Poker Probability

[sotoshihero]

This is why I never win playing with poker, bad odds, bad at bluffing ain't got no future for this game lol.

You must be overconfident in doing these, a do-or-die decision,  so as not to give your opponent to think that your bluffing.  

Do you think the professional poker players memorized this? Does this increase the chances of determining the correct hands of the other players?

Surely they don't memorize this in order to increase your chance of winning. I've watched some poker matches where the poorest hands are able to get the other player with better cards to fold with their bluffing skills. Even Kevin Hart did it succesfuly. The odds will be the same no matter how you memorize this table, it's a mix game of skill and luck as OP said, skills to bluff and luck for cards, that's what makes you win poker base on what I learn from watching videos and reading OPs post.

Sometimes this is more of a psychological game, but if you are good at analyzing those cards you may have a better chance of winning. The more cards are open, the better the probability that you can compare with your on hand and determine the odds for winning. Skill and luck is really a deadly ingredient combination to win.

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[TitanGEL]

Thanks for the share OP.

I learned poker and successfully improved my strategy as I progress but I'm not aware of that.

But yes, just to show the probability of numbers about this game.

Do you think the professional poker players memorized this? Does this increase the chances of determining the correct hands of the other players?

Even they somehow know the probability to win, the key to win is proper execution. That's why even with good cards, it's not an assurance of an easy win.

It is really the execution that can help us to win in poker, I prefer to play poker in real life where it considered as traditional gambling because you are playing physically. The excitement and the feeling is really different for me because I also play poker in different gambling sites where I considered as boring because I do not feel the excitement that I felt playing it physically. When you are playing in real life, you can observe your opponent’s where it can give you an idea on what they are thinking and what cards are they holding. I actually like the thread because this is also the first time for me to see and understand the probability where in you can considered as lucky even though your cards is just a full house because the probability of getting it is just 0.17% 

[Lakai01]

-snip-
as lucky even though your cards is just a full house because the probability of getting it is just 0.17% 

The "just" has now triggered me
I like to play poker both in real life and online, and I can count the hands I've lost on a full house on one hand.

Of course, there is still the chance that someone has an even better hand, but the probability is extremely low. So a Full House is almost a guaranteed win of a round.

[kryptqnick]

I wondered some time ago whether the following improvement to poker websites could be implemented: each player sees the probability of her/his hand and the probability of someone else having a better one. Can this be properly counted, taking into account not the cards which are open on the table and those the player currently holds? Would it be useful?

I think this is a cheat, really, I'd not be in favour as it takes away some of the player's expertise. It's like if there was also an on-screen counter showing running percentages of how often each player has bluffed.

I am not so sure about that. If all players have this option, they can all be relieved by using it. If it makes poker too easy, it means that the best poker players are bots because real people have to put lots of effort into memorizing what's going on in the game and keeping in mind the odds of different hands, whereas a bot could store such data without many difficulties. This would make poker a lot like chess, and I don't think it's true. If a person knows the odds, it doesn't make the game too easy to play or too obvious. We play dice very differently, for instance, even though we always know what are the odds of us losing.

[ashmodeus]

to be honest, i've seen that table calculation since 2016 , and for sure, its not helping much. since its back to your mentality as well, low pair card got raise by 1/2 total chips, i just folded, eventhough i know chance for get 3 of kind or two pair is close already.

It's one of the most exciting card to have especially if only two guys are remaining are on that phase. You can win with the weakest card that you have by simply bluffing, that's all. I mostly bluff if my cards are weak, it's fun yet there are also good players that you can't scare.

nah , i will not take a risk, before, I was also the one who bluffed a lot, even with bad card, but i just learned from youtube how to play safety, since i just play on tournament, its kinda funny if u just playing for 5 minutes on tournament.

[Lorence.xD]

The "just" has now triggered me
I like to play poker both in real life and online, and I can count the hands I've lost on a full house on one hand.

Of course, there is still the chance that someone has an even better hand, but the probability is extremely low. So a Full House is almost a guaranteed win of a round.

I do agree with full house guaranteeing a win, the other upper hand cards are more rare to show on a player's hands, most of the time, the only hands that can defeat a full house is another higher card full house.

[pinggoki]

The "just" has now triggered me
I like to play poker both in real life and online, and I can count the hands I've lost on a full house on one hand.

Of course, there is still the chance that someone has an even better hand, but the probability is extremely low. So a Full House is almost a guaranteed win of a round.

I do agree with full house guaranteeing a win, the other upper hand cards are more rare to show on a player's hands, most of the time, the only hands that can defeat a full house is another higher card full house.

