# Questions tagged [probability]

deals with computing probabilities for many commonly occurring events in the game of poker

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### How many players to consider for probability calculation

if I play on a table with 6 players, websites like https://www.omnicalculator.com/other/poker-odds ask you for the number of opponents. What should I fill in there, the number of opponents initially ...
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### How often are the 5 community cards the best hand?

Can we calculate the probability that the 5 community cards are the best hand, i.e., that all remaining players chop the pot? I imagine that this probability drops as the number of players increases.
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### Optimal strategy for known card distribution

Are there any optimal strategies in THNL if I know the distribution of opponent's cards at each turn?
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### Probability of getting 3 of a kind by at least the river (assuming unpaired hand)

Here's the question: Assuming an unpaired hand of 2 cards in poker (2 & 10, 3 & Q, NOT A&A), what is the probability of having 3 of a kind after all 5 community cards have been dealt? My ...
31 views

### NLH Probablility of Drawing a hand

When dealt 5 cards from a deck the probabilities of seeing a str8 flush, 4 of kind, full house, flush, str8, 3 of kind, two pair, pair, or high card are well known and easily computed: str8 flush ....
289 views

### This is a probability question which will require an expert mathematician's expertise. Below is the criteria

Eight handed Texas Hold-em game using a 52 card deck. This is a 3 1/2 hour session in which there were 105 hands of poker played. One Individual achieved the following four poker hands. A. Quad Eights ...
503 views

### How to calculate the probability of flopping four of a kind with no pocket pair?

My hand is any 2 cards that do not have the same rank. What is the probability of flopping a four of a kind? The formula I used is: (2 c 1)(3 c 3) / (50 c 3) c = chooses 2 c 1 - We have 2 ranks in ...
190 views

### Unpaired hand vs probability that the opponent has a pocket pair

My question is the following : What is the probability of facing a pocket pair (preflop phase) with an off-suit hand? I made some calculations considering a single adversary. I display them here. ...
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1 vote
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### Does 7 card poker hand odds change if i know 2 of the cards? If so how?

In Wikipedia, it shows that the Pair probability for 7-card poker hand is 43.8%. After that 2 card is dealt to me, lets say Ace of Spades and 7 of Diamonds, does knowing these 2 cards effect the ...
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### What are the odds of drawing a seven card straight flush

I had the unbelievable experience of drawing a seven-card straight flush while playing with five other players with one deck. The hand started with the ace of spades and ended with the seven of ...
1 vote
275 views

### What would be the most transparent way to show a fair shuffle literally possible?

I want to make an ios app, for fun to improve my dev skills, to do what no other app/poker site has done and be completely transparent. I just want to match casinos shuffling as imperfect as that may ...
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1 vote
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### What is the probabilty that any of your opponents has any of specifict hands?

I'm creating a database of all choices of 7 cards out of 52. It's quite flexible because it allows to compare choices like: MyHand+FLOP+TURN+RIVER and OpponentsHand+FLOP+TURN+RIVER and tell whether my ...
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1 vote
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### Introduction to Probability with Texas Hold’em Examples #5

You are playing a hand of poker against one individual. Your hole cards are 8♦, 2♦ and your opponent’s hole cards are K♣, Q♣. The four cards on the table after the flop and the turn are J♦, 9♦, T♠, 5♥...
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### Introduction to Probability with Texas Hold’em Example #4

Suppose in a tournament with only three players left, first place receives \$6,000, second place receives \$3,000, and third place receives \$500. You have a 32% chance of winning first place, 30% chance ...
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1 vote
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### How likely is a full house on a paired board vs. a double paired board?

Recently I had a situation where I made a flush on the turn but my opponent made a full house on the river. The board was J5566 so it wasn't too difficult for anyone to make a full house in this case (...
221 views

### Introduction to Probability with Texas Hold’em Examples

In a game of Texas Hold’em, what is the probability that your hole cards will be the same suit?
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### How to calculate pre-flop odds with hands revealed?

I’m trying to create a backend for a Poker odds calculator. I know how to go about calculating odds post-flop, but I’m having a hard time calculating the odds pre-flop. How do I go about calculating ...
533 views

### Probability of flopping a straight

I was thinking about calculating the probability of flopping straights, with certain hands. First, I thought about situations: obviously the difference between two cards can't be higher than 4. If the ...
262 views

### Why are the odds 16 to 6 that any given player does not hold a pocket pair?

In the book Ken Warren teaches Texas Holdem, its explained that there are 1,326 possible combinations of hole cards. Then its explained that if you disregard suits, there are 169 possible two-hole ...
175 views

### Calculating Odds for 3 of a kind

I am confused by this odds calculation here: https://www.pokernews.com/poker-tools/poker-odds-calculator.htm Basically the scenario that I have is below: I understand everything except for the 3 of a ...
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1 vote
305 views

### Total probability of 3 of a kind

I know the probability of getting a pocket pair is 5.88%. I know the probability of then getting the 3 card on the flop is 10.78% (removing possiblity of full house and 4K). So is the total ...
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### Probability that any player will receive any similar hand of the previous hand of any player?

I want ask, how to count this case? I understand that every deal of cards is a separate event, and does not depend on the previous one.
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### Calculating outs on a 9 player table

Suppose you want to calculate the equity for a hand 4 and 8 (the color does not matter). The cards on the flop are A,2,3. To calculate the probability to have a straight you first consider the outs ...
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### What's the probability of each poker combination winning the showdown?

