If you've played poker online or live for any stretch of time  you've seen hands you never thought possible. Runnerrunner flush draws. Runnerrunner straight draws. Oneouters on the river to crush your massive favorite. But how often do these "longshots" really come in? And how often should we expect it?
Below we've compiled a comprehensive list of unusual longshot odds for Texas Hold'em poker – numbers and percentages to impress (or possibly annoy) your fellow players at the table. And, importantly, to unmask ruthless exaggerators who claim the most unlikely things happened to them just the other day.
Odds of Aces v. Aces
Let's start with some rather simple but quite important odds: being dealt aces. There are 1,326 different holecard combinations in Texas Hold'em poker and 6 of them are aces. Thus the odds of being dealt aces in any hand are 6 to 1,320 or 1 to 221 (or 0.45%). You probably already kcaesar slot free coin that. But what are the odds that one of your opponents is dealt aces as well?
At a fullring table (in this case, 9 players) this should happen only once every 154 times you're dealt aces. A spectacular scenario, but quite unlikely. The odds it happens in a $1m buyin tournament? Too painful to even calculate, but it happened to Connor Drinan in the 2014 WSOP Big One for One Drop.
Running into Aces with Kings
With aces you have nothing to fear before the flop. But with pocket kings there is always this nagging thought in the back of your head. Maybe, just maybe, one of your opponents has aces. Is that a likely scenario? The answer is, as it often is in poker, “it depends."
If you're playing headsup you're only up against one opponent. That opponent only has aces roughly once every 220 hands. So, no. It's not likely he has your kings beat.
But at a fullring table (9 players) with 8 opponents, it's suddenly much more likely. Albeit still a longshot, someone may have aces against your kings. The odds for that to happen are 1 in 26. You're almost always better off disregarding this worstcase scenario, but sometimes really good players can make impressive folds with kings before the flop.
Queens into Kings (and Aces)
With kings it's possible, but unlikely, to run into a better hand preflop. But what about queens? Queens are much more vulnerable. And, while it's still much more likely that you're ahead preflop, you should consider the scenario. That one of your opponents has kings or aces. At a fullring table the odds for that to happen are 1 in 13.
A raise, reraise and an allin in front of you might be a decent indicator that this 1 in 13 event is unfolding and that you're better off folding your hand.
Important Odds for Big Pairs
Scenario  Probability  Odds 
Being dealt aces preflop  0.4525%  1:220 
If you have aces headsup, your opponent has aces as well  0.0816%  1:1,224 
If you have aces at a full ring table, one opponent has aces as well  0.6512%  1:153 
If you have kings headsup, your opponent has aces  0.4898%  1:203 
If you have kings at a full ring table, one opponent has aces  3.8518%  1:25 
If you have queens headsup, your opponent has kings or aces  0.9796%  1:101 
If you have queens at a full ring table, at least one opponent has kings or aces  7.5732%  1:12 
Set Over Set
Let's move on to some postflop odds  specifically sets, meaning trips with a pocket pair. How often do you flop a set? Every ambitious poker player should know this number by heart: roughly 12% of the time or once every 9 times you see a flop with your pair. A scenario many poker players are afraid of is the dreaded set over set: you flop a set but one of your opponents flops a better set.
Although quite unlikely, this scenario is not that uncommon. If two players have pocket pairs, both will flop a set simultaneously roughly once every 100 flops. You still need two players to have a pocket pair at the same time for that to happen. At a fullring table you can expect to see a setoverset scenario roughly once every 1,200 hands (assuming all players with pocket pairs always see a flop).
Headsup this scenario is much more unlikely, though. It should happen only once every 42,000 hands. So there's no need to worry about better sets with only one opponent – unless of course you're Phil Ivey playing Scotty Nguyen in one of the biggest headsup tournaments on TV.
Set Over Set Over Set
Set over set situations are already very uncommon. But what about some truly longshot scenarios? What about three players all flopping a set at the same time? The math shows this scenario is extremely unlikely. At a fullring table you'll only see that every 166k hands. With only three players at the table, this number increases to once every 14 million hands. A true longshot!
