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Poker Odds

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OVERALL:

Everybody can learn Texas Hold'em, but it takes a life time to master it.

In this section GetRake will present some basic scenarios so you can see what your odds are of getting dealt certain cards or making certain hands.
And learn the odds as you are playing and raising your profit.


Different flop combinations:

19,600.
MATH: (50*49*48)/(3+2+1)

EXPLANATION:
This is assuming your are dealt 2 cards and want to know how many flop combinations there are with 50 cards left. So there is a 1 in 50 chance of any particular card being the first flop card. There is a 1 in 49 chance of any particular card being the second flop card and a 1 in 48 chance of any particular card being the third flop card. The reason why we divide by 6 is because the order of the cards on the flop doesn't matter so any flops that have the same cards but in different order will be considered "duplicate" flops and will not be considered. There are six differnet ways that a set of 4 cards can be ordered. Either of the 3 cards can be the first card. Then only 2 cards can be the next card and only 1 card can be the last card (3*2*1=6).


19,600 different flop combinations.


Different board combinations:
2,118,760.
MATH: (50*49*48*47*46)/(5+4+3+2+1)

EXPLANATION:
This is assuming you are dealt 2 cards and want to know how many board combinations there are with 50 cards left. Following up on the logic from the last example there are (50+49+48+47+46) different board combinations but like the last example we want to ignore the scenarios where you have combinations that are the same but in different order.


2,118,760 different board combinations


PRE-FLOP:



The probability of being dealt:



Pocket aces
ODDS: 220 to 1.
CHANCES: 1 in 221.
PERCENT: 0.45%.
MATH: (52/4)*(51/3)

EXPLANATION:
The odds of the first card being dealt to you being an Ace are 4 in 52. The odds of your second card being an Ace (given the fact that your first card was an Ace) are 3 in 51.


0.45%.



Either pocket aces or pocket kings:

ODDS: 109.5 to 1.
CHANCES: 1 in 110.5. P
PERCENT: 0.905%.
MATH: (52/8)*(51/3)

EXPLANATION:
The odds of the first card being dealt to you being an Ace or a King are 8 in 52 (4 Aces and 4 Kings). The odds of your second card being the same as your first card are 3 in 51.

or
0.9%


Any pocket pair:
ODDS: 16 to 1.
CHANCES: 1 in 17.
PERCENT: 5.88%.
MATH: (51/3)

EXPLANATION:
The key to the equation here is to realize that to calculate the odds of getting ANY pocket pair is that it doesn't matter what your first card is. It just matters that your secondcard match your first. After you get your first card there are 51 cards left in the deck and only 3 that match the same rank as your first.


5.9%


AK suited:
ODDS: 330.5 to 1. CHANCES:[/color] 1 in 331.5. PERCENT: 0.3%.
MATH: (52/8)*(51/1)

EXPLANATION:
The odds of your first card being an Ace or King is 8 in 52. Then, there is only one other card in the deck that can make you a suited big slick.


0.3%


AK offsuit:
ODDS: 109.5 to 1.
CHANCES: 1 in 110.5.
PERCENT: 0.9%.
MATH: (52/8)*(51/3)

EXPLANATION:
The odds of your first card being an Ace of a King are 8 in 52. The odds of your other card making you unsuited Big Slick are 3 out of 51.


0.9%


AK suited or offsuit:
ODDS: 81.88 to 1.
CHANCES: 1 in 82.88.
PERCENT: 1.21%.
MATH: (52/8)*(51/4)EXPLANATION:
The odds of your first card being an Ace of a King are 8 in 52. The odds of your other card making you Big Slick are 4 out of 51.

or
1.2%


Any two suited cards:
ODDS: 3.25 to 1.
CHANCES: 1 in 4.25.
PERCENT: 23.53%.
MATH: (51/12)

EXPLANATION:
It doesn't matter what your first card is. The second After you get your first card there will only be 51 cards left and only 12 will be the same suit as your first - so 12 out of 51.


