Texas Holdem Flop Odds
Check out the Holdem pair pre-flop odds in high resolution universal.pdf format. High Card Hands (Unpaired) Whoever said that Holdem is a high card game was right. Much of the overall Holdem action involves two unpaired high cards like the typical hands illustrated above. Pre Flop Hand Poker Odds Betting before the flop can sometimes be a blind bet, because when the flop comes things can change drastically. What can seem like a clear advantage can turn into a trap when the Turn or River or Flop cards hit the poker games.
Texas Hold'em Cheat SheetOdds Based on Outs after the Flop. If after the flop, you have: Two outs: Your odds are 11 to 1 (about 8.5 percent) A common scenario would be when you have a pair and you are hoping your pair becomes a three-of-a-kind (a set).
The odds below represent the mathematical probability of one of these specific events occurring after the flop, or “post flop”. You can use these post flop odds along with the Best Texas Hold’em Starting Hands to help determine your best play in a given situation.
Want to know the odds of getting dealt a certain hand pre-flop? Check out our Texas Hold’em pre-flop odds. Or for a quick look at poker odds, check out Quick Reference Chart for Poker Odds.
If you are interested in learning the math behind post flop odds, check out our detailed post flop odds math.
| After the Flop | Odds |
| Q-Q not having a Ace or King by the river | 2.49 to 1 |
| Q-Q versus A-K heads up, A or K hitting by river | 1.987 to 1 |
| Flop being all one kind (J-J-J or Q-Q-Q) | 425 to 1 |
| Four flush improving | 2.859 to 1 |
| Open ended straight flush improving | 11.879 to 1 |
| Open ended straight improving | 3.256 to 1 |
| Two Pair making a full house | 5.972 to 1 |
| Trips improving to full house or better | 2.994 to 1 |
| When You Hold A-K Suited | Odds |
| Q, 10, J (for royal flush) | 19,600 to 1 |
| Improves to four of a kind | 9,800 to 1 |
| Improves to full house | 1089 to 1 |
| Flopped flush | 119.5 to 1 |
| Pair of Aces or Kings w/ four flush | 59 to 1 |
| Two of your suite with board paired 2-Q | 54 to 1 |
| Two of your suite | 9.13 to 1 |
| Any Q, J, 10 | 306 to 1 |
| Q-Q or less, one or less of your suite | 6 to 1 |
| Flop two pair | 22 to 1 |
| Q-Q-Q or 2-2-2 | 445 to 1 |
| Ace or King | 3 to 1 |
| Four to a flush | 9 to 1 |
| A-A or K-K making three of a kind | 74 to 1 |
| When You Hold K-K | Odds |
| Flopping four of a kind | 408 to 1 |
| K-A-A | 1633 to 1 |
| A-K any card | 55.7 to 1 |
| Making any full house | 102 to 1 |
| Three of a kind | 9.3 to 1 |
| A-A-A | 4,900 to 1 |
| A-A -7 | 816.6 to 1 |
| Any pair w/ no K or A-A | 6.74 to 1 |
| A and any other cards besides a K | 5.2 to 1 |
| When You Hold Q-J Off Suit | Odds |
| Flop 4-Q’s or J’s | 9,800 to 1 |
| Q-Q-J or J-J-Q | 1,089 to 1 |
| A-K-10 | 306 to 1 |
| K-10-9 or 8-9-10 | 153 to 1 |
| Flopping any straight | 102 to 1 |
| Open-ended straight | 15.3 to 1 |
| Three suited cards of a suite you hold | 45.54 to 1 |
| Flopping three of a kind (no full house) | 63.63 to 1 |
| No A or K | 1.82 to 1 |
| Q’s up or J’s up | 27.2 to 1 |
| Other Important Odds | Odds |
| No pair improving to a pair on the flop | 3 to 1 |
| Suited hole cards w/four to a flush | 12 to 1 |
| One pair improving by river | 5 to 1 |
| Pocket pair improving to trips after the flop | 12 to 1 |
| Two over cards improving to a pair | 4 to 1 |
| Two overs + gutshot straight draw improving to a pair or better | 2 to 1 |
| Gutshot straight draw hitting by the river | 6 to 1 |
| Gutshot + pair improving to two pair or better | 3 to 1 |
| Backdoor flush | 33 to 1 |
| Backdoor flush w/ over card improving to pair or flush | 6 to 1 |
| Backdoor flush with gutshot improving by the river | 5 to 1 |
| Backdoor flush w/ 2 over cards improving at least a pair | 3 to 1 |
| Odds of holding/not holding an Ace (Expressed in %) | Odds |
| 2 players no ace | 71.783% |
| 3 players no ace | 60.141% |
| 4 players no ace | 49.962% |
| 5 players no ace | 41.118% |
| 6 players no ace | 33.486% |
| 7 players no ace | 26.949% |
| 8 players no ace | 21.396% |
| 9 players no ace | 16.723% |
| 10 players no ace | 12.831% |
| The probability that no one besides you has an ace in his or her two hole cards | Odds |
| 2 players | 88.244% |
| 3 players | 77.448% |
| 4 players | 67.571% |
| 5 players | 58.571% |
| 6 players | 50.408% |
| 7 players | 43.040% |
| 8 players | 36.428% |
| 9 players | 30.530% |
| 10 players | 25.306% |
| Ace on flop, chance that someone has an ace down | Odds |
| 5 players | 49.337% |
| 4 players | 41.250% |
| 3 players | 32.316% |
In the previous article on working out preflop hand probability, we worked out the likelihood of being dealt different combinations of starting hands before the flop.