Important Set Over Set Odds
Scenario  Probability  Odds 
If you have a pair, you hit a set (trips) on the flop  11.7551%  1:8 
Being dealt a pair and flopping a set  0.6915%  1:144 
If two players have pair, both flop a set  1.0176%  1:97 
Headsup both players are dealt a pair and flop a set  0.0024%  1:42,305 
Two players at a 6maxtable are dealt a pair and both flop a set  0.0355%  1:2,819 
Two players at a full ring table are dealt a pair and both flop a set  0.0851%  1:1,174 
Three players at a 3maxtable are dealt and pair and all three flop a set  0.0000%  1:13,960,821 
Three players at a 6maxtable are dealt and pair and all three flop a set  0.0001%  1:698,040 
Three players at a full ring table are dealt and pair and all three flop a set  0.0006%  1:166,199 
How Often Do You Hit Quads?
While sets are great hands, let’s now look at even better poker hands: quads. Only bested by straight flushes, quads are the secondbest possible holding in Texas Hold’em and occur only very infrequently. How infrequently?
Well, if you hold a pocket pair and go all the way with it, you’ll hit a set by the river once every 123 attempts – infrequently, but still more likely than being dealt aces before the flop.
Quads over Quads: Does it Happen?
Set over set is already quite unlikely but what about one step further? Can you calculate the poker odds of two players who start with pocket pairs both hitting quads  quads over quads? Well, the odds for that are pretty slim: With two players holding a pocket pair both will hit quads by the river roughly once every 39,000 attempts.
Factoring in the odds of having two players being dealt pocket pairs before the flop, you’ll see such a scenario at a fullring table only once every 313k hands – for most live poker players, this already is a onceinalifetime scenario.
Odds for Making Quads in Poker
Scenario  Probability  Odds 
If you have a pair, you hit quads until the river  0.8163%  1:122 
If two players have a pair, both hit quads until the river  0.0026%  1:38,915 
Headsup both players are dealt a pair and both hit quads  0.00000008%  1: 11,255,911 
Two players at a 6maxtable are dealt a pair and both hit quads  0.0001%  1:750,393 
Two players at a full ring table are dealt a pair and both hit quads  0.0003%  1:312,663 
How Often Do You Flop a Flush?
Let’s take a look at some more postflop odds. If you hold two suited cards, flopping three cards of your suit is your dream scenario. But usually this doesn’t happen. Actually you’ll only flop a flush once every 119 attempts if you start with two suited cards.
How Likely is Flush over Flush?
Your dream scenario of flopping a flush can occasionally turn into a nightmare if one of your opponents flops a better flush. WSOP Champion Joe McKeehen probably still has the occasional night terror from a flushoverflush hand. Where he was on the receiving end of a bad beat against Fedor Holz during the WSOP $111k High Roller in 2016.
But what are the odds? As a matter of fact, if two players start out with two suited cards of the same suit, the odds of both flopping a flush are not as small as one might think. Once every 206 attempts the flop will show three cards of the same suit. Even flush over flush over flush is not that unlikely. If three players have suited cards of identical suits, they’ll all flop a flush once every 434 attempts.
If you want to know how often this happens at a table, you still have to factor in the odds of all those players being dealt matching suited cards. Considering those odds (and assuming every player with suited cards sees the flop – admittedly a bold assumption) you’ll witness a flopped flush over flush once every 540 hands at a full ring table. The triple flush is much more unlikely though and should happen only once every 29k attempts.
Odds for Flushes in Texas Hold'em
Scenario  Probability  Odds 
If you have suited cards, you flop a flush  0.8418%  1:118 
If two players have suited cards, both flop a flush  0.4857%  1:205 
If three players have suited cards, all three flop a flush  0.2306%  1:433 
HeadsUp, both players are dealt suited cards and flop a flush  0.0051%  1:19,490 
Two players at a 6maxtable are dealt suited cards and both flop a flush  0.0770%  1:1,298 
Two players at a full ring table are dealt suited cards and both flop a flush  0.1847%  1:540 
Three players at a 6maxtable are dealt suited cards and all three flop a flush  0.0012%  1:85,758 
Three players at a full ring table are dealt suited cards and all three flop a flush  0.0035%  1:28,585 
Unlucky Streaks in Poker
Have you ever sat at a poker table for hours and not been dealt a single playable hand? Have you ever had someone claim he wasn’t dealt a single ace over dozens  or even hundreds!  of hands? Let’s run some probabilities!