24%


Either pocket aces, pocket kings or AK:
ODDS: 46.36 to 1.
CHANCES: 1 in 47.36.
PERCENT: 2.11%.
MATH: (52/8)*(51/7)

EXPLANATION:
This is a good calculation to do if you are getting deep into a tournament where you are in the middle of the pack and need to double up in order to get up near the chip lead and want to do it with a really good hands. There are 8 Aces or Kings for you to get as your first card. After that there are 7 Aces or Kings left.

or or
2.1%


Pocket Pair:



Flopping a set or better (with a pocket pair) - 7.5/1 (11.8%)

A set - 8.51/1 (11.76%)
ODDS: 8.51 to 1.
CHANCES: 1 in 9.51.
PERCENT: 11.76%.
MATH: 1-[(48/50)*(47/49)*(46/48)]

EXPLANATION:
Sometimes it is easier to calculate the odds of the opposite. Here I am going to calculate the odds of NOT flopping a set and subtract it from one. To calculate the odds of not flopping a set all the cards on the flop can't have the same rank as your pocket pair. For the first card there are 48 out of 50 cards that won't hit your set. For the second card there are 47 out of 49 cards and for the third card there are 46 out of 48 cards that won't hit your set.


10.8%


FLOP


A full house:


0.7%


FLOP


Quads
ODDS: 407.33 to 1.
CHANCES: 1 in 408.33.
PERCENT: 0.245%.
MATH: (2/50)*(1/49)*(48/48) + (48/50)*(2/49)*(1/48) + (2/50)*(48/49)*(1/48)

EXPLANATION:
There are 3 different board combinations that can give you quads. Either the 1st and 2nd flop cards match your pocket pair, the 2nd and 3rd flop cards hit your pocket pair, or the 1st and 3rd cards hit your pocket pair. And in all 3 scenarios the other card will always NOT match your pocket pair. What we will do here is calculate the odds of all 3 scenarios and add them together. Scenario #1. The odds of the 1st flop card hitting your pocket pair is 2 out of 50. The odds of the second flop card hitting your pair is 1 out of 49. The odds that the third one will not hit your pair are 48 out of 48. That is how we arrive at the first part of the equation - (2/50)*(1/49)*(48/48). The "48/48" comes out to 1 and can be droppeod from the equation. The second and third scenarios will follow the logic of the first.


0.2%


FLOP


Making a set or better by the river - 4.2/1 (19%)



19%


BOARD


Starting with 2 suited cards, the probability of:



Flopping a flush:

ODDS: 117.79 to 1.
CHANCES: 1 in 118.79.
PERCENT: 0.84%.
MATH: (50/11)*(49/10)*(48/9)

EXPLANATION:
There are 13 cards of each suit. Assuming you have 2 suited cards then there are only 11 cards left of that suit. And there are only 50 cards left in the deck. The probability of the first flop card being of your suit is 11 in 50. Then the second card 10 in 49 and then the last card 9 in 48.


0.84%


FLOP


Flopping a flush draw - 8.1/1


10.9%


FLOP


Flopping a backdoor flush draw: (3 flush cards) - 1.4/1



41.6%


FLOP


Making a flush by the river - 15/1



6.4%



BOARD


With 2 unsuited cards, the probability of:


Flopping a flush draw:
ODDS: 43.5 to 1.
CHANCES: 1 in 44.55.
PERCENT: 2.24%.
MATH: (50/24)*(49/11)*(48/10)

EXPLANATION:
There are 13 cards of each suit. Assuming you have 2 unsuited cards then there are only 12 cards left of each suit that you have. And there are only 50 cards left in the deck. The probability of the first flop card being of either of your suits is 24 in 50 (12 of each suit). Then the second flop card has to be the same suit as the first flop card. There will only be 11 of that particular suit left. The river has to be the same suit as the turn and there will only be 10 of that suit left.


2.2%


FLOP


Flopping a backdoor flush draw: (3 flush cards) - 6.8/1 (12.8%)


12.8%


FLOP


Making a flush by the river - 53/1


1.8%


BOARD


With 2 non-pair cards, the probability of flopping:
At least a pair (using your pocket cards) from two non-pair cards - 2.1/1


32.4%

or better
FLOP


Exactly one pair: (using your pocket cards) from two non-pair cards
ODDS: 2.45 to 1.
CHANCES: 1 in 3.45.
PERCENT: 28.96%.
MATH: ((6/50) * (44/49) * (43/48)) + ((44/50) * (6/49) * (43/48)) + ((44/50) * (43/49) * (6/48))


29%


FLOP


Flop scenario:


There are 3 different board combinations that can give you 1 pair on the flop. Either the 1st flop card pairs one of your pocket cards and the next 2 don't, the 2nd flop card matches your pocket card and the 1st and 3rd don't, or the 3rd flop card matches your pocket cards and the first 2 don't. So I calculated the odds of each happening and added them all together.

