Poker Probability Texas Hold 'Em

[Lorence.xD]

I already made a table for 5 hand poker, and here I am, back at it again with the most famous type of poker game, Texas Hold 'Em or 7 hand poker. There isn't much intro so I will just show you the table. I will also add the same additional notes since they are essentially the same.

Hand____________	Frequency__	Probability__	Cumulative__	Odds against
Royal Flush	4,324	0.0032%	0.0032%	30,939 : 1
Straight Flush	37,26	0.0279%	0.0311%	3,589.6 : 1
Four of a Kind	224,848	0.168%	0.199%	594 : 1
Full House	3,473,184	2.60%	2.80%	35.7 : 1
Flush	4,047,644	3.03%	5.82%	32.1 : 1
Straight	6,180,020	4.62%	10.4%	20.6 : 1
Three of a Kind	6,461,620	4.83%	15.3%	19.7 : 1
Two Pair	31,433,400	23.5%	38.8%	3.26 : 1
One Pair	58,627,800	43.8%	82.6%	1.28 : 1
No Pair/ High Card	23,294,460	17.4%	100%	4.74 : 1

I will point it out right now, the Frequency of Two Pair and One Pair is higher than Zilch, compared to 5 hand poker the which increases as the value of the hand decreases. This must be the reason why Texas Hold 'Em Poker is the tournament choice for poker.

Additional Notes
Cumulative probability refers to the probability of drawing a hand as good as or better than the specified one. For example, the probability of drawing three of a kind is approximately 2.11%, while the probability of drawing a hand at least as good as three of a kind is about 2.87%. The cumulative probability is determined by adding one hand's probability with the probabilities of all hands above it.
Odds are defined as the ratio of the number of ways not to draw the hand, to the number of ways to draw it. In statistics, this is called odds against. For instance, with a royal flush, there are 4 ways to draw one, and 2,598,956 ways to draw something else, so the odds against drawing a royal flush are 2,598,956 : 4, or 649,739 : 1. The formula for establishing the odds can also be stated as (1/p) - 1 : 1, where p is the aforementioned probability.
Straight Flush is different from Royal Flush which is comprised of 10, Jack, Queen, King and Ace while the former is comprised of the other card numbers.
Flush is different from Straight Flush and Royal Flush where Straight Flush and Royal Flush has a condition that there is a order of cards of the same suit whereas Flush just needs to have the same suit.
Straight is different from Straight Flush and Royal Flush where both has the condition of Same suit and order for both hands, Straight on the other hand just needs to be in order even if not the same suit.

Note: Thank you @alegotardo

Source: https://en.m.wikipedia.org/wiki/Poker_probability
Link to the topic for comparison: https://bitcointalk.org/index.php?topic=5290561.msg55619133#msg55619133

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[johhnyUA]

You've done a wrong calculation, i see it from high value combos. The real prob to collect Four of a kind is  like 0.00168, not yours 0.168 (16 percents LOL).

You need to find your mistake.

[Lorence.xD]

You've done a wrong calculation, i see it from high value combos. The real prob to collect Four of a kind is  like 0.00168, not yours 0.168 (16 percents LOL).

You need to find your mistake.

It is correct, check the link that I provided. The probability table says that it is 0.168. By the way the probability is already in percentage.

[Timelord2067]

...

As much as I enjoy playing Texas Hold Em, I couldn't help but notice you table in the OP is all over the place, I could have a look at simplifying it for you, if you like, otherwise I'll leave it be if you are happy with it the way it is.

[johhnyUA]

It is correct, check the link that I provided. The probability table says that it is 0.168. By the way the probability is already in percentage.

Yeah, i haven't seen "%" symbol near your calculations. Sorry, my bad. I get used to display probabilities as a number, not as percents, like .5 (50 %) and so on.

Whatever, i checked it by myself and everything is correct. But what you used to get such results? Just interesting for me (there a lot of different ways to calculate probabilities).

[alegotardo]

@Lorence.xD
These odds are always interesting.
Your table is very good, you just need an lyout worthy of the importance of the information you brought us....

Note: Help me create the table, the preview is good but the post is trash sorry

The first line determines the width of the columns, so I added the "_"
Unfortunately, you can't add borders

Hand____________	Frequency__	Probability__	Cumulative__	Odds against
Royal Flush	4,324	0.0032%	0.0032%	30,939 : 1
Straight Flush	37,26	0.0279%	0.0311%	3,589.6 : 1
Four of a Kind	224,848	0.168%	0.199%	594 : 1
Full House	3,473,184	2.60%	2.80%	35.7 : 1
Flush	4,047,644	3.03%	5.82%	32.1 : 1
Straight	6,180,020	4.62%	10.4%	20.6 : 1
Three of a Kind	6,461,620	4.83%	15.3%	19.7 : 1
Two Pair	31,433,400	23.5%	38.8%	3.26 : 1
One Pair	58,627,800	43.8%	82.6%	1.28 : 1
No Pair/ High Card	23,294,460	17.4%	100%	4.74 : 1

Please check the information first, I may have changed something by mistake when formatting.

