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Oct. 28 — When a card comes that can logically make your opponent two pair it is actually less likely to do so combinations wise.

If you have read or listened to my training material in the past, you know how important that I think it is to make thin value bets on the river. In fact, at the mid-to-low stakes games, this can comprise as much as 75 percent of your win rate.

One of the most common mistakes that recreational players make, especially when the pot gets big, is getting scared. Certain cards may come, and because they are incapable of betting for value, then folding to a raise, they just check to take a free showdown. This approach keeps them losers in the game overall.

One of the situations that scares these players the most is when a card falls at the end that can give opponent two pair. Let us take a look at an example. Say we raise under the gun with pocket kings to $20 in a $2-$5 game with $800 effective stacks. Both the cutoff and the button call. The flop comes out Q 3 2. We bet out $45 into $65, and both players call. The turn is an 8 and we bet $125. This time only the cutoff calls. His range is a little stronger than the button’s as he has had to worry about the button behind him. Most likely he has some sort of queen. The river is the J. A lot of weaker players would become scared of this card, as there is a chance now that the cutoff has made two pair with Q-J. What they do not realize, however, is that it is less likely that this player holds Q-J due to combinatorics.

Combinatorics, although sometimes an intimidating word, is simply the study of mathematical combinations. When a card appears on the board, there are now fewer combinations of hands with that card that a player might have. So, for example, if the cutoff only calls with Q-J suited to a raise, he has four combinations total of Q-J, one for each suit. Because the board is Q 3 2 J he can no longer have Q J or Q J, only Q J or Q J. So, before the river, he had three possible combinations of Q-J suited, but after his total is cut by 33 percent. He is more likely to hold K-Q suited, as there are three combinations still remaining instead of the two of Q-J. On a more advanced note, people are more likely to call a raise with K-Q offsuit as opposed to K-Q suited (which they would likely raise), so there actually is a much better chance of that holding.

This is not to be confused with the river pairing the queen, as our opponent has many Q-x hands in his range, although he may also have a busted flush draw. Again, however, basic hand reading reveals that he should have a stronger hand on the flop and the turn, skewed towards a queen because he was next to act after the preflop raiser and still had a player to worry about behind him. Most players also do not call the turn with naked flush draws, so he would have to have a pair or a straight draw with the diamonds in order to continue on.

Remember this article the next time a card comes where you think your opponent may have improved to two pair; chances are it is actually more likely that you still have the best hand.

Nov. 5 — Understanding combinatorics leads to better river value betting. When holding an overpair it’s more likely that your opponent holds top pair.

As long as I am on this combinatorics rant, I wanted to bring up another scenario where people do not realize that they are more likely to hold the best hand at showdown. This spot involves us holding an overpair when a front-door flush draw comes in on the river. Say we raise A A to $8 from under the gun (UTG) plus one in a $1-$2 game with $400 effective stacks. The player in the hijack is the only caller. The board comes out J 2 7. We bet $15 and our opponent calls. The turn is the 3. We fire $30 and the hijack comes along again. The river is the 4. What should be our play here? Because we do not have a jack in our hand, there are more combinations of jacks that our opponent can hold. Even though the river looks scary when we understand how this combo math works, we can make adjustments. If, however, we held a hand like A J, there would be more of a chance that our opponent has made clubs, as there would be fewer combinations of jacks left.

This concept can really be put into practical application when the pot involves multiple players. Say we use the above example, but there are two players that called us preflop and we hold K J. Now, at the river, I would be very concerned that one of my opponents may very well have made a flush as there are only four jacks in the deck. On the other hand, if I held K-K, I could quite reasonably bet for value because both opponents could still hold top pair.

Combo work is very useful when trying to weight an opponent’s hand range, especially at the river when a draw comes in. I have discussed this concept a lot in my training, however, often times it is misapplied. You see, we can also learn a lot about our opponent’s hand range by the turn card. Let us say that in a $5-$5 game we raise to $20 from UTG with Q Q. The button calls. The board comes out 8 4 2. We continuation bet $30 and our opponent calls. The turn is the K. Some players might get scared of this card, but in reality the king is unlikely to improve our opponent’s hand unless he had the king-high flush draw. The right play would be to bet here again to charge the draws. So, we bet out $70 and our opponent calls again. The river is the Q. What is the correct play here?

In previous articles I have mentioned that it is correct to value bet when we are good more than 50 percent of the time when called. On this river we are in a bit of a quandary. We now have a set, which in the absolute sense is a strong hand, but sometimes can be relatively weak given the action and board. Because our opponent continued to call the turn when a scary overcard hit, his range is skewed away from one-pair hands like an eight and now leans more towards a draw. And even if he continued to hero call us with a hand less than a king on the turn, if we bet again, it is very unlikely that a worse hand will call unless he somehow flatted preflop with A-K and called the flop. The correct play usually here would be to check and fold.

So, you can see that in some scenarios a hand that is not that strong can dictate a value bet and other times a very strong hand should check and fold. Hand reading and combinatorics, once grasped correctly, will take your game to the next level. ♠

Follow Bart for daily strategy tips on twitter @barthanson. Check out his podcast “The Seat Open Podcast” on seatopenpoker.net and his video training site specifically for live No Limit players ­—CrushLivePoker.com. He also hosts Live at the Bike every Tuesday and Friday at 10:30 pm ET at LiveattheBike.com.