* Scenario 1.
The chances of the 1st flop card hitting your pocket cards is 6 out of 50. The chances of the second flop card NOT hitting your pocket cards (given the fact that the first one did) is 44 out of 49. The chances that the third one will NOT hit your pocket cards (given the fact the the first one did and the second one didn't) is 43 out of 48. Therefore the chances that the first flop card will match your pocket card while the 2nd AND 3rd won't is (6/50) * (44/49) * (43/48).

* Scaenario 2.
The chances of the first flop card not hitting your pocket cards is 44/50. The chances of the second card hitting your pocket cards (given that the first flop card did) is 6/49. The chances of the third flop card hitting your pocket card (given the fact that the first one didn't and the second one did) is 43/48. Therefore, the chances of only the second flop card hitting you is (44/50) * (6/49) * (43/48).

* Scenario 3.
The chances of the first card not hitting you is 44/50. The chances of the second flop card not hitting you (given the fact that the first one didn't) is 43/49. The chances of the third flop card hitting you (guiven the fact that the first 2 didn't) is 6/48. Therefore, the chances of only the third flop card hitting you is (44/50) * (43/49) * (6/48)

.If we add all 3 scenarios together we get: ((6/50) * (44/49) * (43/48)) + ((44/50) * (6/49) * (43/48)) + ((44/50) * (43/49) * (6/48)) = .2896 or 28.96%


Two pair: (using both of your pocket cards) from two non-pair cards - 49/1


ODDS: 48 to 1.
CHANCES: 1 in 49.
PERCENT: 2.02%.
MATH: ((6/50) * (3/49) * (44/48)) + ((6/50) * (44/49) * (3/48)) + ((44/50) * (6/49) * (3/48))


2%


FLOP


Board combination senarios:


There are 3 different board combinations that can give you 2 pair on the flop using both your hole cards. Either the 1st & 2nd flop card pairs your pocket cards and the last one doesn't, the 1st & 3rd flop cards match your pocket cards and the 2nd doesn't, or the 2nd & 3rd flop cards match your pocket cards and the 1st one doesn't. So I calculated the odds of each happening and added them all together.

* Scenario 1.
The chances of the 1st flop card hitting your pocket cards is 6 out of 50. The chances of the second flop card hitting your OTHER pocket card (given the fact that the first one did) is 3 out of 49. The chances that the third one will NOT hit your pocket cards (given the fact the the first two did) is 44 out of 48. Therefore the chances that the 1st & 2nd flop cards will match each of your pocket cards while the 3rd one doesn't is (6/50) * (3/49) * (44/48).

* Scaenario 2.
The chances of the 1st fop card hitting your pocket cards is 6 out of 50. The chances of the second card not hitting your pocket cards (given that the first flop card did) is 44/49. The chances of the third flop card hitting your OTHER pocket card is 3/48. Therefore, the chances that the 1st and 3rd flop cards will match each of your pocket cards while the second one doesn't is (6/50) * (44/49) * (3/48).

* Scenario 3.
The chances of the first card not matching your pocket cards is 44/50. The chances of the 2nd flop card hitting you (given the fact that the first one didn't) is 6/49. The chances of the 3rd flop card hitting your other pocket card is 3/48. Therefore, the chances of the 2nd & 3rd flop cards hitting each of your pocket cards is (44/50) * (6/49) * (3/48).

If we add all 3 scenarios together we get: ((6/50) * (3/49) * (44/48)) + ((6/50) * (44/49) * (3/48)) + ((44/50) * (6/49) * (3/48)) = .02020 or 2.02%


Board combination senarios:

There are 3 different board combinations that can give you 1 pair on the flop. Either the 1st flop card pairs one of your pocket cards and the next 2 don't, the 2nd flop card matches your pocket card and the 1st and 3rd don't, or the 3rd flop card matches your pocket cards and the first 2 don't. So I calculated the odds of each happening and added them all together.