The probability of not being dealt a single pocket pair over 50 hands is a little bit under 5% – unlikely, but very possible. Expand the streak to 200 hands and the probability drops to less 0.0005%. So is the guy to your right is claiming he hasn’t seen a pair over the last two days? He’s almost certainly bullshitting you.
Now most pocket pairs are only really good if you flop a set with them. Let’s take a look at some probabilities and assume you’ll always see a flop with your pocket pairs. The probability of hitting at least one set (i.e. you’re dealt a pair and you flop a set with it) over 100 hands is almost exactly 50%. So over 100 hands you’re as likely to hit at least one set as you are to not hit one.
Over 500 hands the probability of not hitting a single set drops to only 3%. Over 1,000 hands this number drops to less than 0.1%. So, over a long enough sample, you're practically guaranteed to flop one of those powerhouse hands.
Odds for Streaks in Poker
Scenario  Probability  Odds 
Being dealt no pocket pair over 50 hands  4.8256%  1:20 
Being dealt no pocket pair over 100 hands  0.2329%  1:428 
Being dealt no pocket pair over 200 hands  0.0005%  1:184,410 
Not hitting a set over 100 hands  49.9635%  1:1 
Not hitting a set over 500 hands  3.1136%  1:31 
Not hitting a set over 1000 hands  0.0969%  1:1,031 
Being dealt no ace and no pocket pair over one full ring orbit  17.4226%  1:5 
Being dealt no ace and no pocket pair over 25 hands  0.7798%  1:127 
Being dealt no premium hand (AK, JJ+) over 100 hands  4.6746%  1:20 
Probability of a Royal Flush
Let’s return to individual poker hands once more, namely to the single best poker hand  the royal flush. A hand so rare most poker players will remember every single one they are dealt for their entire life. It's already quite unlikely for the board to allow for a royal flush (by featuring at least three cards ten or higher of the same suit). This happens only once every 60 hands that go to the river.
Let’s say you’re playing at a fullring table where each player tries his or her best to hit a royal flush. That means they never fold their hand until it’s impossible for them to make that royal flush. Then you’ll see a royal flush roughly once every 3,600 hands. In real life the odds are certainly a bit lower since sometimes people fold hands like QTs before the flop. Not everybody chases backdoorroyalflush draws if there are bets and raises in front of them.
But let’s stay at this table where everyone does their best to make a royal flush. If you stood besides this table for 100 hands, the probability of witnessing at least one royal flush is already 2.7%. Still unlikely, but not unheard of. If you stood there for 2,500 hands (or roughly 100 hours of live poker) this probability increased to almost 50%.
All Important Royal Flush Probabilities
The board shows a royal flush  0.0002%  1:649,739 
The board allows for a royal flush  1.6637%  1:59 
One player makes a royal flush at a full ring table  0.0276%  1:3,628 
Witnessing a royal flush over 100 hands at a full ring table  2.7184%  1:36 
Witnessing a royal flush over 2500 hands at a full ring table  49.7922%  1:1 
Witnessing two or more royal flushes over 100 hands at a full ring table  0.0369%  1:2,708 
Odds of Hitting the Bad Beat Jackpot?
Many local card rooms and online poker sites offer bad beat jackpots. If you lose with a very strong hand, you and the entire table receive a share of a significant jackpot. Sometimes those jackpots are worth more than $1m and some people become rich by losing a single hand of poker.
There’s one caveat though: hitting those bad beat jackpots is really unlikely. Card rooms also have strict requirements about which hands qualify for a bad beat jackpot. One of the most frequently used rule sets for those jackpots is: One player must lose with quad eights (or better) and both him and the player with the winning hand must use both hole cards.
Let’s talk numbers: If you’re playing heads up and both you and your opponent do the best to hit the bad beat jackpot. That is not folding pockets eights or better and not folding possible straight flushes. Then, you’ll have a qualifying hand once every 7 million attempts. Talk about unlikely! The odds improve considerably if you increase the number of players at the table since now more players can make a qualifying hand. At a fullring table the odds of any two players hitting the bad beat jackpot are 1 to 194,000.
How Likely is a Bad Beat Jackpot in Poker?
