As long as we are 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 UTG+1 in a $1-$2 game with $400 effective stacks. The player in the highjack 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 highjack 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 is more of a chance that our opponent has made clubs as there are less 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 KK 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 about our opponent’s hand range by the turn card. Let us say that in a $5-$5 game we raise to $20 from under the gun with Q♠ Q♣. The button calls. The board comes out 8♥ 2♠ 4♥. 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% 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 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 AK 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.