The ability to put your opponent on a range of hands is one of the most important skills in poker. Hand reading has nothing to do with reading your opponent’s “soul” and everything to do with pattern recognition and combinatorial analysis.
Pattern recognition is identifying which hands make sense given the villain’s line. Most experienced players have this aspect of hand reading nailed down, but the statistical part of hand reading eludes them. If you’re one of these players, learning combinatorial analysis will definitely improve your game.
What Is It?
Combinatorial analysis is the act of determining how likely your opponent is to hold a certain hand given the number of possible ways the hand can be made. Here’s an example:
You’re in position in a 3-bet pot with AJ and the flop comes J57. Your opponent open shoves for 50 big blinds more. You know he’ll only take this line with JJ, AA or AK. Should you call?
Some players would reason that there are two hands that beat them and one hand that doesn’t therefore their odds of winning are 1-in-3 and they should fold. That reasoning is flawed.
Combinatorial analysis will give us a better understanding of the situation. Since there is a Jack on the board and we’re holding a Jack, there is only one way for our villain to hold JJ. Since we also hold an Ace, there are 3 ways to hold AA and 12 ways to hold AK. All in all, there are only 4 ways for our opponent to hold a hand that beats us and 12 ways for our opponent to hold a hand we beat so we’re almost a 3-to-1 favorite. Even when you consider the fact that AK will out draw us about 12% of the time, it’s a clear call.
Combinations to Remember
There are certain situations that pop up over and over again and it’s worth taking the time to remember the combinations for those situations. Here are some combinations to remember:
Basic Combinations
There are two basic hands a person can hold: two unpaired cards and a pocket pair. Here are the possible combinations.
Any two unpaired cards: 16
Any pair: 6
Combinations to Pair a Card on the Board
Combinatorial analysis becomes more complicated when you use it to consider how likely your opponent is to hit the flop. The first thing you have to do is put your opponent on a range of hands.
Let’s say, for example, that your opponent raises in middle position in a 6-max game and you call on the button with pocket 8s. You know your opponent’s range in mid position is KJs+, KQ+, A2s+, AT+. We’ll ignore pocket pairs to make things easier. The flop comes Ah3s6c. How likely is your opponent to hit that flop?
We know that when a card is on the board, your opponent has 12 ways to hold any unpaired hand. Your opponent’s range has 72 combinations (12 ways for each AT+, 3 ways for each A2s – A9s) that have an ace and 16 combinations (12 for KQ and 4 for KJs) that miss. Your opponent is 4 ½ times more likely to have hit this flop than miss. You should fold when he c-bets.
It’s usually a bad idea to play back at an opponent on the flop when an Ace is showing since Aces make up a large portion of almost every player’s range.
Combinations That Make Trips
There are only three ways to make trips for each card on the board. Assuming all pocket pairs are in a villain’s range, there are 9 ways to make trips using any card on the flop.
Combinations That Make Two Pair
Figuring out the number of combinations that make two pair can get complicated. First you have to put your opponent on a range and figure out how likely the flop helped them.
Let’s say your opponent’s range is AT+ and the flop is AJ3. There are 9 ways your opponent could hold two pair. If the flop is AJT, your opponent now has 18 ways to make two pair.
Things become even more complicated when you add more cards to your opponent’s range. If KQ and JT are added to your opponent’s range on the AJT flop, they now have 16 ways to make a straight and another 9 ways for a JT two pair.
Combinations That Make Flush Draw/Flush Possibilities
It’s much less common to hold a suited hand than an unsuited hand and the number of combinations possible is highly dependent on the villain’s range and whether or not there’s a card from their range on the flop. That’s one reason a suited ace on the flop reduces the odds of a flush draw.
Programs to Help You
Don’t worry if this all seems a little overwhelming. There are free programs available that will do all of this work for you. Two take come to mind are FlopZilla and Pokerazor. Take some time and play with these programs to get a feel for how likely different ranges hit different flops. This information will help you judge when to defend against c-bets as well as make other advanced moves.
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