In this article, I will cover the basics of working out the probabilities behind various possible flops. I'll go ahead and cover the probability basics first in case you missed it in the preflop probability article.
- Probability calculations quick links.
A few probability basics.
When working out flop probabilities, the main probabilities we will work with are the number of cards left in the deck and the number of cards we want to be dealt on the flop. So for example, if we were going to deal out 1 card:
- The probability of dealing a 7 would be 1/52 - There is one 7 in a deck of 52 cards.
- The probability of dealing any Ace would be 4/52 - There four Aces in a deck of 52 cards.
- The probability of dealing any would be 13/52 - There are 13 s in a deck of 52 cards.
In fact, the probability of being dealt any random card (not just the 7) would be 1/52. This also applies to the probability being dealt any random value of card like Kings, tens, fours, whatever (4/52) and the probability of being dealt any random suit (13/52).
Each card is just as likely to be dealt as any other - no special priorities in this game!
The numbers change for future cards.
A quick example... let's say we want to work out the probability of being dealt a pair of sevens.
- The probability of being dealt a 7 for the first card will be 4/52.
- The probability of being dealt a 7 for the second card will be 3/51.
Notice how the probability changes for the second card? After we have been dealt the first card, there is now 1 less card in the deck making it 51 cards in total. Also, after already being dealt a 7, there are now only three 7s left in the deck.
Always try and take care with the numbers for future cards. The numbers will change slightly as you go along.
Working out probabilities.
- Whenever the word 'and' is used, it will usually mean multiply.
- Whenever the word 'or' is used, it will usually mean add.
This won't make much sense for now, but it will make a lot of sense a little further on in the article. Trust me.
Texas Holdem Odds After Flop
Total number of flop combinations.
First of all, lets work out the total number of possible flop combinations. In other words, we will just be working out the probability of 'any random flop'.
To work out this probability we simply multiply the probability of 3 individual cards being dealt.
- (random card) * (random card) * (random card)
- (1/52) * (1/51) * (1/50) = 132,600 possible flops.
Pretty big combination of cards huh? However, we've omitted the fact that we know our 2 holecards, so there will be two less known cards in the deck when we are dealing the flop. So if we amend this calculation by starting at 50 instead of 52:
P = (1/50) * (1/49) * (1/48)
P = 1/117,600.
Better, but this 1/117,600 probability is with exact cards in order. In Texas Hold'em it does not make a difference whether the flop comes A K Q or A Q K. So to account for this we multiply this fraction by 6 (1*2*3 = 6).
P = 1/117,600 * 6
P = 1/19,600.
The order of cards on the flop makes no difference, so multiply the probability by 6 to account for this (1 * 2 * 3 = 6 - this is math probability stuff). Don't worry if you don't know why we do this, just take it as it is.
This means that the probability of the flop being A K Q in any order is 1/19,600 - which is exactly the same probability as the flop coming something like 2 5 9 in any order.
So in total there are 19,600 different possible flops in Texas Hold'em.
Probability of specific flops.
Texas Holdem Flop Odds
To work out the probability of specific flops with the cards in any order we simply multiply the probabilities of each of those cards being dealt.
Multiply the 3 probabilities together.
So let's say we want to find the probability of flopping a heart flush.
- There are 2 hearts in our hand.
- There are 11 hearts left in a deck of 50.
P = (11/50) * (10/49) * (9/48)
P = 990/117600 = 1/119
In this example we do not need to multiply the final probability by 6. This is because the order of the cards and their probabilities are important, as the overall probabilities decrease as each heart is dealt.
Overview of working out flop probabilities.
This is a really basic article for working out flop probabilities in Texas Hold'em. Think of it as more of a taster for working out probabilities on the flop to help you get your feet wet.
If I were to continue with probabilities, I would be delving deeper in to mathematics and further away from poker. That wouldn't necessarily be a bad thing, but my maths is a bit rusty and it's not going to directly improve your game, so I'll stop for now. Maybe I'll address it in a future article, but for now this is as far as I'm going to go.
Pre Flop Texas Holdem Odds
If you're really interested in the mathematics of the game, try the book: The Mathematics of Poker by Bill Chen. It's definitely not a light read, but it's very interesting if you enjoy the maths side of the game. For other books, try the poker books section.
Other useful articles.
- Poker mathematics.
- Pot odds.
- Equity in poker.
Go back to the poker odds charts.
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