Understanding poker odds and probabilities is a necessary foundation for success at the tables. One could argue it also makes the game more fun (mainly because winning is fun).
Luckily, the topic of poker hand odds doesn’t need to be too complicated or difficult. While the mathematical basis of poker is complex, having an understanding of the most important poker odds can make the biggest difference to our game. This will make playing the best US poker sites a breeze.
While the thought of calculating poker hands probability can be daunting at first, we aim to provide a simple overview of all key concepts and situations. This will allow us to know how to play Texas Hold’em in a whole new, much more profitable light.
What are Odds and Probabilities in Poker?
Odds and probabilities are two different concepts that express the same information in separate ways. Probability tells us the percentage chance of something occurring. In poker probability terms, for example, when you take any random five cards out a 52-card deck, you will make a two-pair hand 4.75% of the time.
Odds, on the other hand, are numbers that count and compare two outcomes. This will tell us how often something happens versus how often it does not.
Odds can be converted to probabilities and vice versa. If an event has a probability of 4.75% (we make two pair with five cards), we can convert this into odds by dividing 100 (percent) with 4.75 (percent). This tells us the odds of this event happening will be approximately 1 in every 21 cases. Here, we’re comparing our favorable outcome (making two pair) to all possible outcomes.
We can also express this as “odds for” or “odds against.”
- Odds against making two pair are 20-to-1—this means we will miss two pair 20 times for every 1 time we hit it.
- Odds for making two pair are 1-to-20—this shows the reverse: we will hit two pair 1 time for every 20 times we miss.
In everyday conversation, people sometimes use the terms odds and probabilities interchangeably— for example, they talk about “odds” but use percentages. The important takeaway is that they express the same information and you can easily convert between the two, so you can work with whichever concept feels more comfortable.
How Do We Calculate Odds and Probabilities?
In a typical situation, we calculate poker hand odds by counting individual outcomes.
In other words, we determine cards or combinations of cards that fit a certain scenario or hand (let’s call them favorable outcomes or cards), and compare them to either the number of all possible outcomes (e.g. all remaining cards in the deck) or opposite outcomes (unfavorable outcomes or cards).
For example, when we flop a flush draw, 9 cards make a flush on the turn out of 47 remaining cards (favorable), while 38 cards do not make a flush (unfavorable).
The odds against making a flush are 38:9 and odds for making it are 9:38.
To get odds into the common format (x to 1 or 1 to x), we just need to divide 9 by 38 (odds for) and 38 by 9 (odds against). The simplest way to do this is to always divide the bigger number with the smaller one. In this case 38 divided by 9 = 4.2.
The odds are 4.2-to-1 against us making the flush on the turn, and 1-to-4.2 for the flush.
We can also say that the flush will come in on the turn 9 every 47 times (comparing favorable outcomes to all outcomes), simplified to 1 in 5.2 times or 19% of the time.
That’s it! Now that the math is out of the way, we’re ready to have a closer look at using odds and probabilities at all key stages of a poker hand.
Poker Hand Rankings and Probability
The strength of a poker hand is closely connected to the probability of us making it. The hands that are rare and difficult to make are stronger than the hands that we are more likely to make. So when you learned how to play poker, you probably figured out that’s why poker hand rankings are ordered as such.
For those who may have forgotten or are unfamiliar with poker hand rankings, go check out our convenient poker cheat sheet.
There are 2,598,960 distinct five-card hands (combinations) we can make from a standard 52-card deck. The table below shows the number of combinations for each hand rank in poker and the odds and probabilities of making it.
Odds and Probabilities When Dealt Five Random Cards
| Hand Rank | Combinations | Odds | Probability |
|---|---|---|---|
| Royal Flush | 4 | 1 in 649,740 | 0.000154% |
| Straight Flush | 36 | 1 in 72,193 | 0.00139% |
| Four-of-a-Kind | 624 | 1 in 4,165 | 0.0240% |
| Full House | 3,744 | 1 in 694 | 0.1441% |
| Flush | 5,108 | 1 in 509 | 0.1965% |
| Straight | 10,200 | 1 in 255 | 0.3925% |
| Three-of-a-Kind | 54,912 | 1 in 47 | 2.1128% |
| Two Pair | 123,552 | 1 in 21 | 4.7539% |
| One Pair | 1,098,240 | 1 in 2.4 | 42.2568% |
| High Card | 1,302,540 | 1 in 2 | 50.1177% |
In Texas Holdem, a five-card hand needs to be made by the river, which means that we actually have seven cards to make it. This means the odds in a No Limit Hold’em game are significantly improved.