* Scenario 1.
The chances of the 1st flop card hitting your pocket cards is 6 out of 50. The chances of the second flop card NOT hitting your pocket cards (given the fact that the first one did) is 44 out of 49. The chances that the third one will NOT hit your pocket cards (given the fact the the first one did and the second one didn't) is 43 out of 48. Therefore the chances that the first flop card will match your pocket card while the 2nd AND 3rd won't is (6/50) * (44/49) * (43/48).

* scenario 2.
The chances of the first flop card not hitting your pocket cards is 44/50. The chances of the second card hitting your pocket cards (given that the first flop card did) is 6/49. The chances of the third flop card hitting your pocket card (given the fact that the first one didn't and the second one did) is 43/48. Therefore, the chances of only the second flop card hitting you is (44/50) * (6/49) * (43/48).

* Scenario 3.
The chances of the first card not hitting you is 44/50. The chances of the second flop card not hitting you (given the fact that the first one didn't) is 43/49. The chances of the third flop card hitting you (guiven the fact that the first 2 didn't) is 6/48. Therefore, the chances of only the third flop card hitting you is (44/50) * (43/49) * (6/48).

If we add all 3 scenarios together we get: ((6/50) * (44/49) * (43/48)) + ((44/50) * (6/49) * (43/48)) + ((44/50) * (43/49) * (6/48)) = .2896 or 28.96%


Flop scenario

There are 3 different board combinations that can give you 2 pair on the flop using both your hole cards. Either the 1st & 2nd flop card pairs your pocket cards and the last one doesn't, the 1st & 3rd flop cards match your pocket cards and the 2nd doesn't, or the 2nd & 3rd flop cards match your pocket cards and the 1st one doesn't. So I calculated the odds of each happening and added them all together.

* Scenario 1.
The chances of the 1st flop card hitting your pocket cards is 6 out of 50. The chances of the second flop card hitting your OTHER pocket card (given the fact that the first one did) is 3 out of 49. The chances that the third one will NOT hit your pocket cards (given the fact the the first two did) is 44 out of 48. Therefore the chances that the 1st & 2nd flop cards will match each of your pocket cards while the 3rd one doesn't is (6/50) * (3/49) * (44/48).

*Scaenario 2.
The chances of the 1st fop card hitting your pocket cards is 6 out of 50. The chances of the second card not hitting your pocket cards (given that the first flop card did) is 44/49. The chances of the third flop card hitting your OTHER pocket card is 3/48. Therefore, the chances that the 1st and 3rd flop cards will match each of your pocket cards while the second one doesn't is (6/50) * (44/49) * (3/48).

* Scenario 3.
The chances of the first card not matching your pocket cards is 44/50. The chances of the 2nd flop card hitting you (given the fact that the first one didn't) is 6/49. The chances of the 3rd flop card hitting your other pocket card is 3/48. Therefore, the chances of the 2nd & 3rd flop cards hitting each of your pocket cards is (44/50) * (6/49) * (3/48).

If we add all 3 scenarios together we get: ((6/50) * (3/49) * (44/48)) + ((6/50) * (44/49) * (3/48)) + ((44/50) * (6/49) * (3/48)) = .02020 or 2.02%


Odds that the flop will be:


Three of a kind: - 424/1 (0.24%)

ODDS: 424 to 1.
CHANCES: 1 in 425.
PERCENT: 0.24%.
MATH: (51/3)*(50/2)

EXPLANATION:
This is ignoring what your pocket cards are so we will start with 52 cards. It doesn't matter what the first card on the flop is - only that the second and third flop cards have the same rank as the first flop card. After the first card comes on the flop there are only 3 cards of that rank left and the odds of the second flop card being the same rank as the first are 3 in 51. Then the odds of the third flop card being the same rank as the first two are 2 in 50.