[Lorence.xD]

~

Whatever, I checked it by myself and everything is correct. But what you used to get such results? Just interesting for me (there a lot of different ways to calculate probabilities).

There is a readied calculation. I provided the link there and each hands have their own equations. I am not a math guy but I am fascinated enough to look for this kind of things.

[BigBoy89]

Knowing the Frequency of hands have small to none real value in play.

What you must learn is to count your outs correctly and calculate your odds post-flop. The rule of thumb is, for easy calculation, that one out is 2% on the Turn and 1.75% in you continue to the River.

Example: You have a flush draw, nine outs. Chances to fill the flush on the Turn are roughly 20% and another 15% to the River, 35% to Showdown.
Learn the Basic Math – Odds and Percentages (http://www.pokerology.com/lessons/drawing-odds/) and you are good to go.

Most crucial after that are the observation and note-taking abilities, and adjustment to those observations.
(from a man with 1M+ hands)

[Steamtyme]

These odds are nice for a standard idea around the possibility of what your hand could be at showdown. Problem is you aren't always getting to showdown. More often than not someone is folding out well before, and you often don't get to realize your equity, on say straight or flush draws, then there's hands you don't really chase you just luck into, like a boat(Full House) or quads (Four of a kind) and Straight Flushes.

One of the odds people often look to hit on the flop apart from a decent pair are Set mining with a pocket pair looking to hit 1 of 2 remaining cards on the flop approximately 12%. It's such a killer of a hand if it's a middle to low pocket pair to begin with.

Odds are great, but ranges are way more important once you progress in the game.

As much as I enjoy playing Texas Hold Em

We do hold a tournament series made up entirely of forum users on Betnomi every Sunday - Really nice sponsored prizepool at the moment. Always looking for more members to join.

[swogerino]

This list is a good overview for beginners but Texas holdem pros know exactly what to expect from a hand based on their experience.They know that if 2 aces are down in the cards and they have 2 aces in their hand it is going to be a massive win for them in 99.99% of the cases.

[BigBoy89]

This list is a good overview for beginners but Texas holdem pros know exactly what to expect from a hand based on their experience.They know that if 2 aces are down in the cards and they have 2 aces in their hand it is going to be a massive win for them in 99.99% of the cases.

This is a myth...

You could put some opponents on ranges. It would be best if you always tried to do it. But knowing in 99.99% of the cases is far away from reality.

For example, some opponent types like the passive calling stations, you could not even put them in any range because they are calling your bets with any two cards. In this situation, you are bet/bet/bet with any MID+ and hoping for the best

[Lorence.xD]

This list is a good overview for beginners but Texas holdem pros know exactly what to expect from a hand based on their experience. They know that if 2 aces are down in the cards and they have 2 aces in their hand it is going to be a massive win for them in 99.99% of the cases.

Two pair is not the best case for players for me, I have seen pros got their asses handed to them because they thought that they have the best hand there is, there was this one game that I saw long time ago where one play an all in because of a 3 pair and not knowing that his opponent has a full house, at first the full house guy seems to be in the verge of defeat because he only has a high card and thought of bluffing but the showdown prove otherwise.

[Wexnident]

This list is a good overview for beginners but Texas holdem pros know exactly what to expect from a hand based on their experience.They know that if 2 aces are down in the cards and they have 2 aces in their hand it is going to be a massive win for them in 99.99% of the cases.

This is a myth...

You could put some opponents on ranges. It would be best if you always tried to do it. But knowing in 99.99% of the cases is far away from reality.

For example, some opponent types like the passive calling stations, you could not even put them in any range because they are calling your bets with any two cards. In this situation, you are bet/bet/bet with any MID+ and hoping for the best

99.99% of the time seems a bit overexaggerated, but if you were to calculate it, then the chances of winning against that is a pretty low afaik. Not sure about the numbers exactly, but just looking at the hands that could win against that, then one could assume already the chances of actually getting it. Still, most players know that even if it wasn't ace, as long as they have a pair, they havev a pretty good chance of fighting for a win for that round, most of the time.

