Poker is very much a maths and statistics-based game. While winning isn’t always guaranteed, playing a strategy that is conducive to following correct poker probabilities and odds will undoubtedly increase your chances of success at the felts.
In this article, we break down the odds in poker and the probabilities associated in the game to help you understand the likelihood of particular and also to teach you overall how to play poker with probability in mind.
Table of Contents
Poker Hands Probability
There are 2,598,960 distinct 5-card hands that can be made/dealt in poker. Let’s take a closer look at how these combinations break down into the various ranks of hands that one can attain in this poker probability chart:
|Poker Hand||Frequency (Distinct Hands)||Probability (%)||Odds (~)|
|Royal Flush||4||0.000154%||1 in 649,740|
|Straight Flush||36||0.00139%||1 in 72,193|
|4-of-a-Kind||624||0.0240%||1 in 4,165|
|Full House||3,744||0.1441%||1 in 694|
|Flush||5,108||0.1965%||1 in 509|
|Straight||10,200||0.3925%||1 in 255|
|3-of-a-Kind||54,912||2.1128%||1 in 47|
|Two Pair||123,552||4.7539%||1 in 21|
|One Pair||1,098,240||42.2569%||1 in 2.4|
|High Card||1,302, 540||50.1177%||1 in 2|
There are a few things to note from this poker probability table:
- The ranking of hands goes up sequentially from the easiest hand to make to the most difficult (unlikeliest) one to have. (Therefore, now you know precisely why flushes rank higher than straights in Texas Hold’em.)
- The probability of a pair in poker is ~42%.
- The chances of making a full house poker probability is less than 1% (~0.1441%)
- The probability in poker Texas Hold’em of making a royal flush is just 1 in 649,740 hands!
- The likelihood of a straight flush in poker is 1 in 72,193 hands or 0.00139%.
Please refer to this chart when determining how likely it is for specific poker hands to appear for you in a game.
How To Find the Probability of Poker Hands
Within our vast 888poker Magazine, we have a plethora of articles that already include all the answers to your burning questions about probabilities and odds regarding specific poker hands.
Check them out using the links below:
- Royal Flush Odds
- Straight Flush Odds
- Four-of-a-Kind Odds
- Full House Odds
- Flush Odds
- Straight Odds
- Three-of-a-Kind Odds
- Two Pair Odds
- One Pair Odds
- High Card Odds
Odds of Being Dealt Certain Hole Cards in Poker
Multiply 52 cards in a standard deck by 51 (for the second card) and then divide this product by 2 (because AcKs is the same thing as being dealt KsAc – just the order it’s dealt in is reversed). You’ll see that there are 1,326 unique 2-card combinations you could receive in Texas Hold’em.
Breaking this down further, if you take a hand like AK, you can multiply the 4 Aces by 4 Kings to see that there are 16 combinations of AK total, both suited an unsuited.
Of these 16 combos, as there are 4 suits in poker, 4 of these AK combinations will be suited, leaving there to be 12 unsuited combinations of unpaired hands. (The same figures go for any non-paired poker hands). For pocket pairs, there will be 6 combinations of each value.
Knowing the above information, we can then do some basic maths to determine the likelihood of getting certain combinations of hole cards.
For example, for Pocket Aces, we would divide 6 combinations by 1,326 total combinations to see that we’ll receive this hand every 1 in 221 hands, on average.
For any specific suited hand, because there are only 4 combos of each holding (instead of 6 like with the pocket pairs), you’ll receive suited non-paired hands (of specific values) less frequently than you will pocket pairs. Therefore,you’ll be dealt a hand like AKs specifically every 1 in 332 hands, on average, meaning you’ll be dealt AA more frequently than you will AKs.
For the last point of this section, if you wanted to figure out the chances of being dealt hand X or better, simply add the number of combinations together for each holding.
For example, if we wanted to find the chances of being dealt QQ+ and/or AK, we’ll see that there are 18 pocket pair combos and 16 combos of AK, making for 34 combos total.
Dividing 1,326 total combos by 34 of these specific combos then means you’ll be dealt AK or QQ+ about 1 in every 39 hands.
Here’s a chart summarizing this essential hole card information outlined above, in addition to containing other probabilities for being dealt combinations of particular holdings:
|Hand||Total Hand Combinations||Probability (%)||Odds|
|Any 2 Cards||1326||100%||1 in 1|
|AK (any specific hand)||16||1.2%||1 in 82.8|
|AKs (any specific suited hand)||4||0.3%||1 in 331.5|
|AKo (any specific off-suit hand)||12||0.9%||1 in 110.5|
|AA (any pocket pair)||6||0.5%||1 in 221|
|KK+||12||0.9%||1 in 110.5|
|QQ+||18||1.4%||1 in 73.7|
|JJ+||24||1.8%||1 in 55.3|
|TT+||30||2.3%||1 in 44.2|
|QQ+, AK||34||2.5%||1 in 39|
|JJ+, AK||40||3.0%||1 in 33.2|
|TT+, AK||46||3.4%||1 in 28.8|
|Any Unpaired, Suited Cards||312||23.5%||1 in 4.3|
|Any Unpaired, Unsuited Cards||936||70.6%||1 in 1.4|
|Any Pocket Pair||78||5.8%||1 in 17|
|Any Suited Connectors||52
||3.9%||1 in 25.5|
Odds of Flopping a Made Hand
The above section dealt with the likelihood of getting certain combinations of hole cards. But, what about poker odds on how those hole cards will improve (and to what degree) on specific flops?