Scenario  Probability  Odds 
Hitting quad eights or better and lose (headsup)  0.0000%  1:6,974,878 
Hitting quad eights or better and lose (6max)  0.0002%  1:464,991 
Hitting quad eights or better and lose (full ring)  0.0005%  1:193,746 
Witnessing such a bad beat over 1,000 hands at a full ring table  0.5148%  1:193 
Witnessing such a bad beat over 100,000 hands at a full ring table  40.3180%  1:1 
Being Dealt the Same Hand Twice?
Now that we've covered most of the important longshot odds, let’s look at some more streaks. Have you had a déjà vu when looking at your hole cards because you had the exact same cards (down to the suits) just the last hand? Sounds like the dealer is pretty bad at shuffling, no?
Actually, it doesn't. With a perfect shuffle the odds of you getting the same hand as you had the hand before is 1 in 1,326 – unlikely, but not impossible. The gist with small probabilities is that they quickly become more and more likely if you repeat the event often enough. Over 100 hands it’s already 1 to 13 to be dealt the same two cards in a row at least once. And over 1,000 hands it’s already more likely for this happen at least once than for this to not happen.
Pocket Aces BacktoBack
Now anyone can be dealt 83o twice in row and might not even notice this coincidence (because, who cares about those low cards). But if you’ re dealt pocket aces backtoback, you’ll probably remember this feat for months. Surprisingly this scenario is not as unlikely as you might think. Over 100 hands the odds are roughly 1 to 500; over 1,000 hands already 1 to 50. Over 34,000 hands you’re 50/50 to have been dealt pocket aces twice in a row at least once.
Someone who has certainly played more than 34,000 hands is Phil Hellmuth. And the Poker Brat just recently managed to get dealt pocket aces backtoback live on television during Poker Night in America. But, of course, getting aces is not everything. You first need to get your stack in and you need your hand to hold up.
Probabilities of BacktoBack Hands and Streaks in Hold'em
Being dealt the exact same cards in a row at least once over 100 hands  7.1968%  1:13 
Being dealt the exact same cards in a row at least once over 1,000 hands  52.9368%  1:1 
Being dealt pocket aces twice in a row at least once over 100 hands  0.2016%  1:495 
Being dealt pocket aces twice in a row at least once over 1,000 hands  2.0157%  1:49 
Being dealt pocket aces twice in a row at least once over 34,000 hands  49.9927%  1:1 
Being dealt pocket aces twice within one full ring orbit  0.0722%  1:1,385 
Being dealt pocket aces three times within one full ring orbit  0.0008%  1:131,144 
Being dealt pocket kings or better twice within one full ring orbit  0.2826%  1:353 
Being dealt a premium hand (AK, JJ+) twice within one full ring orbit  2.8448%  1:34 
Being dealt a premium hand (AK, JJ+) 10 or more times over 100 hands  0.0911%  1:1,097 
Hitting at least 5 sets over 100 hands  0.0690%  1:1,447 
How Many Ways to Shuffle the Deck?
Lastly, let's take a look at some rather big numbers: How many ways are there to shuffle a deck of 52 cards? For the first card you have 52 options, for the second 51, for the third 50 and so on. Thus the total number of different ways a deck can be shuffled is 52 × 51 × 50 × … × 1 – or 52! (factorial).
This number is mindbogglingly huge. It has 68 digits and if you like tongue twisters, please try to pronounce it: 80 unvigintillion 658 vigintillion 175 novemdecillion 170 octodecillion 943 septendecillion 900 sexdecillion. Here's the full number:
80,658,175,170,943,900,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
The number of ways to shuffle a single deck of cards is so huge that whenever you shuffle a deck you are virtually guaranteed to have a shuffle that has never been played before and never will be played again.
Number of Possible Different Poker Games
Interestingly enough, the number of different card distributions for poker games is much smaller. The bottom cards of the deck are not used and thus it doesn't matter how they are shuffled. As a matter of fact, for a headsup game of Hold‘em, you only use 9 cards – 4 hole cards and 5 for the board.
The total number of different distributions for a headsup Hold'em game is a bit over 1 trillion: 1,390,690,501,200 – a number much smaller than 52!, but still large enough that you'll never see the same headsup game twice in your lifetime.
