 before) have draws that could beat us. Remember I said earlier that every 10% of hands is 130 combos.  If they call 30% of hands, that’s 400 hand combos total in their range.  They have 86 combos of draws, which means instead of 24% of their range drawing against you it’s now 21.5%.  That’s a bit of a difference that having a blocker makes.

How to practice combo counting

Grab a deck and start dealing!  Practice these two different ways:

1. Deal flop after flop, write each flop down and count what combos of hands make fh’s, sets, 2p’s, fd’s, oesd’s and gs’s.
2. Deal flop after flop with a set of your hole cards; do the same as before, counting combos for possible opponent hands but take your cards into account as blockers to what he could have.

You’ve got to have a way to verify your combo counting, and you can use Flopzilla for this. (you can figure out how to use Flopzilla for this, right?)

Podcast Challenge (18:30)

Here’s my challenge to you for this episode:  Count the combos your opponent might have in this scenario: You open with 88, he calls on the button.  You estimate his calling range as 30% of hands, but he would normally 3bet JJ+ and AK, so you can take those out of his range b/c he just called your open.  The flop comes down 672r.  What hands and drawing hands might he have and how many combos of each?

• Sets
• 2pair
• Open-ended straight draws
• Gut shot draws

Send me your answer via email and I’ll reply with my own assessment of his possible combos.  Let’s learn together, you and me, taking our combo counting game to the next level!

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