Questions tagged [probability]

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

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12
votes
7answers
50k 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
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1answer
226 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♥...
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4answers
126 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 ...
0
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2answers
3k 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 ...
0
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1answer
226 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 ...
0
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0answers
35 views

Kuhn Poker - Blocker Effect - Probability Theory (Bayes Rule)

I am currently studying the blocker effect in the game Kuhn Poker Kuhn Poker Wikipedia. Below you can see the game tree. At the first node, both players have 1/3 of one of the three possible cards (K, ...
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2answers
54 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 ...
0
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1answer
307 views

Combinations and poker probability

How to calculate poker odds using combinations?
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2answers
128 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
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0answers
123 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 (...
2
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1answer
90 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 ...
4
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4answers
11k 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 ...
8
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3answers
11k 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 ...
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1answer
145 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 ...
7
votes
4answers
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?
0
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0answers
109 views

Introduction to Probability with Texas Hold’em Example #3

Let A be the event that your hole cards are AK, and let B be the event that your hole cards are both red. a. Find P(A). b. Find P(A|B). c. Are A and B independent? Why or why not?
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1answer
157 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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0answers
42 views

Maximum Call Amount By Expected Value (e.g. in no limit hold'em)

Recently I started learning the basics of poker and I came across the 2015 MIT course by Kevin Desmond. In Episode 3 he mentioned the concept of Maximum Call Amount. In short, the formula to calculate ...
2
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1answer
90 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
2answers
99 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 ...
4
votes
1answer
122 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 ...
0
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0answers
50 views

Bill Chen's Mathematics of poker p41 : estimating paramers/ bayesian statistics

Dear members of poker stack exchange, I have trouble understanding how the P(B|A) column of the second table is computed. First of all, I guess there is a mistake in the header of this table : it's P(...
6
votes
4answers
2k 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=...
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votes
2answers
335 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
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1answer
65 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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2answers
2k 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 ...
0
votes
1answer
45 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.
6
votes
11answers
20k 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&...
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1answer
206 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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votes
2answers
105 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 ...
0
votes
1answer
137 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 ...
0
votes
3answers
167 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, ...
0
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3answers
8k 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
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1answer
871 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 ...
12
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2answers
20k 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
1answer
59 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 ...
1
vote
2answers
164 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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votes
3answers
498 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 ?
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1answer
184 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 ...
3
votes
3answers
935 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 ...
6
votes
2answers
2k views

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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2answers
267 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)...
2
votes
2answers
287 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 ...
4
votes
3answers
18k views

Probability of flopping straight flush

Assume you're given 2 cards of the same suit, and the next three cards (flop) are also the same suit as your hole cards. What is the probability of that happening? So I figured out that 2 cards have ...
6
votes
4answers
196 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
2answers
544 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
1answer
135 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?
2
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0answers
152 views

Poker pre-flop probability trainer

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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votes
1answer
73 views

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 ...
0
votes
1answer
103 views

Quantify the equity of position (button) heads up

Can the value of the button be quantified heads up. Is there an optimal number of hands to play assuming the SB is going to play GTO? Or if there is an EV based solution? Can use fixed sized ...