Here’s a chart of various poker hole card probabilities to sift through and get accustomed to regarding the chances of flopping a made hand (of varying strengths):
|Your Hole Cards||Flop (Your Hand)||Probability (%)||Odds|
|Unpaired Cards||A Pair||29.0%||1 in 3.5|
|Pocket Pair||A Set||11.8%||1 in 8.5|
Connected Cards (JT thru 54)
|A Straight||1.3%||1 in 77|
|Suited Connectors||A Flush||0.8%||1 in 119|
Poker Odds: Improving Your Drawing Hands
An “out” in poker is a card that will help improve the strength of your hand. The most frequent of outs are those that will help a player make a straight or a flush.
Here’s a table that explains the odds of improving your hand, depending on the number of outs you have:
Basic Probability Rules Poker
Now, of course, it’ll be difficult to refer to this chart for every hand to see what chances you’ll have of improving and then relate this to the pot odds you’re getting. So, to give you a basic shortcut, use the following trick to help you with how to calculate the probability of your poker hands improving:
If you multiply the number of outs you have on the flop by 4, you’ll get a solid approximation for the chances of making your hand by the turn or river (i.e. with two cards to come).
If you multiply the number of outs you have on the flop or the turn by 2, you’ll get a reliable approximation for the chances of making your hand on the very next card.
Sometimes, you’ll want to vary perhaps the number of outs that will help you improve your hand, to account for the chances of it also helping your opponent improve to an even better hand.
For example, if you think your opponent might have a higher flush draw or if the board pairs giving you a flush and your opponent perhaps a full house, you might lessen your “outs” slightly (e.g. 8.5 outs instead of 9). This adjustment will account for this possibility, when relating it to your pot odds and how you should proceed in the hand.
What If I Wanted To Practice Poker Probability Myself?
The methodology behind practising poker probability problems without using shorthand can certainly still be done.
To do this, you need to add together the probabilities of specific outcomes occurring, for example:
- Hitting one of your outs on the turn
- Hitting one of your outs on the river, but not the turn
EXAMPLE PROBLEM #1: A Normal Flush Draw
To work through a typical poker probability problem, suppose you have a flush draw after the flop and want to simply know the chances of improving to a flush by the river.
With 4 of 13 cards of the suit being revealed already, there are 9 remaining cards (“outs”) that can help you.
And with two hole cards and three flop cards already accounted for, there are 47 unknown cards to you in the deck.
Knowing this, you can do the appropriate calculations and add the results together to determine your chances of making your flush:
- Odds of hitting your flush on the turn: (9/47) = 19.15%
- Odds of hitting your flush on the river: (39/47)*(9/46)= 16.23%
- Odds of making your flush on the turn OR the river: 19.15% + 16.23% = 35.38%
Here, you can see the odds of making a flush by the river after flopping a flush draw is 35.38%. If you take the “shortcut” rule outlined above, you can see that 9 outs multiplied by 4 equals 36%, which is pretty close to the exact answer here.
EXAMPLE PROBLEM #2: A Backdoor Flush Draw
To practice the probabilities of hitting a backdoor flush, you would have to multiply (10 flush outs /47 unknown cards) for the turn by (9 flush outs /46 unknown cards) on the river. The result wouldshow that there’s a ~4.2% chance of a 3-flush on the flop becoming a full, 5-card flush by the river.
Calculating Probability of Poker Hands Heads-Up
One critical thing to note in poker is the difference in terms of equity spread when there is only one opponent versus multiple opponents in a poker hand with you.
Against many players, the equity of everyone’s respective hands is going to be lower than if it was heads-up because it’ll be divided and spread out among the other remaining players.
Take Pocket Aces for example. Against the following Villain range for your opponent(s) -
- Any pocket pair
- Any suited Ace
- Any two broadway cards
- Suited connectors: 54s to T9s
- One-gapped suited connectors: 86s to J9s
- Q9s, K9s
Here are the equity percentages that Pocket Aces has against:
- One opponent: 83.4%
- Two opponents: 70.6%
- Three opponents: 60.2%
- Four opponents: 51.4%
As you can see, the more opponents there are in a hand, the lower the chance AA has of winning, which is why it is so advantageous to have these big pairs play out in a heads-up, low-SPR pot.
And for when you have drawing hands in a multi-way scenario, having more opponents may not change the number of outs you have to improve. However, the chances of someone else having a better draw than you or a hand that could later outdraw you certainly goes up with more opponents.
Additionally, when action is multi-way, it is essential to note that players tend to bluff less and bet more for value if they do bet.
Therefore, considering the last two points, it is crucial always to remember how many opponents are in a hand and determine the best way to go about playing accordingly.
Poker Probability Summary
To increase the probability of winning poker, you must become accustomed to the odds and probabilities that are presented to you in the game. Become familiar with outs and calculating your percentages of improving and be able to quickly relate these to the pot odds you may be getting, so that you can determine if you can call profitably or not.
(For more info on pot odds and bet sizing, check out this Comprehensive Bet Sizing Guide).
Remember also that you don’t always need to “just call” whenever you have a draw. Sometimes, it can be advantageous to bet or raise. This way, you can either win by improving later on to the best hand or getting your opponent to fold.
(See more about equity and fold equity here.)
In summary, and to quote The Hunger Games: “May the (poker) odds be ever in your favour!” Good luck at the felts!
Learn to Turn Your Pocket Aces into Consistent Winners!