Possible Distributions for Texas Hold'em Games
Number of different headsup deals  1,390,690,501,200 
Number of different 6max deals  1,411,633,731,355,660,000,000 
Number of different full ring deals  874,314,668,608,292,000,000,000,000 
Number of ways to shuffle the deck  806,581,751,709,439 * 10^53 
All LongShot Odds in Poker
Below we've listed all odds and probabilities mentioned in this article. Below each scenario we have provided the mathematical formula for how to calculate the probability. Keep in mind that all probabilities assume that each player stays in the hand until the mentioned scenario can no longer be reached. For example, the probabilities for sets assume that no player ever folds pocket pairs.
#  Scenario  Probability  Odds 
1  Being dealt aces preflop  0.4525%  1:220 
6/52c2  
2  If you have aces headsup, your opponent has aces as well  0.0816%  1:1,224 
1/50c2  
3  If you have aces at a full ring table, one opponent has aces as well  0.6512%  1:153 
1 – ( (50c2 – 1) / 50c2 )^8  
4  If you have kings headsup, your opponent has aces  0.4898%  1:203 
6/50c2  
5  If you have kings at a full ring table, one opponent has aces  3.8518%  1:25 
1 – ( (50c2 – 6) / 50c2 )^8  
6  If you have queens headsup, your opponent has kings or aces  0.9796%  1:101 
12/50c2  
7  If you have queens at a full ring table, at least one opponent has kings or aces  7.5732%  1:12 
1 – ( (50c2 – 12) / 50c2 )^8  
8  If you have a pair, you hit a set (trips) on the flop  11.7551%  1:8 
1 – 48c3 / 50c3  
9  Being dealt a pair and flopping a set  0.6915%  1:144 
13 * 6 / 52c2 * (1 – 48c3 / 50c3)  
10  If two players have pair, both flop a set  1.0176%  1:97 
2 * 2 * 46 / 48c3  
11  Headsup both players are dealt a pair and flop a set  0.0024%  1:42,305 
13c3 * 4^3 / 52c3 * 9 / 49c2 * 6/47c2  
12  Two players at a 6maxtable are dealt a pair and both flop a set  0.0355%  1:2,819 
13c3 * 4^3 / 52c3 * 6c2 * 9 / 49c2 * 6/47c2  
13  Two players at a full ring table are dealt a pair and both flop a set  0.0851%  1:1,174 
13c3 * 4^3 / 52c3 * 9c2 * 9 / 49c2 * 6/47c2  
14  Three players at a 3maxtable are dealt and pair and all three flop a set  0.0000%  1:13,960,821 
13c3 * 4^3 / 52c3 * 9 / 49c2 * 6 / 47c2 * 3 / 45c2  
15  Three players at a 6maxtable are dealt and pair and all three flop a set  0.0001%  1:698,040 
13c3 * 4^3 / 52c3 * 6c3 * 9 / 49c2 * 6 / 47c2 * 3 / 45c2  
16  Three players at a full ring table are dealt and pair and all three flop a set  0.0006%  1:166,199 
13c3 * 4^3 / 52c3 * 9c3 * 9 / 49c2 * 6 / 47c2 * 3 / 45c2  
17  If you have a pair, you hit quads until the river  0.8163%  1:122 
48c3 / 50c5  
18  If two players have a pair, both hit quads until the river  0.0026%  1:38,915 
44 / 48c5  
19  Headsup both players are dealt a pair and both hit quads  0.00000008%  1: 11,255,911 
13c2 * ( 4c2)^2 * 44 / 52c5 * 2 / 47c2 * 1 / 45c2  
20  Two players at a 6maxtable are dealt a pair and both hit quads  0.0001%  1:750,393 
13c2 * ( 4c2)^2 * 44 / 52c5 * 6c2 * 2 / 47c2 * 1 / 45c2  
21  Two players at a full ring table are dealt a pair and both hit quads  0.0003%  1:312,663 
13c2 * ( 4c2)^2 * 44 / 52c5 * 9c2 * 2 / 47c2 * 1 / 45c2  
22  If you have suited cards, you flop a flush  0.8418%  1:118 
11c3 / 50c3  
23  If two players have suited cards, both flop a flush  0.4857%  1:205 
9c3 / 48c3  
24  If three players have suited cards, all three flop a flush  0.2306%  1:433 