I play a poker-like game on a casino site, which offers dynamically changing coefficients for each hand on the table. Each round (blind, preflop, flop, turn) gamblers can bet that one of each hands ...
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### What is the probability of 2 players each holding two cards of the same suit in a 9-handed Texas Hold 'em game?

What's the probability of two players each holding two cards of the same suit in a 9-handed Texas Hold 'em?
1 vote
508 views

### How are Texas Holdem pre-flop hand rankings mathematically determined?

How are hand rankings like the one below determined? https://en.wikipedia.org/wiki/Texas_hold_%27em_starting_hands I'm specifically looking for the math behind the ranking. As a specific example, 22 ...
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236 views

### Could it happen, from a theoretical point of view, that all players at a table tie?

I know of hands where the pot gets split among 2 or 3 players, but could it ever occur that the same happens for 4, 5, 6 players and so on up to 9, at least from a theoretical point of view? If so, ...
1 vote
1k views

### Does AA have the highest Equity in "double-board-bomb-pot" with 9 players?

I fielded a Poker StackExchange question the other day about whether AA is the best starting hand in Texas Hold-Em No Limit vs. 8 other players. Indeed, it is so. Now I have a variant of this ...
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1 vote
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### How Does EV Change As More Cards Come Up?

I am trying to find a resource/simulator that tracks how EV changes as more cards get delt throughout the hand and then showing the overall EV (assuming an average of all the different EVs at each ...
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1 vote
343 views

### Playing with an infinite copies of a deck

Let's assume we are no longer having a deck with 52 cards, but infinite cards, where every card has a probability of 1/52 to be received. With the logic, if you have two cards, the probability for a ...
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### Probability of two royal flushes' played in a row

So the situation was the following yesterday: 3 players in game: I have two kings in my hand, and with the flop I receive a quad of kings, player 2 folds, player 3 goes all in - I call. He gets the ...
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### Chance of winning heads-up by always shoving pre-flop

I've been generally wondering about what sort of winrate good players can expect vs. worse players, and thought of an interesting limit to this winrate. In NLHE, if the worse player just blindly ...
1 vote
189 views

### Which probability to get any combination on flop with AA?

I want know which probability to get various combinations with AA vs 1 opponent to flop: Which probability to get one pair? Which probability to get two pair? Which probability to get set? Which ...
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1 vote
305 views

### What to do if you are dealt AA at the begining of a tournament

Imagine you are in a tournament no rebuys allowed, you are on the big blind with AA and someone on early position pushes all in, should you take a chance on variance against a probably (AA, AK, KK, QQ)...
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### Why isn't every value player rich?

I'm a beginner, sorry if this question is absurd. If a player simply bets with probabilities in mind, and always made the correct move for every action, would s/he become rich in the long run? If ...
762 views

Suppose there is some situation where Player A moves all-in and ALL Players call such that all players are all-in (they have equal amounts of chips, so no side-pots). Is there a possible distribution ...
152 views

### Draw poker should you keep AK

5 card draw and you have AK and junk. Assume unsuited. A♠K♣T⋄8♣5♠ Should you keep AK or just the A?
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### Poker pre-flop probability training tool

Is there a freeware, better FLOSS, online or preferably offline trainer for preflop probabilities. I imagine different play modes with entering percentages under measurement of time resulting in ...
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### Can I get probability of winning a HU SNG tournament out of ROI % against an opponent?

I am currently trying to evaluate my expected value in HU SNG. One part of this is using a binomial distribution to understand P to win exactly or fewer tournaments out of some amount. So, I have a ...
515 views

### Probability your opponent has a pocket pair when you are paired versus not

If I am holding a pocket pair does that effect the probability my opponent has a pocket pair.
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559 views

### What are the 5 card hand probabilities

Of all the 5 card poker hands what are the probabilities? And how are probabilities derived?
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1 vote
3k views

### Odds Of Someone Having A Flush

I recently played at a rather loose table where it seemed to be acceptable practice to chase a flush no matter what amount of bets were made. Let's say you are at a 9 player table. There are 2 suited ...
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### Probability of flush on board and no player has a flush card

What is the chance the board has a flush. And two players have no flush card.
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### Probabilities for each high card hands in draw poker

What are the probabilities in draw poker of being dealt 3 cards to a flush, straight flush or royal flush 4 cards to a flush, straight flush or royal flush 3 cards to a straight 4 cards to a ...
1 vote
242 views

### What are the odds of the river containing a full house?

I was watching a game in a bar the other day and the river ended up containing a full house. What are the odds of this?
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### Combining poker hand probabilities (Texas Hold'em)

This is the board : Board: [9d 8h 7c] My hand : [10d 7s] Opponents (unknown): [Xx Xx] Cards remaining in the deck is 45. As there is still a turn and river to come, the total combination of hands is ...
4k views

### Short deck probability

Short deck is remove 2-5 so 36 cards left. A6789 is a straight. What is the hand order and probability. For example a flush is harder to make but a straight is easier. Ideally post the ...
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1 vote
4k views

### How to calculate probability of flopping a set (with pocket pairs)?

Building a poker program and would like to make sure I have my calculation correct. If a player is holding pocket pair, how does one calculate the probability of flopping a set (one card out of the ...
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### How to count the number of starting hands in Texas Hold 'em

I'm revisiting the excellent book by Tony Guerrera, Killer Poker by the Numbers. In the first chapter he goes over how to count the number of possible starting hands but leaves, as an exercise for the ...
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