NLHE Foundations Course
This is the first lesson in the free No-Limit Hold’em Foundations course that I’m running here on FlopTurnRiver. There’s a lot more to these lessons than what you see here. If you would like to take part in this, all you have to do is post in this forum thread that you would like to participate, and you’ll get access to all of the materials and instructions for the course as they become available.
With that out of the way, let’s get started.
Ranges are what we call groups of hands in poker, and no-limit hold’em ranges in particular are what we are going to focus on in this lesson. Our goal here is to build a basic understanding of how we can work with ranges as a part of a solid foundation for being able to play and learn the game of no-limit hold’em. The very first step we need to take towards this goal is learning how to count starting hand combinations.
Required Reading: Read #1, #2 and #3 from the first post in this thread now. Don’t worry about reading past #3 on the list, and don’t waste time going through the rest of the posts in this thread. This was my original post on counting hand combinations, but it still holds today, and there’s no use in wasting time by reading more than you need to.
Your goal for this lesson is to be able to accurately count the number of combinations that are available for different starting hands.
Examples for Individual Hands
I’m going to work through a few examples to show you how this works. Suppose we hold AQ on a board of AKT where suits don’t matter. How many ways can our opponent have AK, AQ, AJ, QJ, AA, KK or JJ?
- AK – There are two aces left in the deck and three kings left in the deck. We do 2 * 3 to get a total of 6 combinations of cards that can make this hand.
- AQ – There are two aces and three queens left in the deck. This gives us 2 * 3 = 6 ways that our opponent could be dealt AQ.
- AJ – There are two aces and four jacks left in the deck. That means there are 2 * 4 = 8 ways that our opponent could have AJ.
- QJ – With three queens and four jacks left in the deck, there are 3 * 4 = 12 ways our opponent could have QJ.
- AA – Remembering the 6310 shortcut for finding the number of paired combinations, we see that there are two aces on the board or in our hand. That means there is only one way our opponent could be dealt AA.
- KK – Again with the 6310 shortcut for paired hands, there is one king that we see on the board or in our own hand. This means there are three ways our opponent could have KK.
- JJ – Using 6310 once again, we see that there are no jacks on the board or in our hand. That leaves us with knowing that there are six ways our opponent could have JJ.
Note: A quick way to write these is to list out the hands with the number of combinations in parentheses. For the above example, you could write it like AK(6), AQ(6), AJ(8), QJ(12), AA(1), KK(3), JJ(6). In the exercise I give you below, this is how I suggest you write out your answers in final form, but feel free to type out how you come to those conclusions so that we can look at any mistakes in your thought process and fix them before we go on to our next lessons.
It’s really, really, really important that you’re able to do this, and the more you practice it, the faster and more accurate you’ll be able to do it.
Why This Skill is Important
A common misconception about counting hold’em hand combinations is that you’re somehow expected to do this at the table for large ranges. That’s not the point, and it’s not really reasonable to expect you to be able to do that. Instead, I want you to be able to count these combinations when you’re analyzing hands and situations.
There are two benefits to being able to do this. First, I’m going to show you how to find the right play in a lot of situation in your study on your own as a major point of this foundations series. Second, I’ll be able to use this idea to prove certain points to you in an effort to teach you important concepts quicker and more efficiently than you would be able to do otherwise.
I’m going to give you a situation where you have a certain hand on a certain board, and I want you to post in this thread with your answers to the exercises. Look over each others answers and discuss any differences you see. Here’s the situation to look at:
You hold 8s7s on a board of Ks8h5s. Find the number of starting hand combinations for the following hands: AK, AQ, AA, KK, A8, 76.
Remember to write these in the format I talked about above, and I look forward to seeing your answers.