7c3 / 46c3  
25  HeadsUp, both players are dealt suited cards and flop a flush  0.0051%  1:19,490 
13c3 * 4 / 52c3 * 10c2 / 49c2 * 8c2 / 47c2  
26  Two players at a 6maxtable are dealt suited cards and both flop a flush  0.0770%  1:1,298 
13c3 * 4 / 52c3 * 6c2 * 10c2 / 49c2 * 8c2 / 47c2  
27  Two players at a full ring table are dealt suited cards and both flop a flush  0.1847%  1:540 
13c3 * 4 / 52c3 * 9c2 * 10c2 / 49c2 * 8c2 / 47c2  
28  Three players at a 6maxtable are dealt suited cards and all three flop a flush  0.0012%  1:85,758 
13c3 * 4 / 52c3 * 6c2 * 10c2 / 49c2 * 8c2 / 47c2 * 6c2 / 45c2  
29  Three players at a full ring table are dealt suited cards and all three flop a flush  0.0035%  1:28,585 
13c3 * 4 / 52c3 * 9c2 * 10c2 / 49c2 * 8c2 / 47c2 * 6c2 / 45c2  
30  Being dealt no pocket pair over 50 hands  4.8256%  1:20 
( 1 – ( 13 * 6 ) / 52c2 )^50  
31  Being dealt no pocket pair over 100 hands  0.2329%  1:428 
( 1 – ( 13 * 6 ) / 52c2 )^100  
32  Being dealt no pocket pair over 200 hands  0.0005%  1:184,410 
( 1 – ( 13 * 6 ) / 52c2 )^200  
33  Not hitting a set over 100 hands  49.9635%  1:1 
( 1 – 13 * 6 / 52c2 * (1 – 48c3 / 50c3) )^100  
34  Not hitting a set over 500 hands  3.1136%  1:31 
( 1 – 13 * 6 / 52c2 * (1 – 48c3 / 50c3) )^500  
35  Not hitting a set over 1000 hands  0.0969%  1:1,031 
( 1 – 13 * 6 / 52c2 * (1 – 48c3 / 50c3) )^1000  
36  Being dealt no ace and no pocket pair over one full ring orbit  17.4226%  1:5 
((1326 – 13 * 6 – 13 * 16)/1326)^9  
37  Being dealt no ace and no pocket pair over 25 hands  0.7798%  1:127 
((1326 – 13 * 6 – 13 * 16)/1326)^25  
38  Being dealt no premium hand (AK, JJ+) over 100 hands  4.6746%  1:20 
((1326 – 3 * 6 – 16)/1326)^100  
39  The board shows a royal flush  0.0002%  1:649,739 
4 / 52c5  
40  The board allows for a royal flush  1.6637%  1:59 
5c3 * 47c2 * 4 / 52c5  
41  One player makes a royal flush at a full ring table  0.0276%  1:3,628 
4 / 52c5 + 5 * 4 * 47 / 52c5 * 9 * 45 / 47c2 + 5c3 * 47c2 * 4 / 52c5 * 9 * 1 / 47c2  
42  Witnessing a royal flush over 100 hands at a full ring table  2.7184%  1:36 
1 – ( 1 prob. Above)^100  
43  Witnessing a royal flush over 2500 hands at a full ring table  49.7922%  1:1 
1 – ( 1 prob. Above)^2500  
44  Witnessing two or more royal flushes over 100 hands at a full ring table  0.0369%  1:2,708 
1 – BinomDist(1;100;prob. Above)  
45  Hitting quad eights or better and lose (headsup)  0.0000%  1:6,974,878 
46  Hitting quad eights or better and lose (6max)  0.0002%  1:464,991 
47  Hitting quad eights or better and lose (full ring)  0.0005%  1:193,746 
48  Witnessing such a bad beat over 1,000 hands at a full ring table  0.5148%  1:193 
1 – ( 1 prob. Above)^1000  
49  Witnessing such a bad beat over 100,000 hands at a full ring table  40.3180%  1:1 
1 – ( 1 prob. Above)^100000  
50  Being dealt the exact same cards in a row at least once over 100 hands  7.1968%  1:13 
1 – (1325 / 52c2)^(1001)  
51  Being dealt the exact same cards in a row at least once over 1,000 hands  52.9368%  1:1 
1 – (1325 / 52c2)^(10001)  
52  Being dealt pocket aces twice in a row at least once over 100 hands  0.2016%  1:495 
53  Being dealt pocket aces twice in a row at least once over 1,000 hands  2.0157%  1:49 
54  Being dealt pocket aces twice in a row at least once over 34,000 hands  49.9927%  1:1 
55  Being dealt pocket aces twice within one full ring orbit  0.0722%  1:1,385 