0.24%


A pair :- 5/1





Three suited cards:

ODDS: 18.32 to 1.
CHANCES: 1 in 19.32.
PERCENT: 5.18%.
MATH: (51/12)*(50/11)

EXPLANATION:
This is ignoring what your pocket cards are so we will start with 52 cards. It doesn't matter what the first card on the flop is - only that the second and third flop cards have the same suit as the first flop card. After the first card is dealt there is only 12 cards left of that suit. After the turn there aer only 11 cards left of that suit.


5.2%


Two suited cards: - 0.8/1




No suited cards:
ODDS: 1.51 to 1.
CHANCES: 1 in 2.51.
PERCENT: 39.76%.
MATH: (51/39)*(50/26)

EXPLANATION:
This is ignoring what your pocket cards are so we will start with 52 cards. It doesn't matter what the first card on the flop is - only that the other two flop cards don't match the suit of each other. When the second card comes it has to be one of the 3 other suits (13 cards of each suit) than the first flop card. So that's 39 cards out of 51. Then the third flop card needs to be one of the 2 suits that hasn't been flopped yet. So that is 26 cards out of 50.


Three cards in sequence - 28/1:



3.5%


Two cards in sequence - 1.5/1:



40%

No cards in sequence - 0.8/1:


56%


The turn:



The probability of making:
A full house or better from a set on the next card

ODDS: 5.71 to 1.
CHANCES: 1 in 6.71.
PERCENT: 14.89%.
MATH: (47/7)

EXPLANATION:
There are 6 cards to make you a full house and 1 card to make you quads so the odds are 7 out of 47.


15%


A full house from two pair on the next card:
ODDS: 10.75 to 1.
CHANCES: 1 in 11.75.
PERCENT: 8.51%.
MATH: (47/4)

EXPLANATION:
You have 4 cards to hit your boat.


9%



A flush from a four-flush on the next card:

ODDS: 4.22 to 1.
CHANCES: 1 in 5.22.
PERCENT: 19.15%.
MATH: (47/9)

EXPLANATION:
You have 9 cards left of your suit to hit your flush.


19%



A straight from an open-ended straight draw on the next card

ODDS: 4.88 to 1.
CHANCES: 1 in 5.88.
PERCENT: 17.02%.
MATH: (47/8)

EXPLANATION: You have 8 cards left to hit your straight.


17%



A straight from a gutshot straight draw on the next card


ODDS: 10.75 to 1. CHANCES: 1 in 11.75. PERCENT: 8.51%.
MATH: (47/4)

EXPLANATION:
You have 4 cards left to hit your straight.


9%


A pair or better from two overcards by the river - (6 outs) 3.2 to 1


24%



Flop to River:


The probability of making:
A full house or better from a set by the river - 2/1



33%



A full house or better from two pair by the river (4 outs) - 5.1 to 1


17%



A flush from a four-flush by the river (9 outs) - 1.9 to 1



35%



A backdoor flush by the river - 23 to 1



4.2%



Hand Matchups - Pre-Flop


Overpair vs. Underpair:



80.9%

19.1%


80.2%

19.8%


Pocket Aces vs. non-pair:


86,3%

13.6%


80.1%

19.3%


Pocket Aces vs. Suited Connectors:


77%

23%


Pair vs. Two Overcards:



56.9%

43.1%


51.6%

48.3%


Pair vs. One Overcard (unsuited)


70.3%

29.7%


Pair vs. One Overcard (suited)



66.6%

33.8%


Dominated Hands



73.7%

26.3%


69.4%

30.6%


72.6%

27.4%


Two Overcards vs. Non-Pair


62.6%

37.4%


58.8%

41.2%


One overcard vs. Non-pair


56.2%

43.9%


52.6%

47.4%


Hand Matchups - On the Flop


Flush draw vs. Top Pair


38.6%

BOARD

61.4%


Flush draw vs. 2 Pair



35.9%

BOARD

64.1%


Flush draw vs. A set


25.6%

BOARD

74.4%


Flush vs. Top Pair



97.1%

BOARD

2.9%


Flush vs. 2 Pair


82.5%

BOARD

17.5%


Flush vs. A Set



65.5%

BOARD

34.5%


Bottom 2 pair vs. Top pair


74.5%

BOARD

25.5%


Bottom 2 pair vs. An overset


0.2%

BOARD

99.8%


Top 2 pair vs. An underset



16.8%

BOARD

83.2%


Top pair(bad kicker) vs. Top pair (good kicker)


