# Questions tagged [poker]

Poker is a card game with several variants (Draw, Texas Hold'em, ...), the common goal being to collect face value patterns such as "four of a kind", "full house" or "straight" or all of a suit ("flush") with five cards. Questions about combinatorics, probabilities, strategies (bluffing and betting).

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### Expected number of aces in a poker hand

So I'm having difficulty understanding a certain idea. Say I have a standard $52$ card deck (fairly shuffled, etc.) and I pull $5$ cards from it. We ask, what is the expected value of the number of ...
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### Stud Poker Probability Knowing 2 Cards

Good afternoon, I find many topics on how to calculate the probability of a full house, a straight, and so on. But I did not find a source where the counting proceeds with the knowledge of some cards. ...
1answer
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### Extremal poker: the most favored that a currently weakest hand can be

We are playing heads-up Texas hold 'em poker. I want to find a situation where my hand is currently weaker than my opponent's (in the sense of hand rank if no more cards were to be drawn), but has the ...
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### Probability of getting a full house in five-card poker with 4 cards added? [closed]

a) If I draw 5 cards randomly what are the chances of getting a full house ? b) Which other card can you remove to maximize your chances of getting full house? So you have in total 56 cards, the 4 ...
1answer
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### Poker cards combinatorics question

Question Suppose you draw 7 cards from a standard deck of 52 cards. What is the probability that you draw three pairs of cards if the three pairs must have distinct denominations? the three pairs don'...
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### What is the probability that the hand contains more than one ace, given that it contains an ace of spades?

A poker hand of 5 cards is dealt from a normal deck of 52 cards. What is the probability that the hand contains more than one ace, given that it contains an ace of spades? I'm assuming that I need to ...
1answer
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### Can someone explain why the probability of getting a royal flush is only based on the choosing the suit?

So $|S| = 52C5, |E| = 4C1$ therefore $P = \frac{1}{649740}$. If you only select the suit, how do you guarantee that the cards OF the suit will be 10, J, Q, K and Ace? It seems so random that only $4C1$...
1answer
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### What is the Group of symmetries of Texas Holdem Poker hands?

In Texas Holdem poker, each player is dealt two cards from a standard deck of 52 playing cards. (2,3,4...Queen,King,Ace). What is the group of all the symmetries of all (two-card) poker hands? (Given ...
0answers
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### Number Of Two Pair (Poker) Combinations Allowing For Pairs Or The “Junk” Card To Be Of The Same Rank

The standard two pair formula is ${13\choose2}{11\choose1}{4\choose2}{4\choose2}{4\choose1}$ but this assumes that in the poker hand AABBC the rank of AA, BB and C cannot be the same (to avoid for ...
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### Probability of hitting a quad when the flop has a three of a kind in Texas Hold'em

Let's assume that I am playing Texas Hold'em with 5 of my friends (total 6 players). I have pockets Kings (KK). Now the flop has 3 A (AAA). I want to figure out if anyone on the board has beaten me ...
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### Poker Counting Problem

In Poker, I receive $2$ cards and they are a pair of $8$s. What are the chances of me getting, just a pair, 2 pair, and three of a kind(but nothing higher) as the other three cards are placed down? I ...
0answers
194 views

### Probability of at least 3-of-a-kind in a 7-card poker hand [duplicate]

This problem asks to explain why the method used is overcounting or undercounting cards in a 7-card poker hand that contains at least two 3-of-a-kind (3-of-a-kind means three cards of the same rank) ...
2answers
105 views

### Probability of a five-card poker hand containing 2 pairs

I am trying to solve this question in my own way. I tried counting like this- First card can be chosen in 52 ways, second in 3 ways because it has to be of same kind as first, third in 48 ways, fourth ...
0answers
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### Poker Combination problem

A little while ago I made a post on here and this is basically a follow up to it as I ran into some problems. Basically two people , player A and B, are playing a version of poker where there's 3 ...
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### Probabilities associated with each possible value of random variable ; 5-card poker hand

A five-card poker hand may contain from zero to four aces. If $X$ is the random variable denoting the number of aces, enumerate the range space of $X$. What are the probabilities associated with each ...
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### Counting pair in a poker hand - counting confusion

I want to be good enough to do math competitions, and one of the main topics in them is always combinatorics. So I'm going through a combinatorics book, "A Walk through Combinatorics." The confusion ...
2answers
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### Numbering system for poker hands

I figure that this is surely either a solved problem or it is provably impossible. But I'm not able to track down an answer. There are ${52 \choose 5}$ = 2,598,960 distinct ways to deal five cards ...
2answers
127 views

### Calculating the number of poker hands that have exactly 4 different denominations

I'm been working through some examples of questions mentioned in the title and came across this one that I wasn't entirely if I was approaching this correctly. My initial approach to solving this ...
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### Texas hold'em pecularity with different number of players

While simulating Texas hold'em poker hands, to find the probability that certain two cards would give the best hand after river, I found a pattern that I can't explain. I made $100,000$ simulations ...
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### How to calculate the number of unsuited hands in Texas Hold'em opening hand

I was just going back and refreshing my knowledge on binomial coefficients/probability and I was trying to calculate some poker odds since I would be able to look them up and verify my attempts. I ...