BinomDist(7;9;(1326 – 6) / 1326;1)  
56  Being dealt pocket aces three times within one full ring orbit  0.0008%  1:131,144 
BinomDist(6;9;(1326 – 6) / 1326;1)  
57  Being dealt pocket kings or better twice within one full ring orbit  0.2826%  1:353 
BinomDist(7;9;(1326 – 2 * 6) / 1326;1)  
58  Being dealt a premium hand (AK, JJ+) twice within one full ring orbit  2.8448%  1:34 
BinomDist(7;9;(1326 – 4 * 616) / 1326;1)  
59  Being dealt a premium hand (AK, JJ+) 10 or more times over 100 hands  0.0911%  1:1,097 
BinomDist(90;100;(1326 – 4 * 616) / 1326;1)  
60  Hitting at least 5 sets over 100 hands  0.0690%  1:1,447 
BinomDist(95;100;1 – 13 * 6 / 52c2 * (1 – 48c3 / 50c3);1)  
61  Number of different headsup deals  1,390,690,501,200  
52c5 * 47c4 * 3 * 1  
62  Number of different 6max deals  1,411,633,731,355,660,000,000  
52c5 * 47c12 * 11 * 9 * 7 * 5 * 3 * 1  
63  Number of different full ring deals  874,314,668,608,292,000,000,000,000  
52c5 * 47c20 * 17 * 15 * 13 * 11 * 9 * 7 * 5 * 3 * 1  
64  Number of ways to shuffle the deck  806,581,751,709,439 * 10^53  
52! 
XcY is the (X choose Y), e.g. 52c2 = 52! / ( 2! * (52  2)! )
Poker Odds FAQs

What are poker odds?
In Texas Hold'em, poker odds are THE probability tool you need as a poker player. In fact, you should always be thinking about poker odds  yours and your opponents'  when making decisions. In short, poker odds is the probability of you winning that hand, or the price it offers (pot odds). 
How to learn poker odds?
You can learn poker odds by studying our poker odds chart and trying hand situations in our poker odds calculator. 
How to calculate poker odds quickly?
To calculate your poker equity  or how often you should win a hand, you can use a simple formula. Count how many outs you have. For example, if you're drawing to a flush, you have 13 suited cards, two in your hand, two on the board  leaves 9 outs. The chance of you hitting on the turn is 9*4 (+4) = 40%. On the river it's half of that  9*2 (+2) = 20%.
 For a half pot bet, you get 3:1, and so need 25% equity or more to call.
 With a 3/4 pot bet, you have 7:3 pot odds and need +30% equity to call.
 With a pot sized bet, you get 2:1 pot odds and need +33% equity to call.
 With a 2x pot bet, it's 3:2 pot odds and you need 40% equity to call.
So, say your opponent has a hand lesser than a flush and you're drawing to a flush. They bet the pot size on the flop, you may elect to call. But if they bet the pot on the turn, your equity has decreased. Not to mention that if they have a hand like two pair, they also have equity to hit a full house and beat whatever cards you're drawing to. 
What is the best poker odds calculator?
We can offer a great, fast poker odds calculator right here on this page. 
In Poker, what are implied odds?
Implied odds is the relationship between the size of the current pot and the pot you're expected to win. Because sometimes the pot doesn't lay the correct odds, even when you decide to play. Because you're expecting to get more action and win more when you hit your hand.
Implied odds changes things. For example, in Limit Hold'em your opponent bets $20 into an $80 pot and your call gives you pot odds of 51 (you're risking $20 to win $100). But, if you expect your opponent to call a bet or raise on the river if you make your hand, your implied odds are 61 or 71. 
Poker odds: When to call?
