Questions tagged [probability]

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

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Calculating probabilities for 3, 4, 5 card Straight/Flush/Straight Flush

I am playing around with creating a new card game, similar to poker, and I am really struggling with figuring out the math behind calculating the probability of certain hands. Heres the overview of ...
581 views

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 ...
1 vote
226 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 ...
1 vote
45 views

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 ...
303 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 ...
528 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 ...
17k views

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 ...
54 views

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.
190 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 ...
433 views

Combinations and poker probability

How to calculate poker odds using combinations?
15k views

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 ...
27 views

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?
1 vote
352 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 ...
213 views

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 ...
59k views

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 ...
1 vote
486 views

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?
1 vote
1k views

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 ...
33 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 ....
1 vote
280 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 ...
198 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. ...
27k views

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 ...
1 vote
325 views

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♥...
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 ...
1 vote
336 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 ...
1 vote
316 views

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 (...
914 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 ...
158 views

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 ...
2k views

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?
224 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?
592 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 ...
179 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 ...
269 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 ...
3k views

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=...
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
325 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 ...
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 ...
47 views

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.
25k views

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&...
1 vote
535 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 ...
443 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 ...
296 views

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 ...
243 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, ...
10k views

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 ...
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 ...
23k views

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 ...
1 vote
68 views

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 ...
531 views

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 ?
1 vote
190 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 ...