[zonefloor]

I don't know much about the game of poker. But I like to play together. I will experiment with these statistics. Hope i win. serves to provide. I like this kind of sharing. I'm adding this title to favorites section. Thank you

[Darker45]

Still, most players know that even if it wasn't ace, as long as they have a pair, they havev a pretty good chance of fighting for a win for that round, most of the time.

It actually matters a lot which pair you have in your hand. If its an ace, it has a moderate fighting chance. But if you don't have a pair of high cards, I don't consider your hand as having a pretty good chance of fighting for a win.

And it also matters how many you are playing on a certain table. If you are at least 5, I'm afraid a pair doesn't have a really good winning chance. If somebody raises a big amount after the flop, I might not call at all. Or perhaps I'd take the risk and call up to the fourth street. After that, I guess I would just fold my pair if another big raise is happening.

[Mauser]

I don't know much about the game of poker. But I like to play together. I will experiment with these statistics. Hope i win. serves to provide. I like this kind of sharing. I'm adding this title to favorites section. Thank you

The statistics are great to know but they won't help you in how to play your hand much. For example, a full house is very rare but you can still manage to get it twice in a row, even though it's very unlikely. If we only play the best hands we become very easy to read by our opponents. It's advice able to try to bluff atleast sometimes to make it harder for our opponents.

[Fredomago]

I don't know much about the game of poker. But I like to play together. I will experiment with these statistics. Hope i win. serves to provide. I like this kind of sharing. I'm adding this title to favorites section. Thank you

The statistics are great to know but they won't help you in how to play your hand much. For example, a full house is very rare but you can still manage to get it twice in a row, even though it's very unlikely. If we only play the best hands we become very easy to read by our opponents. It's advice able to try to bluff atleast sometimes to make it harder for our opponents.

Poker is a full of Bluffing players that sometimes people don't buy this even if you are serious in you lays.
and i think Bluffers now also hesitate dealing with this strategy as Players specially New players has a strong character that will fight the Bluff without hesitations.

I don't know much about the game of poker. But I like to play together. I will experiment with these statistics. Hope i win. serves to provide. I like this kind of sharing. I'm adding this title to favorites section. Thank you

Just try experimenting with your Buddies and not in casino's that you might lose bigger.
make your friends a easy target using the statistics and if do good then try little amount in casinos and then learn more and more before finally do the big games.

[kryptqnick]

I've seen this table in Bitcointalk discussions before. The table itself is not extremely useful because the hierarchy of combinations in poker is aligned with it. However, keeping it close before making tough poker decisions might be a bit helpful because knowing the odds of your hand being beaten is important.
I've asked this question before, but not many people commented on this, so I'd like to ask it again: wouldn't it be useful if poker websites showed the probabilities of a player's hand being beaten by some other hand in the game to every person?

[wxa7115]

This list is a good overview for beginners but Texas holdem pros know exactly what to expect from a hand based on their experience.They know that if 2 aces are down in the cards and they have 2 aces in their hand it is going to be a massive win for them in 99.99% of the cases.

This is not accurate, to my knowledge the probability of winning with a pair of aces in the pocket is only 80%, as you may guess this is the highest probability among the starting hands and this is simply because your opponent can always draw something better than what you have in your hand, and this is because it is difficult to improve your hand, for the most part the most likely scenario is that you get a three of a kind rather than any other hand but your opponents can get two pairs, a straight or a flush so they have more draws than you.

Also there is no guarantee that you will win big, you need to manipulate your opponent to do that, this is why I love a player like Johnny Chan that plays his pairs of pocket aces slow and traps his opponent with this strategy.

[Lorence.xD]

I don't know much about the game of poker. But I like to play together. I will experiment with these statistics. Hope i win. serves to provide. I like this kind of sharing. I'm adding this title to favorites section. Thank you

Thank you for considering to put it in your favorite section, never seen that kind of compliment before. Although this will not help you much because it just shows the statistics behind the game.

I've seen this table in Bitcointalk discussions before. The table itself is not extremely useful because the hierarchy of combinations in poker is aligned with it. However, keeping it close before making tough poker decisions might be a bit helpful because knowing the odds of your hand being beaten is important.
I've asked this question before, but not many people commented on this, so I'd like to ask it again: wouldn't it be useful if poker websites showed the probabilities of a player's hand being beaten by some other hand in the game to every person?

To answer your question subjectively, I assume that it will be in real time so pardon if that is not what you meant. Having a stat counter during play time is very problematic because it removes the risk of going in even if you do not have a good card. They already do this kind of thing with poker tournaments although it is in spectator mode. If not in real time, I do not think that it will be of much help to put a stat counter because the game already ended and it will be difficult to analyze one game because as we all know, poker is fast pace.