You'll often be asking this question if you're drawing to a straight or a flush. So you'll need to calculate if you're getting good enough odds to call a bet or raise on the flop or turn. First, you need to calculate how often you'll hit your draw  by first counting your outs.
If you're drawing to a flush, you have two suited cards in your hand and two on the board, that means 9 cards of that suit left in the deck. On the flop, it's 9*4 (+4) = roughly 40% of hitting. Meanwhile, on the turn (so the odds of hitting on the river) is 9*2 (=2) = roughly 20% of hitting.
With pot odds, think of the number of cards again. 52 in the deck, two in your hand and three on the board (flop). That means 47 unseen cards (including your opponents' hole cards). Nine cards can save you but 38 cards don't complete your draw. So that's a 38:9 ratio  or 4:1 (or 25%). So if you're not getting 4:1 / 25% pot odds, you shouldn't call. This ratio changes again when you consider implied odds. 
What are GOOD poker odds?
Say you're drawing to a flush and have 9 outs  you have roughly 40% equity on the flop and 20% on the turn.
 For a half pot bet, you get 3:1, and so need 25% equity or more to call.
 With a 3/4 pot bet, you have 7:3 pot odds and need +30% equity to call.
 With a pot sized bet, you get 2:1 pot odds and need +33% equity to call.
 With a 2x pot bet, it's 3:2 pot odds and you need 40% equity to call.
So, say your opponent has a hand lesser than a flush, like two pair. They bet the pot size on the flop, you may elect to call. But if they bet the pot on the turn, your equity has decreased. Not to mention that if they have a hand like two pair, they also have equity to hit a full house and beat whatever cards you're drawing to. 
In poker, what are pot odds?
Pot odds refers to the relationship between the size of the pot and the size of the bet. For example: If there's $10 in the pot and you have to call a $2 bet. Then you are getting pot odds of 51. If you have to call a $5 bet in the same $10 pot, you're getting pot odds of 21. How big is the pot; how big is the bet? 
Do poker odds change with more players?
Absolutely. The more players involved in a pot, the less your chances of winning it. That's why it may make sense to shove preflop with certain hands instead of just calling, hoping to narrow the field to just one, or perhaps zero!
what are the odds of someone not having a flush with 3 suited cards on the board ;full ring holdem.
Hi Floyd,
Why not try out our odds calculator by visiting here http://clasesingles.com/whichhandwinscalculator.
let us know if you need any further assistance.
Thanks,
Manal
The odds of making the runnerrunner flush is about 4%. It’s a very unlikely outcome, but it does happen, even in livegames and does not mean that online games are rigged.
Kresten
caesar slot free coin
What are the odds that 4 of the same suit will hit the board by the river if only 2 of that suit comes up on the flop? This happened to me TWICE IN A ROW in an online tournament. I had pocket aces, followed by pocket queens. With my queens, I hit a set, my opponent went all in, so I called. He had K(c)6(d). The flop had 2 diamonds. The next 2 cards were also diamonds, so his 6high flush beat my set of queens. Same thing with my aces, but I never hit my set. My opponent never paired, but beat me with a Jack of clubs, after getting 4 running clubs. I was 13th out of 789 players in a tourney, and busted out after my queens lost. What are the odds? Does this mean the computer/ online games are rigged? Did I misplay my hands? I was always in the lead until the river. Please help me with this.
Hello,
I’m curious of the odds of what happened at a tournament I was in recently. 4 way all in on the flop of A34 rainbow. I was the set of 3s lol
1. Set of threes
2. Set of fours
3. Top two with Ace 4
4. Straight with five deuce (52)
Ty
@Dustin:
With 4 players holding 33, 44, A4 and 52 respectively there are 44 * 43 * 42 / (3 * 2 * 1) = 13,244 possible flops.
Exactly 2 * 3 = 6 of those are A43.
So the odds of the flop being A43 given the 4 holdings are 6 / 13,244 = 0.00045 or 0.045% or 1 in 2,207.
What are the odds of all three community cards being the same on the flop?
@Lanny: Assuming you know nothing about any hole cards there are 52 * 51 * 50 / (3 * 2 * 1) = 22,100 flops possible. 13 * 4 = 52 of them contain trips (e.g. KKK). Thus the odds of seeing trips on the flop are 52 / 22,100 = 0.235% or 1 : 424.