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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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 ...
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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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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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What is the probability of seeing a royal flush and a four of a kind in the same round with ten players?
We were wondering and concluded it is possible to have two players, one having a royal flush, the other having four of a kind, if there is a pair and three high cards on the table. But the situation ...
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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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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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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 ...
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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 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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Pocket pair starting hands vs. probability of opponent having a pocket pair
According to Wikipedia, the probability of being dealt any pocket pair as the starting hand is ~6% (78/1326=0.0588), but yet the probability of facing another player holding a larger pair when holding ...
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On the turn pot odds to call versus outs
When facing a bet on the turn (river card to come) how to equate call a bet to number of outs?
You think you are beat but you have a number of outs.
When is it profitable to call?
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AA versus AA what is the chance of winning
AA versus AA the only way to win or lose is a flush
What is the chance of a flush?
To me a general answer on how to calculate odds is not a duplicate. I think most or many people on this site ...
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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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Best hand versus AA
Statistically what is the best hand versus AA (other than AA)
I had read 56, 67, 78
Suited not the suit of any ace
56 being the best
I cannot figure how 56 is better
Ran on poker stove
...
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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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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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What are the actual odds of being dealt pocket Aces?
I have been looking at the way people calculate the odds of poker hands for a few hours and i think there is a HUGE flaw. In poker a player is never dealt two CONSECUTIVE cards. This in my view ...
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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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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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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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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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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 ...
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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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Probability of x pocket pairs at a table of n people (NLHE)?
With n people at a table, what is the probability that x of them are dealt pocket pairs? There are several easy ways to approximate this but I was wondering there was an elegant solution. Any takers?
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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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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 ...
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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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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 ...
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Formula for making a single pair on the flop
I'm trying to get the probability of pairing only one hole card on the flop. According to this calculator,
http://www.texasholdem-poker.com/calculator?card1=8&card2=13&chance_format=...
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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?
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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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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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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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What are the odds of having 2 Quads in the same hand?
Just watched a video that went as follows:
Player 1 (Button): Q♥Q♠
Player 2: 9♥9⋄
Player 3: 2♣2♠
Flop: Q⋄9♠Q♣
Turn: 5♠
River: 9&...
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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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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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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, ...
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Holding suited connectors odd of flopping 2 pair or better
Pre flop with suited connector what are the odds of flopping 2 pair of better?
For example if I am facing a bet and a raise from big stacks and I have 78s what are my odds. I am up against an ...
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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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Starting hands probability
The following is a passage from Wikipedia on starting hands probability:
The 1,326 starting hands can be reduced for purposes of determining the probability of starting hands for Hold 'em—since ...
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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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You have AA in the BB. The BU opens to 3.5x. What is your line?
You have AA in the BB. The BTN opens to 3.5x. What is your line ?
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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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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 ...
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Starting hands head up
Does anyone have charts for starting hands heads by position up or even order of hands?
I know any Ace and any pair is valuable but I cannot find more specific guidelines.
I found order of hands ...
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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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