Odds and Probabilities in Texas Hold’em (Made Hand By the River)
| Hand Rank | Combinations | Odds | Probability |
|---|---|---|---|
| Royal Flush | 4,324 | 1 in 30,939 | 0.00323% |
| Straight Flush | 37,260 | 1 in 3,590 | 0.0278% |
| Four-of-a-Kind | 224,848 | 1 in 594 | 0.168% |
| Full House | 3,473,184 | 1 in 37.5 | 2.60% |
| Flush | 4,047,644 | 1 in 33.05 | 3.025% |
| Straight | 6,180,020 | 1 in 21.65 | 4.62% |
| Three-of-a-Kind | 6,461,620 | 1 in 20.7 | 4.83% |
| Two Pair | 31,433,400 | 1 in 4.26 | 23.50% |
| One Pair | 58,627,800 | 1 in 2.23 | 43.83% |
| High Card | 23,294,460 | 1 in 5.75 | 17.41% |
If we make it to the river in Texas Hold’em, we can see that we make a pair more often than not, and a hand will sooner make two pair than no pair at all.
Hole Cards: How Often Is a Hand Dealt in Texas Hold’em?
There are 1326 total distinct combinations hole cards that we can be dealt, though they can be sorted into just a few common categories. Here are the combinations, odds and probabilities for starting hands in Texas Hold’em:
| Starting Hand | Combinations | Odds | Probability |
|---|---|---|---|
| Any Hand | 1,326 | 1 in 1 | 100% |
| AA (or any specific pocket pair) | 6 | 1 in 221 | 0.45% |
| Any pocket pair | 78 | 1 in 17 | 5.88% |
| Pair KK+ | 12 | 1 in 110.5 | 0.90% |
| Pair QQ+ | 18 | 1 in 73.7 | 1.4% |
| Pair JJ+ | 24 | 1 in 55.3 | 1.8% |
| AKs (or any specific suited hand) | 4 | 1 in 331.5 | 0.30% |
| AKo (or any specific offsuit hand) | 12 | 1 in 110.5 | 0.90% |
| AK (or any specific unpaired hand) | 16 | 1 in 82.8 | 1.21% |
| Pair TT+ or AK | 46 | 1 in 28.8 | 3.4% |
| Suited cards (any) | 312 | 1 in 4.3 | 23.53% |
| Connected cards | 208 | 1 in 6.4 | 15.7% |
| Suited connectors | 52 | 1 in 25.5 | 3.92% |
| Suited broadways (T or better) | 40 | 1 in 33 | 3.02% |
Heads Up: Odds of Two Hands Against Each Other
We are now going to look at how various hands fare against each other preflop. Each row in the chart below represents a common heads-up scenario where two players are all in preflop.
| Hero Hand | Villain Hand | Hero Win Probability | Villain Win Probability | Odds to Win |
|---|---|---|---|---|
| KK | 77 | 80% | 20% | 4:1 |
| KK | 82.2% | 17.8% | 4.6:1 | |
| AKo | 57% | 43% | 1.32:1 | |
| 88 | AJo | 55.5% | 44.4% | 1.25:1 |
| 88 | AJs | 52.5% | 47.5% | 1.16:1 |
| KK | AJo | 72% | 28-29% | 2.4:1 |
| KK | AJs | 67.3% | 32.3% | 2.09:1 |
| AKo | JTo | 63% | 36% | 1.75:1 |
| AKo | J2o | 68% | 32% | 2.1:1 |
| AKo | 87s | 58-59% | 41-43% | 1.4:1 |
| AQo | QTo | 72% | 26.5% | 2.7:1 |
| A7o | QTo | 56% | 43.7% | 1.28:1 |
| ATo | J9o | 62% | 37.6% | 1.65:1 |
| AA | 87s | 77% | 22% | 3.4:1 |
| AA | AKo | 93% | 6% | 15.5:1 |
The shown odds and probabilities for various scenarios are averages and approximations. In some cases, two similar match-ups are shown to show the differences within scenarios. For example, all pair vs. pair odds are not the same.
All in all, heads-up odds are affected by factors such as shared suits, connectedness, proximity of the cards, and suitedness. It’s worth looking at these concepts to get an idea what makes a hand fare better or worse against other hands.
If the suits are shared between two unsuited hands, higher cards (paired or not) will have more of an advantage against lower cards than if the suits are not shared. The difference in all of these situations is not a lot, usually up to 2 % in equity.
Proximity of the Cards
Heads-up odds are affected by the proximity of cards (for both unpaired and paired hands). Proximity always works in the favor of the hand that is ahead in equity.
For example, 77 will do slightly better against KK than QQ. This is because the opponent’s kings reduce straight options for the queens. Similarly, 76 will do about 3% better against AK than QJ, and AK will do about 2.5% better against 88 than against QQ.
