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POKER ODDSOVERALL
The probability of being dealt:
Flopping a set or better (with a pocket pair) - 7.5/1 (11.8%)
 
     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
 or better32.4% 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 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 happeneing 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 fop 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 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 happeneing 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% Any two pair from two non-pair cards - 24/1 ODDS: 24 to 1. CHANCES: 1 in 23. PERCENT: 4.04%. MATH: ((6/50) * (3/49) * (44/48)) + ((6/50) * (44/49) * (6/48)) + ((44/50) * (9/49) * (6/48))
 4% FLOP There are 3 different board combinations that can give you 2 pair on the flop. Scenario #1: The 1st flop card hits one of your pocket cards, the 2nd one hits your other pocket card, and the 3rd one misses. Scenario #2: The 1st flop card hits one of your pocket cards, the 2nd one misses your pocket cards, and the last flop card hits EITHER your other pocket card or pairs the card on the board that DIDN'T pair you. Scenario #3: The 1st flop card misses your pocket cards, the 2nd flop card pairs EITHER one of your pocket cards OR the first flop card, and the 3rd flop card hits whatever unpaired cards there are (they could be both of your pocket cards if the board is paired on the first 2 flop cards or it could be your unpaired pocket card and the unpaired board card). So I calculated the odds of each happeneing 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 EITHER your unpaired pocket card OR the unpaired board card is 3+3/48. Therefore, the chances that the 1st and 3rd flop cards will match any unpaired cards while the second one doesn't is (6/50) * (44/49) * (6/48). Scenario #3. The chances of the first card not matching your pocket cards is 44/50. The chances of the 2nd flop card matching either of your hole cards of the first card on the flop is 3+3+3/49. The chances of the 3rd flop card hitting the available unpaired cards is 3+3/48. Therefore, the chances of the 2nd & 3rd flop cards matching any unpaired cards is (44/50) * (9/49) * (6/48). If we add all 3 scenarios together we get: ((6/50) * (3/49) * (44/48)) + ((6/50) * (44/49) * (6/48)) + ((44/50) * (9/49) * (6/48)) = .040408 or 4.04% Trips (using one of your pocket cards) from two non-pair cards - 73/1
 1.35% FLOP A full house (using both of your pocket cards) from two non-pair cards - 1087/1
 0.09% FLOP Quads (using one of your pocket cards) from two non-pair cards ODDS: 9,799 to 1. CHANCES: 1 in 9,800. PERCENT: 0.01%. MATH: (50/6)*(49/2)*(48/1) EXPLANATION: The first card has to be of the same rank as one of the 2 cards you hold. So that is 6 cards out of 50. The second flop card has to be the same as the first flop card and there are 2 of those left so that is 2 out of 49. The last flop card is the only card left out of 48 of the rank of the other 2 on the flop.
0.01% FLOP 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 17% 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 55% 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.   40% 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 from two overcards ODDS: 6.83 to 1. CHANCES: 1 in 7.83. PERCENT: 12.77%. MATH: (47/6) EXPLANATION: You have 6 cards to hit your pair. 
13% 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% A straight from an open-ended straight draw by the river - (8 outs) 2.2 to 1 (32%)
32% A straight from a gutshot straight draw by the river - (4 outs) 5.1 to 1 (17%)
17% A pair or better from two overcards by the river - (6 outs) 3.2 to 1
24% The River The probability of making: A full house or better from a set ODDS: 3.6 to 1. CHANCES: 1 in 4.6. PERCENT: 21.74%. MATH: (46/10) EXPLANATION: You have 9 different cards to hit your boat and 1 card to hit quads.
22.7% A full house from two pair on the final card ODDS: 10.5 to 1. CHANCES: 1 in 11.5. PERCENT: 8.7%. MATH: (46/4) EXPLANATION: You have 4 cards left that match your two pair.
8.7% A flush from a four-flush on the final card ODDS: 4.11 to 1. CHANCES: 1 in 5.11. PERCENT: 19.57%. MATH: (46/9) EXPLANATION: You have 9 cards to hit your pair.
 20% An open-ended straight draw ODDS: 4.75 to 1. CHANCES: 1 in 5.75. PERCENT: 17.39%. MATH: (46/8) EXPLANATION: You have 8 cards to hit your straight.
 17% A gutshot straight draw ODDS: 10.5 to 1. CHANCES: 1 in 11.5. PERCENT: 8.7%. MATH: (46/4) EXPLANATION: You have 4 cards to hit your straight.
 8% A pair from two overcards ODDS: 6.67 to 1. CHANCES: 1 in 7.67. PERCENT: 13.04%. MATH: (46/6) EXPLANATION: You have 8 cards to hit your straight.
 13% 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:
77.0% 23.0% 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
18.2% BOARD 81.2% Flush draw vs. A set
15.9% BOARD 84.1% Flush vs. 2 Pair
90.1% BOARD 9.0% 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% QUESTION: What is the probability that I will get pocket pairs on 4 out of 4 hands?
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. |