In live poker you can easily determined if the cards of your enemy is better than you just for example you are holding a full house and yout enemy is holding a higher full house than you, you can easily know if it is a higher or just a bluff, unlike online poker you can't read the face of your enemy, just the call or re-raise of the enemy will determined if it is a bluff or not. Anyways, if you are holding a full house, for us gamblers we can assured that full house is already a sure win set of cards in poker, unless it would be a fish or "katkong" in tagalog if they have a higher full house or set of cards than you have.

[Poker Player]

I take it that table is talking about getting those hands at the flop if you play Texas Holdem or before discarding if you play 5-card draw.

One thing I've learned over the years is that unlikely events occur.

The likelihood of those hands is not as important as how strong is your hand compared to your rival's.

According to the table, a straight has 0.3925% chance to occur and a flopped flush 0.1965%. I see flopped straights or flushes almost every day.

If you play a couple of thousand hands a day on average you are going to see a lot of those unlikely events to occur.

[davis196]

That's great,but what's the point of sharing this info.Do you want to teach us how to play poker?
Did you copy pasted this info from somewhere?Can you mention the source?
I'm not interested in math and I don't care about the probability of getting a particular hand,when I play poker."Psychological" elements like having patience,persistence,and the ability to decide when to play aggressively and when to quit and the the ability to bluff are more interesting to me.

[Lorence.xD]

That's great,but what's the point of sharing this info.Do you want to teach us how to play poker?
Did you copy pasted this info from somewhere?Can you mention the source?
I'm not interested in math and I don't care about the probability of getting a particular hand,when I play poker."Psychological" elements like having patience,persistence,and the ability to decide when to play aggressively and when to quit and the the ability to bluff are more interesting to me.

Just wanted to share this info to others who might be curious about the math behind poker, obviously you are not one of them. The source is copied in Wikipedia, not many goes to search there so I had an inkling to search it and share it as some might be interested in it. There is an article about psychological elements of poker if I am right, you can search for it.

[iv4n]

...

Just wanted to share this info to others who might be curious about the math behind poker, obviously you are not one of them. The source is copied in Wikipedia, not many goes to search there so I had an inkling to search it and share it as some might be interested in it. There is an article about psychological elements of poker if I am right, you can search for it.

I think you have a nice share here, math behind poker, but it's just a half of the story, or to say one side of the poker! Psychology is the other part, and to have a complete story you should include it in your post!
Math is easy to handle, you learn your odds pretty fast! But when in comes to live game with other people, in some hand's psychology is more important than math!
Steamtyme, tokeweed, figmentofmyass and a few others have awesome conversation about poker, with deep analyzes of poker strategies, some hands and how you should play them! https://bitcointalk.org/index.php?topic=5214582.msg53510089#msg53510089
It's a long thread, but who wish to learn more about poker and how to play it should read it! Good luck people and join bitcointalk private series: https://bitcointalk.org/index.php?topic=5288276.0

[Saint-loup]

Poker by far is my favorite when it comes to gambling, it is a good mixture of skill with the ability to bluff other players to the point that you can win a zilch even though he got a better hand, and luck by the probability of getting the better hand than your opponents. In this post, I will focus on the probability of getting a higher hand. The table below only presents 5-card hand poker game. If you are curious as to what is the math behind poker, hopefully this post will satisfy you.

|

Hand

|

Distinc Hands

|

Frequency

|

Probability

|

Cumulative Probability

|

Odds Against

|

|

Royal Flush

|

1

|

4

|

0.000154%

|

0.000154%

|

649,738:1

|

|

Straight Flush

|

9

|

36

|

0.00139%

|

0.0015%

|

72,192 1/3:1

|

|

Four of a Kind

|

156

|

624

|

0.0240%

|

0.0256%

|

4,156:1

|

|

Full House

|

156

|

3,744

|

0.1441%

|

0.17%

|

693.17:1

|

|

Flush

|

1,277

|

5,108

|

0.1965%

|

0.367%

|

508.8:1

|

|

Straight

|

10

|

10,200

|

0.3925%

|

0.76%

|

253.8:1

|

|

Three of a Kind

|

858

|

54,912

|

2.1128%

|

2.87%

|

46.33:1

|

|

Two Pair

|

858

|

123,552

|

4.7539%

|

7.62%

|

20:1

|

|

One Pair

|

2,860

|

1,098,240

|

42.2569%

|

49.9%

|

1.366:1

|

|

No Pair/High Card

|

1,277

|

1,302,540

|

50.1177%

|

100%

|

0.995:1

|

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.