Connectivity
Connected, unpaired hands have more equity than disconnected unpaired hands. For example, T9o (36-37%) does about 5-6% better against AKo than J2o. Despite the ten being lower than the jack, T9o can make many straights with just three of the community cards while J2o will need the help of four cards to make a rare straight.
Suitedness
Suitedness of unpaired hands adds around 2-4 % in equity to a hand in almost any situation.
Using Poker Probability Charts and Other Tools
Even though suits, connectivity, and proximity of cards can affect the odds in a concrete matchup, the differences between different hands in similar scenarios are small. Poker is a game of small edges in the long run, so these percentages will add up significantly over time.
Remembering and understanding just a few of these key scenarios and matchups goes a long way. Looking at these hand characteristics more closely will deepen our understanding of the game. We can do this by using poker odds calculators and other tools to analyze specific hand matchups on any street.
By using a simple poker probability calculator and studying using the best poker training sites like GTO Wizard, we can tweak our poker tournament strategy to be more profitable.
Postflop: Common Texas Hold’em Poker Hands Odds
Often, the most interesting numbers to poker players are the ones that apply to specific scenarios of how hands are likely to develop on the flop, turn and river.
Odds of Flopping a Made Hand
| Hole Cards | Flopped Made Hand | Odds | Probability |
|---|---|---|---|
| Unpaired Hand | Pair | 1:3.5 | 29% |
| Unpaired Hand | Two Pair | 1 in 49.5 | 2.02% |
| Unpaired Hand | Trips | 1 in 73 | 1.35% |
| Pocket Pair | Set | 1 in 8.5 | 11.8% |
| Connected Cards | Straight | 1 in 77 | 1.3% |
| Suited Cards | Flush | 1 in 119 | 0.8% |
Unpaired Hands Making One Pair
As we can see, an unpaired hand will improve to a pair 29% of the time on the flop.
If we combine the odds for two pair, trips, and straight draws, an unpaired connected hand will make a draw or make a one pair or better hand around 32% of the time.
Pocket Pairs
When assessing the strength of our pocket pair, we first have to ask ourselves: “How likely it is that our opponent has a higher pair or two overcards?” The odds may be higher than you think.
The lower the pair, the more likely it is that our opponents has an overpair, which has us in a very unfavorable position (4 to 1 odds against us). In addition, when our opponents have two overcards, they always have 45-50% equity to win.
Here is how likely it is that at least one of our opponents is dealt an overpair in the three most common scenarios – heads-up, six-handed, and full ring (9 players).
| Pair | Opponent's overpair probability (heads-up) | Opponent's overpair probability (6-max) | Opponent's overpair probability (full ring) |
|---|---|---|---|
| KK | 0.5% | 2.5% | 4% |
| 1% | 4.9% | 7.6% | |
| JJ | 1.5% | 7.1% | 11.2% |
| TT | 1.9% | 9.4% | 14.7% |
| 99 | 2.4% | 11.7% | 18.3% |
| 88 | 2.9% | 13.9% | 21.4% |
| 77 | 3.4% | 16.1% | 24.6% |
| 66 | 3.9% | 18% | 27.4% |
| 55 | 4.4% | 20% | 30.3% |
| 44 | 4.9% | 22.4% | 33.1% |
| 33 | 5.4% | 24.1% | 35.8% |
| 22 | 5.9% | 26% | 38.3% |
It is also interesting to see how often a pair will see at least one overcard on the flop, which will make playing postflop a bit tougher.
| Pocket Pair | Probability of 1+ overcards on the flop |
|---|---|
| KK | 22.6% |
| 41.4% | |
| JJ | 57% |
| TT | 69.5% |
| 99 | 79.3% |
| 88 | 86.7% |
| 77 | 92.1% |
| 66 | 95.8% |
| 55 | 98.1% |
| 44 | 99.4% |
| 33 | 99.9% |
| 22 | 100% |
This information can affect our strategy in a few ways. Lower pairs can sometimes benefit from playing passively, trying to see a flop and to hit a very strong hand (a set) cheaply, preferably against multiple opponents.
Other times, we may play middling pairs more aggressively preflop. We want to thin the field to lower the chances that our opponent(s) beat us when an overcard comes on the flop.
Decisions like this depend on many factors, such as the game and format we are playing, our opponents, position, stack, and previous play at the table.
Odds do not define the way we will play any particular hand, as there’s no specific way how to play Texas Hold’em. Whether we raise, call, or fold, we should always know the reason we make every single decision on the table.
Set
A pocket pair will flop a set 11.8% of the time. Sets are often hidden monsters andis a big part of the reason why pocket pairs, even small ones, are such a strong and desired hand.
A set can even improve to a full house on later streets, which can see us get paid by very strong hands, such as trips, straights, and flushes.
