Counting Combinations

Question 1

How many combinations (combos) are there of unpaired hands preflop? Any two cards

Answer 1

16 combos

Suited:
4 - suited (clubs, spades, hearts, diamonds)

Off suit
12 - off suit (clubs, spades, hearts, diamonds)

Question 2

How many combinations (combos) are there of a pocket pair preflop?

Answer 2

6 of any rank

Question 3

How do we calculate the number of combinations (combos) there are for a set?

Answer 3

( x * (x-1)) / 2

where x is the number of available cards remaining in the deck.

C = ( A * (A-1)) / 2

where C = combos & A = available cards

Question 4

How do we calculate the number of combos for unpaired hands?

Answer 4

(x * y)

where x & y are the number of available cards remaining in the deck for each rank.

C = A1 * A2

where C = combos
A1 = available cards for first rank
A2 = available cards for 2nd rank

Question 5

How do we calculate the number of combos for two pair?

Answer 5

(x * y)

where x & y are the number of available cards remaining in the deck for each rank.

C = A1 * A2

where C = combos
A1 = available cards for first rank
A2 = available cards for 2nd rank

Question 6

How do we calculate the number of combos for top pair?

Answer 6

(x * y)

where x & y are the number of available cards remaining in the deck for each rank.

C = A1 * A2

where C = combos
A1 = available cards for first rank
A2 = available cards for 2nd rank

Question 7

How do we calculate the number of combos for middle pair?

Answer 7

(x * y)

where x & y are the number of available cards remaining in the deck for each rank.

C = A1 * A2

where C = combos
A1 = available cards for first rank
A2 = available cards for 2nd rank

Question 8

How do we calculate the number of combos for bottom pair?

Answer 8

(x * y)

where x & y are the number of available cards remaining in the deck for each rank.

C = A1 * A2

where C = combos
A1 = available cards for first rank
A2 = available cards for 2nd rank

Question 9

How many total combinations are there of a set preflop?

Answer 9

9

Question 10

When there is 1 card of a rank on the board, how many possible sets are there?

What about when there are 2 cards out on the board?

Answer 10

1 card out - 3 possible combos of a set

2 cards out - 1 possible combo of a set

** Note - assuming there are two cards of the same rank, or we hold one of the cards in our hand.

Question 11

When you have a card in your hand, how many possible pocket pairs does that leave someone to have a pocket pair of one of those cards.

Answer 11

3 possible combos

(3 * (3-1)) / 2

When I have a card, or there is a card on the board, that leaves 3 possible combos.

Question 12

How many combos of pocket 99s are there?

Answer 12

6 combos

AsAd AsAc AsAh
AdAc AdAh AcAh

Question 13

How many combos of KQ are there?

Answer 13

16 combos
suited - 4
off suit - 12

Question 14

What is the pocket pairs formula?

Answer 14

C = ( A * (A-1)) / 2

where C = combos & A = available cards

(4 * (4-1)) /2
(4 * 3 ) / 2
12 / 2
6

Question 15

What is the unpaired formula?

Answer 15

C = A1 * A2

where C = combos
A1 = available cards for first rank
A2 = available cards for 2nd rank

KQ = 4 possible K * 4 possible Q = 16

Question 16

When on the flop, how do we quickly determine how many combinations of top pair our opponent has?

Flop is Kh 6c 5d
KQ
K6
K5

Answer 16

(A1 * A2)

Flop is Kh 6c 5d
KQ - 3 * 4 = 12
K6 - 3 * 3 = 9
K5 - 3 * 3 = 9

Question 17

On a Flop of Kh 6c 5d
We hold Kc6d in the BB.  
How many combinations of the following remain
KQ
K6
K5
Sets
Over pairs

Answer 17

Kh 6c 5d
We hold Kc6d in the BB.

KQ - 2 * 4 = 8
K6 - 2 * 2 = 4
K5 - 2 * 3 = 6
Sets - 5
Over pairs - 6

sets =
K - ( 2 * (2-1)) / 2 = 1
6 - ( 2 * (2-1)) / 2 = 1
5 - (3 * (3-1)) / 2 = 3

Question 18

What is the shortcut to know how many possible combos of sets an opponent may have?

Answer 18

1 card is known - 3 possible combos of sets

2 cards is known - 1 possible combo of a set

Question 19

How many combinations of sets on Kh 6c 5d when we hold 8c 7d?

Answer 19

9 possible sets are remaining on this flop

3 combos of pocket kings
3 combos of pocket 6s
3 combos of pockets 5s

Question 20

How do we know the number of suited two pair combinations a player has when 2 cards of the suit is known?

Ex 1: How many suited Q7 combos can he have on a Qh, 7d, 2c board?

Ex 2: How many suited K8 combos can he have on a 4c 8h Kh board?

Ex 3: How many suited K8 combos can he have on a 4c 8c Kd board?

1 card of the rank is known
2 cards of the suit is known
2 cards of different suit

Answer 20

2 suited Q7 possibilities

2 cards of the suit is known - 3
For example, on 4c 8h Kh, K8 suited would have 3 other suited combos

2 cards of different suit - 2
For example 4c 8c Kd, K8 would only have 2 other suited combos available.

*** note, it’s important to know that you should consider doing the off suited cards first. The suited cards fall into this category and are not separate.

For example, when looking at K8o, 3 * 3 = 9. the K8 suited combos are part of this combo of 9, so you do not have to do them separately.

Do off suits first, then do suited that were not part of off suits.

Question 21

How many outs do we have on a straight draw plus a flush draw?

On the flop

Answer 21

15

9 flush outs
6 straight outs (2 of the cards are counted for in the flush outs)