Questions tagged [probability]

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

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20 views

What are the odds, Split pot 7 card stud between Royal flushes? [closed]

It is rumored to have happened by a dealer named Al Bass, a few decades ago at the Sahara.
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31 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 ...
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72 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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100 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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167 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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131 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 ...
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104 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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128 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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177 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 ...
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38 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 ...
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1answer
70 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 ...
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1answer
87 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 ...
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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(...
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66 views

How do estimate if the EV loss, between two strategy, is acceptable?

with poker solver, i have set two strategy on flop, optimal and simplify(more easy to use and replicable in game): Pot is 220. Effettive stack is 890. Strategy 1 - optimal : the EV is 120,62. Strategy ...
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2answers
90 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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1answer
52 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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43 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.
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86 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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116 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 ...
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2answers
230 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?
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1answer
183 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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3answers
153 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, ...
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1answer
694 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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1answer
54 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 ...
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2answers
142 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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2k 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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812 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 ...
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178 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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2answers
261 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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195 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 ...
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504 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 ...
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1answer
127 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 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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72 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 ...
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2answers
363 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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1answer
341 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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1answer
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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1answer
81 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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66 views

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 ...
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1answer
163 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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223 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 ...
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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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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 ...
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1answer
755 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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267 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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2k views

How to deal with players who limp into every hand - and always see the river [duplicate]

I play poker quite regularly with friends. A smallish game usually between 5-7 players. Generally I can read the other players easily. They either play too tight so i fold early or as soon as they try ...
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445 views

Outs when needing more than one card

I recently learnt about outs, and the magic 4-2 rule. However all the examples that I see use the example of needing one card to complete your set. Why we don't consider the fact that I can have two ...
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269 views

Chances of an opponent not having a flush on 3-flush board

If there are 5 cards on the board and 3 of them are hearts and I don't have any hearts in my hand, what is the probability of someone else NOT having 2 hearts in their hand?
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501 views

Nash-like table for a full 9 players table?

I'm wondering, is there anything like the Nash Equilibrium that I can use to know when to go all in if my blinds a low in a full 9 players table?
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275 views

Determining probability of opponents succeeding + yourself?

To get the probability of the next card being your card that you need, you simply get all the cards that match the definition / total cards not pulled. However, at river how do you determine your ...