Combinations are all the possible ways of having hands in a Poker game, so, for instance, one combination of AKo is A♠ K♦ and in total there are 12 combinations AKo and this is true for every unsuited hand.
There are 4 combinations of each suited hand, which is pretty self-explanatory.
Then we have pocket pairs, there are 6 combinations of each pocket pair possible.
To work this out we will have the First card with all the other suits, so in this example 5♥ with every other suit possible, so Clubs, Spades and Diamonds, that is 3 possible combinations.
Then we take the 5♦ and pair that with Clubs and Spades because we have already paired it with Hearts, so that’s another 2 combinations.
The final combination of possible pocket fives will be the final 5♠ which we haven’t seen yet, this will be paired with the 5♣, giving us the total 6 combinations.
How can we use combinations to help us?
So now we know what hand combinations are, how can we use these in our game… well we can take into account how likely someone is to be bluffing or value betting by working out how many combinations of value hands they will have in pots compared to how many combinations of bluffs they could possibly have.
To do this we will want to spot imbalances in our opponents possible hand combinations, let’s say there are only a few combinations of hands that make sense for value bets on the River and there are tonne of missed draws and bluff combinations that we beat, well this is most likely a great time for a hero call, as our opponent is going to be more weighted towards a bluff with the possible combinations they make the River with.
On the other end of this scale let’s say we are seeing a dry board and there aren’t too many bluff possibilities for our opponents hand, then the likelihood is the number of value combinations in our opponents hand is going be much higher, so in spots like this we will want to be careful and probably be making a lot of folds.
Bluff to Value Ratio in action
Let’s play this hand and see what we think our opponents bluff to value ratio
So we begin this hand by flat calling our opponent’s opening raise from the Cut-Off on the Button.
The flop comes down monotone with Queen high in Hearts and our opponent bets the Flop and then continues to fire out on the Turn and River when an Ace hits the end.
What hands will our opponent have for Value firstly?
Our opponent could have KTs, T9s or 98s in Hearts. (3)
They could have the 3 remaining combos of QQ (3), 3 remaining combos of JJ (3) and the 3 remaining combos of AA (3).
They could also have all the suited Ace high Heart combinations remaining that are A2, A3, A5, A6, A7, A8, A9, AT, AK. (9)
There are some two pairs in their range too, with AQo and AJo with the Ace of hearts in their range most definitely (2)
So right away we can see our opponent has a huge amount of value bets on this board with them having a total of 23 combinations of hands they could bet all three streets of action with on this board.
What bluffs could they have?
There just aren’t too many bluffs in our opponents range here, if they aren’t opening any offsuit connectors and not turning any one pair hands into a bluff on this River then our opponent can conceivably only have the other T9s and 98s combinations that they might continue to bluff with. (6)
So that doesn’t make too many combinations of hands compared to the number of value hands.
We have 23 combinations of value against 6 possible bluffs, 23:6, this means our opponent will have a bluff around 26% of the time here.
So depending on the Bet size, we would need to be getting an incredibly low price to make a winning call on any bet on the River in this pot.
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