Very interesting topic, thank you for posting it.
But what are your sources for those probabilities please? Is it a personal work? Did you count them yourself? If it's a personal observation they are maybe not totally universal

[imstillthebest]

Very interesting topic, thank you for posting it.
But what are your sources for those probabilities please? Is it a personal work? Did you count them yourself? If it's a personal observation they are maybe not totally universal

he didnt add sources . this can only be his personal observation but i can say that his observation is close to being accurate because that is what i observed too whenever i play poker .
its hard to get a good combination but its easy to get a common cards or bad combination .
 i played poker and card games on a crypto casino and on the side they will put the probability for each card and combination , theres no major difference from this table made by op .

[Mauser]

That's great,but what's the point of sharing this info.Do you want to teach us how to play poker?
Did you copy pasted this info from somewhere?Can you mention the source?
I'm not interested in math and I don't care about the probability of getting a particular hand,when I play poker."Psychological" elements like having patience,persistence,and the ability to decide when to play aggressively and when to quit and the the ability to bluff are more interesting to me.

There are many courses online to learn how to play poker. There are plenty of different poker variants out there and you also need to decide if you want to go into tournaments or prefer cash games. Watching a few tutorials online from YouTube can definitely help to make up your mind. But in my opinion to really learn a game you will need to put in the hours and actually play. Maybe try with play money first.

[bonjouros]

I really suck in uderstanding this kind of of probability even if I love playing poker though in my cases I am not into 5 cards instead I am into 2 cards only.

So I guess, I cannot use this probability to my advantage but if it can be applied also to 2 cards then I will try my best to understand it and use it to my  advantage if possible. But I am hoping that I will not get any headache before I can understand how I can get an advantage by understanding these probability as  there are percentage that I am having a difficulty in understanding.

[johhnyUA]

This is a great example that chances to have 4 of a kind is really low.However it shows that the more down we come like one pair or two pairs chances are generally pretty high.Beside these statements which I think everyone should copy to a notepad or word document to keep always present during poker gameplays let’s also not forget that also skill and patience also play a big role if you want to be a successful poker player.

And the water is warm, yes? 

You can not copy this, you can count it by yourself in your head. For example, 4 of a kind.
we have 13 denominations, How many ways we can choose one of it? Pretty obvious answer - 13 ways.
And how many ways we can choose 3 another cards of the same denomination from number of cards which left? This is binomial coefficient, C(48, 3)

And our probability will be the multiply of 13 * C(48, 3) divided by all possible combinations (this also will be binomial coefficient or combination of k sets from n set, where n = 52 and k = 5) C(52, 5).

And you will get needed probability. Looks a little complicated, but after you will handle such powerfull theory you will be able to count probabilities with more practical view, for example what a probability to get two cards of the same denomination if you already has 2 on your hands 

[Globb0]

Have you made any charts around opening hands and perhaps relative position.

Sort of ranges. Maybe I am not explaining t very well.

I know it still depends what everyone else does and I don't even repeat myself if I can.

The bad beats you listed, happen, but like mentioned all to often it I someone going in with k7 and they hit 3 sevens  :/


Cheers

[FontSeli]

~
Source:https://en.m.wikipedia.org/wiki/Poker_probability

Poker is really the most interesting gambling game in my opinion, with the exception of guessing the price of Bitcoin (joke). When I saw this topic, I thought I would find something interesting in it, but you just copied part of the article posted on Wikipedia.
I think you needed to add something else from yourself. What do you think?

[cabalism13]

~
Source:https://en.m.wikipedia.org/wiki/Poker_probability

Poker is really the most interesting gambling game in my opinion, with the exception of guessing the price of Bitcoin (joke). When I saw this topic, I thought I would find something interesting in it, but you just copied part of the article posted on Wikipedia.
I think you needed to add something else from yourself. What do you think?

Looking at the numbers I think there's nothing more to add, as I play poker on different apps, threse numbers speaks so loud in my ears, all of the chances are quite right in my opinion. Besides it doesn't matter to me as long as I can bluff my own way to winning 😅

[FontSeli]

~
Source:https://en.m.wikipedia.org/wiki/Poker_probability

Poker is really the most interesting gambling game in my opinion, with the exception of guessing the price of Bitcoin (joke). When I saw this topic, I thought I would find something interesting in it, but you just copied part of the article posted on Wikipedia.
I think you needed to add something else from yourself. What do you think?

Looking at the numbers I think there's nothing more to add, as I play poker on different apps, threse numbers speaks so loud in my ears, all of the chances are quite right in my opinion. Besides it doesn't matter to me as long as I can bluff my own way to winning 😅

I'm not really interested in which combination comes out more often and which less often. I'm more interested in why everyone discards their cards when I have 2 aces and I'm ready to go all the way.
Sometimes I think that my opponents see my cards, or everything is just easy to read on my face))