Once we hit a set, the probability of making a full house or four-of-a-kind by the river is 33.4%, or about one in three times.
The Flush Draw and the Flush
Suited hands are significantly more valuable than unsuited hands as they have a much higher percentage of hitting a flush. When we play our suited cards, the chances that we will make a flush by the river are 6.5%.
Flopping a flush only happens 0.8% of the time, but flopping a flush draw is much more common.
When holding two suited cards, the odds of flopping a flush draw (four cards of the same suit) is about 1 in 9 hands (10.94%).
The probability of making the flush on the turn is 19.2% (9 out of the remaining 47 cards). We have about the same odds (9 in 46) to make it on the river (19.6%).
If we flop a flush draw, the probability to make our flush by the river is 35%.
Open-Ended Straight Draw (OESD)
Similarly to the flush, we rarely flop a straight. When we are holding connected cards (like T9), it only happens 1.3% of the time.
However, we flop an open-ended straight draw with a connected hand 9.6% of the time, or just under 1 in 10 times. An open-ended straight draw gives us 8 outs to a straight (ie. T9 on QJ4). Double-gutshots are also counted here (ie. T9 on Q86).
With one-gappers (ie. T8 or 75), the OESD will only come in 7.26% of the time.
With two-gappers (ie. J8 or 85), we will flop an OESD 4.47% of the time.
Once we hold an OESD, we will hit the straight on the turn 17% of the time, and on the river 17.4% of the time. Together, we will make a straight by the river 31.45% of the time.
Gutshot Straight Draw
Gutshot straight draws are hands where we make four cards to a straight, but we have only 4 outs to make that straight (ie.AQ on JT6). We flop a gutshot with connected cards around 16% of the time.
Gutshot straight draws can be troublesome hands, as they make a straight only 8.5% of the time on the turn and 16.5% of the time by the river.
To summarize, let’s take another look at how often we flop the most common draws with our suited and connected hands.
| Hole Cards | Flopped Hand | Odds | Probability |
|---|---|---|---|
| Suited Cards | Flush Draw | 1 in 9 | 10.94% |
| Connected Cards (JT to 54) | OESD | 1 in 10.4 | 9.6% |
| Connected Cards (JT to 54) | Gutshot | 1 in 6.25 | 16% |
| Suited Hand | Pair or Better or Flush Draw | 1 in 2.37 | 41.6% |
| Suited Connectors (JTs to 54s) | Straight Draw and/or Flush Draw | 1 in 3.4 | 29.05% |
| One-Gappers (QT to 53) | OESD | 1 in 13.8 | 7.26% |
| Two-Gappers (Q9 to 63) | OESD | 1 in 22.4 | 4.47% |
Odds of Improving on the Turn or by the River
And here is an overview of how often the most frequently played hands and the chances that they’ll improve on the turn and/or the river.
| Hand on Flop | Improved Hand | # of Outs on Turn | Made Hand on Turn % | # of Outs on River | Made Hand on River % | Made Hand Turn/River % |
|---|---|---|---|---|---|---|
| One Pair | Two Pair or Trips (hole cards only) | 5 | 10.6% | 5 | 10.9% | 21.35% |
| Trips | Full House or Quads | 7 | 14.9% | 7 | 15.2% | 27.8% |
| Set | Full House or Quads | 7 | 14.9% | 10 | 21.7% | 33.4% |
| Two Overcards | Pair (hole cards only) | 6 | 12.7% | 6 | 13% | 24.1% |
| Flush Draw | Flush | 9 | 19.1% | 9 | 19.6% | 35% |
| OESD | Straight | 8 | 17% | 8 | 17.4% | 31.5% |
| Gutshot | Straight | 4 | 8.5% | 4 | 8.7% | 16.5% |
| Two Overs + Flush Draw | Pair (hole cards only) or Flush | 15 | 31.9% | 15 | 32.6% | 54.1% |
| Flush + OESD | Straight or Flush | 15 | 31.9% | 15 | 32.6% | 54.1% |
| Flush Draw + Gutshot | Straight or Flush | 12 | 25.5% | 12 | 26.1% | 45% |
| Pair + Flush Draw | Two Pair (hole cards only), trips, or flush | 14 | 29.8% | 14 | 30.4% | 51.2% |
| Two Overs + Gutshot | Pair or Straight | 14 | 29.8% | 14 | 30.4% | 51.2% |
Conclusion
We’ve now covered just about all of the key poker hand odds and probabilities. While this may seem like a lot of information to a beginner, these odds become easier to think about and apply quickly over time.
Until this information becomes second nature, we recommend that you print out guides, poker probability charts or use poker odds calculators as you learn the game. All the players who play the best online poker tournaments today had to start somewhere.