Questions tagged [probability]

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

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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 ...
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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 ....
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Probability of one player making Royal Flush in a 6-person Texas Hold'em game

See also: Probability of two royal flushes' played in a row One person making Royal Flush in Texas Hold'em with 5 community cards is 1 in 30,940. How about 6 players combined, assuming no one ...
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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 ...
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2 answers
383 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 ...
0 votes
1 answer
179 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
2 answers
299 views

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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2 votes
1 answer
570 views

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
4 answers
252 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
2 answers
201 views

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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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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-1 votes
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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 (...
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1 answer
210 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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1 answer
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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 ...
2 votes
1 answer
364 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 ...
4 votes
1 answer
231 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 ...
4 votes
2 answers
166 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
1 answer
234 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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1 answer
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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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2 answers
334 views

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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1 answer
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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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2 answers
1k views

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
1 answer
405 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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3 answers
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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
1 answer
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
1 answer
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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
4 answers
312 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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2 answers
4k views

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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3 votes
3 answers
2k views

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
1 answer
188 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
2 answers
303 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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6 votes
4 answers
215 views

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 ...
9 votes
2 answers
721 views

Drawing Dead Preflop?

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 ...
2 votes
1 answer
151 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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2 votes
0 answers
181 views

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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1 answer
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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 ...
3 votes
2 answers
510 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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2 votes
1 answer
530 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
1 answer
2k 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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1 answer
170 views

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 ...
2 votes
1 answer
226 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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1 answer
278 views

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 ...
2 votes
1 answer
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
2 answers
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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2 votes
1 answer
978 views

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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2 votes
2 answers
356 views

Quads sevens 5 times in one night

I got quad sevens five times in 3 hours . The first three times were within the same round of ten hands. Without a technical explanation what are the odds of three times in ten hands and five times ...
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