12.7%

BOARD

87.3%


Open-ended straight draw vs. A set


25.9%%

BOARD

74.1%


Open-ended straight draw AND a flush draw vs. Top pair


55.3%

BOARD

44.6%


Open-ended straight draw AND a flush draw vs. A set


40.6%

BOARD

59.4%


A set vs. A higher set


4.3%

BOARD

95.7%


Inside straight draw vs. Over Pair



18.7%

BOARD

81.3%


Inside straight draw vs. Under Pair



38.6%

BOARD

61.4%


Inside straight draw vs. Two pair


19.7%

BOARD

80.3%


Inside straight draw vs. A set


13.7%

BOARD

86.2%

Underpair vs. 2 overcards


75.3%

BOARD

24.7%


Hand Matchups - Going Into the River


Flush draw vs. Top Pair



20.5%

BOARD

79.5%


Flush draw vs. 2 Pair


20.5%

BOARD

79.5%


Flush draw vs. A set


15.9%

BOARD

84.1%


Flush vs. 2 Pair



90.1%

BOARD

9.9%


Flush vs. A Set


77.3%

BOARD

22.7%


Bottom 2 pair vs. Top pair


81.8%

BOARD

18.2%


Top pair(bad kicker) vs. Top pair (good kicker)



6.8%

BOARD

93.1%


Open-ended straight draw vs. A set


18.2%

BOARD

81.2%


Open-ended straight draw AND a flush draw vs. Top pair


34.1%

BOARD

65.9%


Open-ended straight draw AND a flush draw vs. A set


29.5%

BOARD

70.5%


A set vs. A higher set


2.3%

BOARD

97.7%


Inside straight draw vs. Over Pair


9.1%

BOARD

90.1%


Inside straight draw straight draw vs. Under Pair



22.7%

BOARD

77.3%


Inside straight draw straight draw vs. Two pair



9.1%

BOARD

90.9%

Inside straight draw straight draw vs. A set


9.1%

BOARD

90.1%


Questions and Answer



QUESTION:

What is the probability of getting pocket pairs 4 hands in a row when i play 200 hands?


ANSWER:
The odds against getting a pocket pair are 16-1, meaning that there is a one in 17 chance. 17^4 = 83,521. So, the odds that your next four hands will contain pocket pairs is 83,520 to 1.

The probability that during a given sequence of 200 hands you will see four consecutive pocket pairs is approximately 1 in 83,521/197 = about 1 in 424. Note that 197 is used (not 200) because the beginning of the sequence of four hands can't start after the 197th hand.

The exact probability of seeing at least one group of four consecutive pocket pairs in 200 hands is 1-(83,520/83,521)^197.


Open-ended straight draw AND a flush draw vs. A set


29.5%

BOARD

70.5%


A set vs. A higher set



2.3%

BOARD

97.7%


Inside straight draw vs. Over Pair



9.1%

BOARD

90.1%


Inside straight draw straight draw vs. Under Pair



22.7%

BOARD

77.3%


Inside straight draw straight draw vs. Two pair


9.1%

BOARD

90.9%


Inside straight draw straight draw vs. A set


9.1%

BOARD

90.1%


QUESTION:

What is the probability that I will get pocket pairs on 4 out of 4 hands?


ANSWER:

The odds against getting a pocket pair are 16-1, meaning that there is a one in 17 chance. 17^4 = 83,521. So, the odds that your next four hands will contain pocket pairs is 83,520 to 1.


QUESTION:

What is the probability of getting pocket pairs 4 hands in a row when i play 200 hands?


ANSWER:

The odds against getting a pocket pair are 16-1, meaning that there is a one in 17 chance. 17^4 = 83,521. So, the odds that your next four hands will contain pocket pairs is 83,520 to 1.

The probability that during a given sequence of 200 hands you will see four consecutive pocket pairs is approximately 1 in 83,521/197 = about 1 in 424. Note that 197 is used (not 200) because the beginning of the sequence of four hands can't start after the 197th hand.

The exact probability of seeing at least one group of four consecutive pocket pairs in 200 hands is 1-(83,520/83,521)^197.


Chances of flopping:




Poker Odds Charts: