Poker Tips

What are the probabilities? A listing of long run probabilities in Texas Holdem

If you performed stay or on-line poker for some time – even a really brief time – you noticed arms you by no means thought potential.

Shade prints of runners. Draw of the runners. One-outers on the river to crush your large favourite.

However how usually do these "characteristic movies" actually come into play? And the way usually ought to we count on it?

Beneath we’ve compiled an exhaustive checklist of excellent long-term odds for Texas Maintain'em – numbers and percentages to impress (or maybe annoy) your colleagues on the desk.

And above all, to unmask the unscrupulous exaggerants who declare that essentially the most inconceivable issues occurred to them the opposite day.

 0156 Connor Drinan "data-class =" image-position "information reframing =" " /> </a></p>
<p> Aces over aces? </p>
<h2> Alternatives in opposition to Aces </h2>
<p> Let's begin with pretty easy however essential odds: aces are distributed. </p>
<p> There are 1,326 completely different gap card mixtures <a href= in Texas Maintain & # 39; em and 6 of them are ace.

Thus, the chances of receiving ace in any hand have been 6 to 1320 or 1 to 221 (or zero.45%).

You most likely already knew it. However what are the probabilities that one in every of your opponents might be handled as properly?

At a spherical desk (for this text, "full ring" means 9 gamers per desk), this could happen solely as soon as each 154 instances .

A spectacular situation, however not possible.

Are the chances of getting a $ 1 million buy-in match? Too painful to calculate however for Connor Drinan within the Massive One for One Drop 2014 [WSOP 2014]. Right here is the hand of Aces-vs-Aces with Drinan and Cary Katz:

Struggling in opposition to aces with kings

With Aces you don’t have anything to worry earlier than the flop . However with pocket kings, there's at all times that nagging thought at the back of your head that perhaps, maybe, one in every of your opponents has aces.

 frankkings "data-class =" image-position-alt "cropping =" " /> </a></p>
<p> He folded the Kings within the Foremost Occasion! </p>
<p> Is that this a possible situation? The reply is, as is commonly the case in poker, "it relies upon" </p>
<p> In case you play heads-up, you solely should face one opponent. This opponent solely has aces as soon as each 220 arms. </p>
<p> So no. It’s unlikely that he beat your kings. </p>
<p> However at a spherical desk (9 gamers) with eight opponents, there’s instantly extra luck – even when it's a protracted shot – that somebody has ace in opposition to your kings. </p>
<p> The probabilities for this to occur are <strong> 1 in 26 </strong>. It's nearly at all times greatest to disregard this worst-case situation, however generally superb gamers could make spectacular folds with kings earlier than the flop. </p>
<p> Right here is the younger German rifle <strong> Christopher Frank </strong> doing simply that on the WSOP 2016 Foremost Occasion: </p>
</p>
<h2> Queens in kings (and as) </h2>
<p><a class=  setup "data-class =" image-position "data-cropping ="  "/> </a></p>
<p> So inconceivable, so painful. </p>
<p> With kings, it’s potential, however unlikely, <a href= to come across a greater pre-flop . However what about queens?

Queens are far more susceptible and, though it’s much more doubtless that you’re forward earlier than the flop, it is best to think about the situation that one in every of your opponents has kings or kings. aces.

At a spherical desk, the possibilities of this taking place are 1 in 13.

A elevate, elevate, and all-in entrance of you could point out that this 1 of 13 occasion is happening and also you'd higher fold your hand.

Vital odds for giant pairs

State of affairs
Chance
odds
Be handled as preflop
zero.4525%
1: 220
When you’ve got aces in heads-up, your opponent additionally has aces
zero.0816%
1: 1,224
When you’ve got aces at a full desk, an opponent additionally has aces
zero.6512%
1: 153
When you’ve got kings in thoughts, your opponent has ace
zero.4898%
1: 203
When you’ve got kings at a full desk, an opponent has ace
Three.8518%
1:25
When you’ve got queens within the lead, your opponent has kings or ace
zero.9796%
1: 101
When you’ve got queens at a full desk, at the very least one opponent has kings or ace
7.5732%
1:12

Play set

Allow us to flip to post-flop rankings – particularly units, particularly journeys with a pocket pair.

How usually do you flop collectively ? Each formidable poker participant ought to know this quantity by coronary heart: about 12% or as soon as each 9 instances you see a flop along with your pair.

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Set set, child.

One situation that many poker gamers worry is the dreaded set: you make a set fail however one in every of your opponents flops a greater set.

Though not possible, this situation will not be so uncommon. If two gamers have pocket pairs, each will flop a set concurrently about as soon as each 100 flops .

Two gamers at all times must have a pocket pair on the similar time for this to occur. On a full ring desk, you’ll be able to count on a situation of as soon as each 1200 arms (assuming all gamers with pairs of pockets at all times see a flop).

Nevertheless, this situation is far more unlikely. This could solely occur as soon as each 42,000 arms . There isn’t any want to fret about higher units with just one opponent – except you’re Phil Ivey taking part in Scotty Nguyen in one of many greatest televised heads-up tournaments:

Set Over Set Set

Set-set conditions are already very uncommon. However what about some actually lengthy eventualities? What about three gamers who all beat one set on the similar time?

The calculation exhibits that this situation is extraordinarily unlikely. On an entire ring desk, you’ll solely see each 166,000 arms. With solely three gamers on the desk, this quantity jumps to as soon as each 14 million . An actual lengthy shot!

Vital rankings on the set

State of affairs
Chance
odds
When you’ve got a pair, you hit a set (journeys) on the flop
11.7551%
1: eight
Being handing out a pair and beating a set
zero.6915%
1: 144
If two gamers have a pair, each flop collectively
1.0176%
1:97
Heads-up each gamers obtain a pair and flop a set
zero.0024%
1: 42.305
Two 6-max-table gamers obtain a pair and each flop a set
zero.zero355%
1: 2,819
Two gamers at a full ring desk obtain a pair and each flop a set
zero.0851%
1: 1,174
Three gamers at a Three-max desk are dealt and the three flop a set
zero.000zero%
1: 13,960,821
Three gamers at 6-max-table are distributed and the three flop a set
zero.0001%
1: 698,zero40
Three gamers at a full ring desk are dealt and the three flop and a set of flop
zero.0006%
1: 166,199

How usually do you hit the quads?

Whereas the units are in good arms, let's now see higher poker arms: the quads. The quads are the second absolute best place in Texas Maintain'em and happen very not often.

 Andrew Robl "data-class =" image-position "cropping information ="  "/> </a></p>
<p> Quads over quads! </p>
<p> Uncommonly? </p>
<p> In case you maintain a pair of pocket and also you pull your self as much as the top, you’ll attain the plateau of the river <strong> as soon as each 123 makes an attempt </strong> – not often, however nonetheless extra doubtless the flop. </p>
<h2> Quads over Quads: does this occur? </h2>
<p> The set-set is already unlikely, however what about yet one more step? What are <a href= the chances that two gamers hit quads after they each begin with a pair ?

This situation grew to become notorious for Andrew Robl and Toby Lewis on the World Poker Celebration Open just a few years in the past:

The chances are quite slim: with two gamers in possession of a pair, they may hit the quads close to the river as soon as each 39,000 makes an attempt .

Given the possibilities that two gamers obtain pairs earlier than the flop, you will note such a situation at a full desk as soon as each 313ok arms – for many stay poker gamers, 39 is already a singular situation.

Possibilities of doing quads in poker

State of affairs
Chance
odds
When you’ve got a pair, you hit the quads as much as the river
zero.8163%
1: 122
If two gamers have a pair, each hit the quads as much as the river
zero.0026%
1: 38.915
Heads-up each gamers obtain a pair and each hit quads
zero.000zero0008%
1: 11,255,911
Two 6-max-table gamers obtain a pair and each contact quads
zero.0001%
1: 750.393
Two gamers at a full spherical desk obtain a pair and each hit quads
zero.0003%
1: 312.663

How usually flops a flush?

Let's check out the post-flop ranking.

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<p> Rinsing. </p>
<p> When you’ve got two matching playing cards, <a href= you keep away from three playing cards of your swimsuit. However normally, this doesn’t occur.

In reality, when you begin with two matching playing cards, you’ll solely flip as soon as each 119 makes an attempt .

What’s the frequency of flushing?

The situation of your dream of flipping a colour can generally flip right into a nightmare if one in every of your opponents flopps higher with you.

WSOP Champion Joe McKeehen most likely nonetheless has occasional terror on the a part of one hand on account of an overshoot when suffered a foul shot in opposition to Fedor Holz ] on the WSOP $ 111ok Excessive Curler 2016:

However what are the probabilities? In reality, if two gamers begin with two matching playing cards of the identical colour, the chances that the 2 flop a colour are usually not as small as one may suppose.

 Royal Flush "data-class =" image-position "data-cropping =" " /> </a></p>
<p> <strong> As soon as all 206 makes an attempt </strong> the flop will present three playing cards of the identical colour. Even a colour on a colour will not be so inconceivable. </p>
<p> If three gamers have matching playing cards in similar costumes, they may all beat one colour <strong> each 434 makes an attempt </strong>. </p>
<p> If you wish to understand how usually this occurs at a desk, it is best to at all times think about the probabilities that each one gamers will obtain matching matching playing cards. </p>
<p> Given these possibilities (and assuming that every participant with matching playing cards sees the flop – a daring assumption), you’ll witness a flush flush <strong> as soon as each 540 </strong>. </p>
<p> The triple hunt is far more unlikely than this and will happen solely <strong> as soon as each 29,000 makes an attempt </strong>. </p>
<h3> Searching Probabilities in Texas Maintain 'em </h3>
<p>State of affairs<br />
Chance<br />
odds<br />
When you’ve got matching playing cards, you flop a colour<br />
zero.8418%<br />
1: 118<br />
If two gamers have matching playing cards, each flop one colour<br />
zero.4857%<br />
1: 205<br />
If three gamers have matching playing cards, all three flop a colour<br />
zero.2306%<br />
1: 433<br />
Heads-Up, each gamers obtain matching playing cards and flop a colour<br />
zero.0051%<br />
1: 19,490<br />
Two gamers at 6-max-table obtain matching playing cards and each flop a colour<br />
zero.0770%<br />
1: 1,298<br />
Two gamers at a full ring desk obtain matching playing cards and each flop a straight<br />
zero.1847%<br />
1: 540<br />
Three 6-max-table gamers obtain matching playing cards and all three flop a straight<br />
zero.0012%<br />
1: 85.758<br />
Three gamers on the full spherical desk obtain matching playing cards and the three flop a straight<br />
zero.0035%<br />
1: 28.585</p>
<h2> Unfortunate Traces of Poker </h2>
<p> Have you ever ever been sitting at a poker desk for hours with out receiving a single playable hand? Have you ever ever <a href= had anybody to faux that he had not handled a single ace on tens, even a whole bunch! – arms ?

 Mike Matusow 2 "data-class =" image-position-alt "Crop =" " /> </a></p>
<p> Probably the most turbulent man in poker? </p>
<p> Let's transfer on to some possibilities! </p>
<p> The chance of not receiving a single pair of greater than 50 arms is rather less than 5% – unlikely, however very potential. Broaden the sequence to 200 arms and the chance drops to lower than zero.0005%. </p>
<p> The man in your proper says he has not seen a pair for 2 days? He's nearly actually bullshitting you. </p>
<p> Now most pocket pairs are solely actually good when you make them fail a set. Let's take a look at some possibilities and suppose you'll at all times see a flop along with your pocket pairs. </p>
<p> The chance that <strong> reaches at the very least one pair (that’s, you performed a pair and also you failed with a pair) with greater than 100 arms is nearly precisely 50% </strong> . Thus, on 100 arms, you’ve gotten as many probabilities to the touch at the very least one recreation as to not contact one. </p>
<p> Greater than 500 arms, the chance of not touching a single recreation <strong> drops to solely Three%. </strong> Greater than 1,000 arms, this quantity falls to <strong> lower than zero.1% </strong>. So, on a sufficiently lengthy pattern, you’re just about assured to defeat one in every of these highly effective arms. </p>
<h3> Odds for poker streaks </h3>
<p>State of affairs<br />
Chance<br />
odds<br />
Not having obtained any pocket pair of greater than 50 arms<br />
four.8256%<br />
1:20<br />
Not receiving any pocket pair of greater than 100 arms<br />
zero.2329%<br />
1: 428<br />
Not having obtained any pocket pair greater than 200 arms<br />
zero.0005%<br />
1: 184.410<br />
Don’t hit a set on 100 arms<br />
49.9635%<br />
1: 1<br />
Don’t hit a set of greater than 500 arms<br />
Three.1136%<br />
1:31<br />
Don’t hit a recreation over 1000 arms<br />
zero.0969%<br />
1: 1,zero31<br />
Having no aces and no pocket pair on an entire orbit<br />
17.4226%<br />
1: 5<br />
Receiving no ace and no pocket pair of greater than 25 arms<br />
zero.7798%<br />
1: 127<br />
Not having any premium hand (A-Ok, JJ +) on 100 arms<br />
four.66746%<br />
1:20</p>
<h2> Chance of royal flush </h2>
<p> Let's return to the person poker arms, particularly <a href= the very best poker hand – the royal flush . A hand so uncommon that the majority poker gamers will bear in mind every one of all of them their lives.

 Royal Flush "data-class =" image-position "cropping ="  "/> </a></p>
<p> Royaled. </p>
<p> It’s already fairly inconceivable that the portray permits a royal flush (with at the very least three playing cards of ten or extra of the identical colour). </p>
<p> This happens <strong> solely as soon as each 60 arms </strong> who go to the river. </p>
<p> Let's say you play a spherical desk the place every participant tries to do his greatest to get a royal flush. </p>
<p> Which means they by no means fold their arms till it’s unattainable for them to make this royal flush. </p>
<p> You’ll then see a royal flush <strong> about as soon as each Three,600 arms </strong>. In actual life, the chances are actually a bit decrease, as a result of generally folks fold like QTs earlier than the flop. </p>
<p> Not everyone seems to be chasing attracts on the again door if there are bets and raises in entrance of them. </p>
<p> Let's keep at this desk the place everyone seems to be doing their greatest to make a royal flush. In case you stood subsequent to this desk for 100 arms, the chance of attending at the very least one royal flush <strong> is already 2.7% </strong> – nonetheless unlikely, however not unknown. </p>
<p> In case you stood there for two,500 arms (about 100 hours of stay poker), this chance <strong> elevated to just about 50% </strong>. Right here we will supply three royal colours (and <strong> Phil Hellmuth </strong> by successful one) in lower than 10 minutes: </p>
</p>
<h3> All main royal drain possibilities </h3>
<p>The portray exhibits a royal flush<br />
zero.0002%<br />
1: 649.739<br />
The board permits a royal flush<br />
1.6637%<br />
1:59<br />
A participant makes a royal flush on the spherical desk<br />
zero.0276%<br />
1: Three.628<br />
Attend a Royal Flush on 100 arms on the spherical desk<br />
2.7184%<br />
1:36<br />
Attend a Royal Flush on 2500 Palms at a Roundtable<br />
49.7922%<br />
1: 1<br />
Witness of two or extra Royal Flushes, greater than 100 arms on the spherical desk<br />
zero.0369%<br />
1: 2,708</p>
<h2> Possibilities of hitting the jackpot of the dangerous beat? </h2>
<p> Many native card rooms and <a href= some on-line poker websites supply badly battered jackpots. In case you lose with a really robust hand, you and the entire desk obtain a share of an enormous jackpot.

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<p> Oh no </p>
<p> <a href= Typically these jackpots are value greater than one million and a few folks get wealthy by shedding only one poker hand.

Nevertheless, it’s essential to make a warning: It’s actually not possible to succeed in these giant jackpots .

Card rooms even have stringent necessities for qualifying arms for a foul beat jackpot.

Some of the steadily used rule units for these jackpots is: A participant should lose with a quad (or higher) and he and the participant with the successful hand should use each playing cards.

Right here is a wonderful instance of a hand that qualifies for such a foul jackpot:

Sadly, for Motoyuki Mabuchi who simply misplaced with quads in opposition to a royal flush, had this hand on the WSOP that doesn’t supply dangerous jackpots.

Let's discuss numbers: In case you play head-to-head and your opponent and also you do your greatest to hit the detrimental beat jackpot (ie, qualifying hand as soon as each 7 hundreds of thousands of makes an attempt Discuss improbably!

In case you improve the variety of gamers on the desk, the chances enhance significantly. On the bargaining desk, the chances of two gamers hitting the beat beat jackpot are 1 to 194,000 .

How Unhealthy is a Unhealthy Beat Jackpot?

State of affairs
Chance
odds
Hit 4 quarters or higher and lose (heads-up)
zero.000zero%
1: 6,974,878
Hit 4 quarters or higher and lose (6-max)
zero.0002%
1: 464 991
Hit 4 quarters or higher and lose (full ring)
zero.0005%
1: 193.746
Attending such an evil beat over 1000 arms at a full desk
zero.5148%
1: 193
Attending such an evil beat greater than 100,000 arms on the roundtable
40.3180%
1: 1

To be inflicted twice the identical?

Now that we’ve coated many of the essential odds, let's take a look at some further streaks.

Have you ever ever seen your playing cards closed since you had the identical playing cards (as much as the mixtures) simply the final hand? Seems just like the seller may be very badly beating, proper?

 Daniel Negreanu eliminates Hellmuth 2 "data-class =" image-position "data-cropping =" " /> </a></p>
<p> Didn’t I’ve it? </p>
<p> In reality, this isn’t the case. With an ideal combine, the possibilities of you getting the identical hand you had beforehand are <strong> 1 of 1 326 </strong> – unlikely, however not unattainable. </p>
<p> The important of the possibilities is that they shortly change into increasingly doubtless when you repeat the occasion very often. <strong> Greater than 100 arms, they’re already 1 to 13 </strong> to obtain the identical two playing cards at the very least as soon as. And greater than 1,000 arms, it’s already extra doubtless that this can occur at the very least as soon as in order that it doesn’t occur. </p>
<h2> Pocket Aces again to again </h2>
<p> Now everybody might be handled twice and perhaps not even discover this coincidence (as a result of these playing cards are usually not essential). However if in case you have pocket aces again to again, you'll most likely bear in mind this feat for months. </p>
<p> Surprisingly, this situation will not be as inconceivable as one may suppose. On 100 arms, likelihood is about <strong> 1 to 500; </strong> greater than 1,000 arms already <strong> 1 to 50. </strong> Greater than 34,000 arms <strong> 50/50 </strong> have been distributed twice in a row at the very least as soon as. </p>
<p> Somebody who has actually performed greater than 34,000 arms is <strong> Phil Hellmuth </strong>. And the Brat Poker just lately managed to get pocket-sized back-to-back aces stay on tv throughout <strong> Poker Evening in America </strong>. </p>
<p> However, after all, getting ace will not be every little thing. You have to first get your stack and also you want your hand to carry. Hellmuth appears to have hassle with the latter on this clip: </p>
</p>
<h3> Chances of arms and streaks consecutive to Maintain & # 39; em </h3>
<p>Have the identical playing cards at the very least as soon as in 100 arms<br />
7.1968%<br />
1:13<br />
Have the identical playing cards at the very least as soon as per 1,000 arms<br />
52.9368%<br />
1: 1<br />
Having obtained two pocket aces at the very least as soon as per 100 arms<br />
zero.2016%<br />
1: 495<br />
To have obtained two pocket aces at the very least as soon as per 1,000 arms<br />
2.0157%<br />
1:49<br />
Having obtained twice in a row at the very least 34,000 arms<br />
49.9927%<br />
1: 1<br />
Receiving pocket ace twice in an entire orbit<br />
zero.0722%<br />
1: 1.385<br />
Receiving three aces in an entire orbit<br />
zero.0008%<br />
1: 131,144<br />
Be handled with pocket kings or higher twice in an entire orbit<br />
zero.2826%<br />
1: 353<br />
Have obtained a premium hand (A-Ok, JJ +) twice in an entire orbit<br />
2.8448%<br />
1:34<br />
Receiving a premium hand (A-Ok, JJ +) 10 instances or extra on 100 arms<br />
zero.0911%<br />
1: 1,zero97<br />
Hit at the very least 5 units on 100 arms<br />
zero.zero690%<br />
1: 1,447</p>
<h2> What number of methods to scramble the bridge? </h2>
<p> Lastly, let's check out some fairly essential numbers: what number of methods is there to combine a deck of 52 playing cards? </p>
<p><a class=  GeorgeLonelyDealer "data-class =" image-position-alt "cropping information ="  "/> </a></p>
<p> Let me rely the means. </p>
<p> For the primary card, you’ve gotten 52 choices, for the second 51, for the third 50, and so forth. Thus, the overall variety of alternative ways to combine a deck is 52 × 51 × 50 × … × 1 – or 52! (Factorial). </p>
<p> This quantity is extremely large. </p>
<p> It has 68 digits and when you like tongue twisters, attempt to pronounce it: 80 unvigintillion 658 vigintillion 175 novemdecillion 170 octodecillion 943 septendecillion 900 sexdecillion. </p>
<p> Voici le numéro complet: </p>
<p> <strong> <span style= 80 658 175 170 703 900 000 000 000 000 000 000 000 000 000 000 000 000 000

Le nombre de façons de mélanger un jeu de cartes est si élevé que chaque fois que vous mélangez un jeu, vous êtes assuré d&#39;avoir un mélange jamais joué auparavant et qui ne sera plus jamais joué.

YouTuber Vsauce a produit une superbe vidéo qui montre à quel level le nombre de manières de mélanger un deck est absurde:

Nombre de jeux de poker possibles

Il est intéressant de noter que le nombre de distributions de cartes différentes pour jeux de poker est beaucoup plus petit.

Les cartes du bas du paquet ne sont pas utilisées et la façon dont elles sont mélangées n&#39;a donc aucune significance. En fait, pour un jeu de heads-up de Maintain’em, vous n’utilisez que 9 cartes – four cartes fermées et 5 cartes pour le plateau.

Le nombre whole de distributions différentes pour un jeu de heads-up Maintain&#39;em est un peu plus de 1 000 milliards: 1 390 690 501 200 – un nombre beaucoup plus petit que 52! voir le même jeu de heads-up deux fois dans votre vie.

Distributions possibles pour les jeux de Texas Maintain&#39;em

Nombre de tête-à-tête différents
1 390 690 501 200
Nombre de différentes offres 6-max
1 411 633 731 355 660 000 000
Nombre de différents accords complets
874 314 668 608 292 000 000 000 000
Nombre de façons de mélanger le jeu
806.581.751.709.439 * 10 ^ 53

Toutes les probabilities du poker

Nous avons répertorié ci-dessous toutes les cotes et probabilités mentionnées dans cet article. En dessous de chaque scénario, nous avons fourni la formule mathématique pour calculer la probabilité. Gardez à l&#39;esprit que toutes les probabilités supposent que chaque joueur reste dans la principal jusqu&#39;à ce que le scénario mentionné ne puisse plus être atteint. Par exemple, les probabilités pour les ensembles supposent qu&#39;aucun joueur ne plie jamais une paire de poche.

#
Scénario
Probabilité
Probabilities
1
Être traité as preflop
zero,4525%
1: 220

6 / 52c2
2
Si vous avez des as en heads-up, votre adversaire a aussi des as
zero,0816%
1: 1,224

1 / 50c2
Three
Si vous avez des as à une desk complète, un adversaire a aussi des as
zero,6512%
1: 153

1 – ((50c2-1) / 50c2) ^ eight
four
Si vous avez des rois en tête, votre adversaire a des as
zero,4898%
1: 203

6 / 50c2
5
Si vous avez des rois à une desk complète, un adversaire a des as
Three.8518%
1:25

1 – ((50c2 – 6) / 50c2) ^ eight
6
Si vous avez des reines en tête, votre adversaire a des rois ou des as
zero.9796%
1: 101

12 / 50c2
7
When you’ve got queens at a full ring desk, at the very least one opponent has kings or aces
7.5732%
1:12

1 – ( (50c2 – 12) / 50c2 )^eight
eight
When you’ve got a pair, you hit a set (journeys) on the flop
11.7551%
1:eight

1 – 48c3 / 50c3
9
Being dealt a pair and flopping a set
zero.6915%
1:144

13 * 6 / 52c2 * (1 – 48c3 / 50c3)
ten
If two gamers have pair, each flop a set
1.0176%
1:97

2 * 2 * 46 / 48c3
11
Heads-up each gamers are dealt a pair and flop a set
zero.0024%
1:42,305

13c3 * four^Three / 52c3 * 9 / 49c2 * 6/47c2
12
Two gamers at a 6-max-table are dealt a pair and each flop a set
zero.zero355%
1:2,819

13c3 * four^Three / 52c3 * 6c2 * 9 / 49c2 * 6/47c2
13
Two gamers at a full ring desk are dealt a pair and each flop a set
zero.0851%
1:1,174

13c3 * four^Three / 52c3 * 9c2 * 9 / 49c2 * 6/47c2
14 years previous
Three gamers at a Three-max-table are dealt and pair and all three flop a set
zero.000zero%
1:13,960,821

13c3 * four^Three / 52c3 * 9 / 49c2 * 6 / 47c2 * Three / 45c2
15
Three gamers at a 6-max-table are dealt and pair and all three flop a set
zero.0001%
1:698,zero40

13c3 * four^Three / 52c3 * 6c3 * 9 / 49c2 * 6 / 47c2 * Three / 45c2
16
Three gamers at a full ring desk are dealt and pair and all three flop a set
zero.0006%
1:166,199

13c3 * four^Three / 52c3 * 9c3 * 9 / 49c2 * 6 / 47c2 * Three / 45c2
17
When you’ve got a pair, you hit quads till the river
zero.8163%
1:122

48c3 / 50c5
18
If two gamers have a pair, each hit quads till the river
zero.0026%
1:38,915

44 / 48c5
19
Heads-up each gamers are dealt a pair and each hit quads
zero.000zero0008%
1: 11,255,911

13c2 * ( 4c2)^2 * 44 / 52c5 * 2 / 47c2 * 1 / 45c2
20
Two gamers at a 6-max-table are dealt a pair and each hit quads
zero.0001%
1:750,393

13c2 * ( 4c2)^2 * 44 / 52c5 * 6c2 * 2 / 47c2 * 1 / 45c2
21
Two gamers at a full ring desk are dealt a pair and each hit quads
zero.0003%
1:312,663

13c2 * ( 4c2)^2 * 44 / 52c5 * 9c2 * 2 / 47c2 * 1 / 45c2
22
When you’ve got suited playing cards, you flop a flush
zero.8418%
1:118

11c3 / 50c3
23
If two gamers have suited playing cards, each flop a flush
zero.4857%
1:205

9c3 / 48c3
24
If three gamers have suited playing cards, all three flop a flush
zero.2306%
1:433

7c3 / 46c3
25
Heads-Up, each gamers are dealt suited playing cards and flop a flush
zero.0051%
1:19,490

13c3 * four / 52c3 * 10c2 / 49c2 * 8c2 / 47c2
26
Two gamers at a 6-max-table are dealt suited playing cards and each flop a flush
zero.0770%
1:1,298

13c3 * four / 52c3 * 6c2 * 10c2 / 49c2 * 8c2 / 47c2
27
Two gamers at a full ring desk are dealt suited playing cards and each flop a flush
zero.1847%
1:540

13c3 * four / 52c3 * 9c2 * 10c2 / 49c2 * 8c2 / 47c2
28
Three gamers at a 6-max-table are dealt suited playing cards and all three flop a flush
zero.0012%
1:85,758

13c3 * four / 52c3 * 6c2 * 10c2 / 49c2 * 8c2 / 47c2 * 6c2 / 45c2
29
Three gamers at a full ring desk are dealt suited playing cards and all three flop a flush
zero.0035%
1:28,585

13c3 * four / 52c3 * 9c2 * 10c2 / 49c2 * 8c2 / 47c2 * 6c2 / 45c2
30
Being dealt no pocket pair over 50 arms
four.8256%
1:20

( 1 – ( 13 * 6 ) / 52c2 )^50
31
Being dealt no pocket pair over 100 arms
zero.2329%
1:428

( 1 – ( 13 * 6 ) / 52c2 )^100
32
Being dealt no pocket pair over 200 arms
zero.0005%
1:184,410

( 1 – ( 13 * 6 ) / 52c2 )^200
33
Not hitting a set over 100 arms
49.9635%
1:1

( 1 – 13 * 6 / 52c2 * (1 – 48c3 / 50c3) )^100
34
Not hitting a set over 500 arms
Three.1136%
1:31

( 1 – 13 * 6 / 52c2 * (1 – 48c3 / 50c3) )^500
35
Not hitting a set over 1000 arms
zero.0969%
1:1,zero31

( 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 arms
zero.7798%
1:127

((1326 – 13 * 6 – 13 * 16)/1326)^25
38
Being dealt no premium hand (A-Ok, JJ+) over 100 arms
four.6746%
1:20

((1326 – Three * 6 – 16)/1326)^100
39
The board exhibits a royal flush
zero.0002%
1:649,739

four / 52c5
40
The board permits for a royal flush
1.6637%
1:59

5c3 * 47c2 * four / 52c5
41
One participant makes a royal flush at a full ring desk
zero.0276%
1:Three,628

four / 52c5 + 5 * four * 47 / 52c5 * 9 * 45 / 47c2 + 5c3 * 47c2 * four / 52c5 * 9 * 1 / 47c2
42
Witnessing a royal flush over 100 arms at a full ring desk
2.7184%
1:36

1 – ( 1- prob. Above)^100
43
Witnessing a royal flush over 2500 arms at a full ring desk
49.7922%
1:1

1 – ( 1- prob. Above)^2500
44
Witnessing two or extra royal flushes over 100 arms at a full ring desk
zero.0369%
1:2,708

1 – BinomDist(1;100;prob. Above)
45
Hitting quad eights or higher and lose (heads-up)
zero.000zero%
1:6,974,878

46
Hitting quad eights or higher and lose (6-max)
zero.0002%
1:464,991

47
Hitting quad eights or higher and lose (full ring)
zero.0005%
1:193,746

48
Witnessing such a foul beat over 1,000 arms at a full ring desk
zero.5148%
1:193

1 – ( 1- prob. Above)^1000
49
Witnessing such a foul beat over 100,000 arms at a full ring desk
40.3180%
1:1

1 – ( 1- prob. Above)^100000
50
Being dealt the very same playing cards in a row at the very least as soon as over 100 arms
7.1968%
1:13

1 – (1325 / 52c2)^(100-1)
51
Being dealt the very same playing cards in a row at the very least as soon as over 1,000 arms
52.9368%
1:1

1 – (1325 / 52c2)^(1000-1)
52
Being dealt pocket aces twice in a row at the very least as soon as over 100 arms
zero.2016%
1:495

53
Being dealt pocket aces twice in a row at the very least as soon as over 1,000 arms
2.0157%
1:49

54
Being dealt pocket aces twice in a row at the very least as soon as over 34,000 arms
49.9927%
1:1

55
Being dealt pocket aces twice inside one full ring orbit
zero.0722%
1:1,385

BinomDist(7;9;(1326 – 6) / 1326;1)
56
Being dealt pocket aces thrice inside one full ring orbit
zero.0008%
1:131,144

BinomDist(6;9;(1326 – 6) / 1326;1)
57
Being dealt pocket kings or higher twice inside one full ring orbit
zero.2826%
1:353

BinomDist(7;9;(1326 – 2 * 6) / 1326;1)
58
Being dealt a premium hand (A-Ok, JJ+) twice inside one full ring orbit
2.8448%
1:34

BinomDist(7;9;(1326 – four * 6-16) / 1326;1)
59
Being dealt a premium hand (A-Ok, JJ+) 10 or extra instances over 100 arms
zero.0911%
1:1,zero97

BinomDist(90;100;(1326 – four * 6-16) / 1326;1)
60
Hitting at the very least 5 units over 100 arms
zero.zero690%
1:1,447

BinomDist(95;100;1 – 13 * 6 / 52c2 * (1 – 48c3 / 50c3);1)
61
Variety of completely different heads-up offers
1,390,690,501,200

52c5 * 47c4 * Three * 1
62
Variety of completely different 6-max offers
1,411,633,731,355,660,000,000

52c5 * 47c12 * 11 * 9 * 7 * 5 * Three * 1
63
Variety of completely different full ring offers
874,314,668,608,292,000,000,000,000

52c5 * 47c20 * 17 * 15 * 13 * 11 * 9 * 7 * 5 * Three * 1
64
Variety of methods to shuffle the deck
806,581,751,709,439 * 10^53

52!

XcY is the Binomial Coefficient (X select Y), e.g. 52c2 = 52! / ( 2! * (52 – 2)! )

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