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 ...

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Poker game probability [closed]

From a deck of 52 cards, pick 3 cards randomly, what is the probability that there is a pair among the three cards? (A pair means that two of the cards are the same number) I guess it allows to have ...
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1answer
43 views

How many $3$-of-a-kinds are possible if one ace is missing?

So I know how to do the simpler 'How many $3$-of-a-kinds are possible' question - it has been asked on here multiple times too. But what if say an Ace is missing. How would you go about starting the ...
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2answers
38 views

Explanation for solution of a combinatorial problem

The given problem is: An ordinary deck of cards is dealt to four people: Joe, Bob, Jim, and Larry. If Larry has exactly one ace, what is the probability that Jim has all the remaining aces? My ...
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2answers
56 views

Probability of Poker Hands with Joker

Need help with a homework question: If a five card hand from a standard deck of 52 with an added joker (wildcard) is drawn: What is the probability that a hand contains at least one pair? ...
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1answer
30 views

Simulated probability doesn't match closed-form answer

I am trying to calculate the probability of a hand of 13 cards containing at least five pairs. Three of a kind counts as one pair; four of a kind counts as two pair. I simulated millions of hands and ...
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0answers
38 views

Has two player five-card draw poker been solved?

I know that some other types of Poker have recently been solved with computers but has five-card draw poker been solved and if so, is there any place for mathematical analysses in the game? I need to ...
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2answers
489 views

What is the expected number of suits in a hand of 4 cards?

To find the expected number of suits the formula is $E(Num Suits) = 1*P(1 Suit) + 2*P(2 Suit) + 3*P(3 Suit) + 4*P(4 Suit)$ For the probability of getting 4 suits I got ${13 \choose 1}^4 {4 \choose ...
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1answer
50 views

How many poker hands have exactly two pairs?

I found an interesting solution to the combinatorial question of "How many poker hands have exactly two pairs?" and I cannot figure out (or find) the reasoning of the solution. The answer I found in ...
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1answer
54 views

What's more likely with 7 dice - Straight, Full House, or 3-of-a-Kind

Here's a problem I'm having. I have 7 dice. I want to rank the difficulty of achieving a particular 5 dice combination after all 7 dice have been rolled. A straight is when at least 5 of the seven ...
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1answer
80 views

Expected value of the call option in Caribbean Stud Poker: examples

For the game Caribbean Stud Poker, compute the expected value of the call option for the following cases. I try to solve part (a). There are $\mathsf{A}\mathsf{K}\mathsf{J}$ there. If $\mathsf{Q}$ ...
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0answers
37 views

On Casino Holdem game

For the game Casino Holdem, I am told to compute the expected value of the call option for the following hole cards and flop. (8♠,9♣) and (10♣,J♣,2♠) Can anyone help me on this problem. The rule ...
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1answer
26 views

Find the probability that at least one of poker opponents hits a card

In Texas hold'em, when you see the flop there is about 33% chance that one of your 2 cards hits something on the flop, maybe not exactly but let's say it's 33% that your opponent did hit something on ...
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3answers
138 views

Probability of get 3 cards out of 4

How to calculate a probability of choose 3 off-suited and off-ranked cards out of 4 given cards from a standard 52-cards deck (the situation when all the cards off-suited/off-ranked should be avoid). ...
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0answers
37 views

How can I find the probability of drawing cards in these cases?

Given 2 players A and B. We will draw 5 cards for A and then 5 cards for B. Find the probability of this event: A receives Two Pair (contains two cards of the same rank, plus two cards of another ...
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1answer
32 views

Poker probabilities 3 of a kind, 2 pair, 1 pair

I'm finding it hard to understand why the answers are what they are. correct # ways to get 3 of a kind: $13C1·4C3·12C2·4C1·4C1$ my thinking: $13C1 * 4C3 * 12C1 * 4C1 * 11C1 * 4C1$ the logic is ...
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1answer
29 views

Probability Poker Question

You are dealt $20$ cards. What is the probability you have all kings given that you hold at least one king? So I set it up like $$ P(4\textrm{ Kings | at least one king}) =\frac{{4 \choose 4}{48 ...
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1answer
57 views

Another way to calculate probability of full house

I am struggling to understand why my calculation is off by a factor of ten. P(AAABB)= $4/52 * 3/51 * 2/50 * 13 * 4/49 * 3/48 * 12$ My thinking is like this: P(full house) = P(3 of same card) * (# of ...
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1answer
63 views

Probability of five card stud flush

I'm not really good dealing with poker problems... I am doing a practice problem for a midterm coming up, and help would be appreciated. Consider the probability that, in a game of five-card stud, ...
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2answers
62 views

What is the logic behind the probability of getting 'four of a kind' in poker?

This hand ($5$ cards of $52$) has the pattern $AAAAB$ where $A$ and $B$ are from distinct kinds. The number of such hands is $\binom{13}{1} \binom{4}{4} \binom{12}{1} \binom{4}{1}$. The probability ...
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1answer
59 views

Odds of two specific Hold'Em hands and an exact board?

The goal is to solve the probability of a Texas Holdem hand occurring where at the river one player has quad $9$s and the other player has exactly a $9$-high straight flush. (For non poker players ...
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2answers
65 views

Poker odds: Chances of a straight flush, given H4,H5

I'm trying to learn Bayes's formula, and am coming up with some poker problems to learn this. My problem is as following: given a $H4,H5$ ($4$ of hearts, $5$ of hearts) hand, what are the odds that ...
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0answers
59 views

Probability of royal flush dealt to table of n players

I'm interested in calculating the probability of a royal flush being dealt to ANY of the n players seated at a Texas Hold'em poker game (2 hole cards, 5 community cards). The probability of YOU being ...
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1answer
84 views

Ways of getting three of a kind in a 52 card deck

This question has probably been asked before, but just to be clear here, I am NOT asking for the answer, I know the answer. What i want to know is why my solution is not equivalent to the actual ...
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2answers
46 views

Conditional Probability in Poker

I'm thinking of a ten person Texas hold'em game. Each person is dealt 2 cards at the start of the game. The question is: GIVEN that you have been dealt 2 hearts (Event B), what is the probability ...
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1answer
44 views

Applying Bayes Rule to Cards

I was playing poker with a friend last night when a question occured to us. I had a two Jacks and the flop came out: King Queen and 4. So, suddenly my pocket Jacks are not so great, unless another ...
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0answers
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What are the best $3$ pocket cards in Omaha poker?

In Texas Hold'em poker, the best $3$ pocket cards are AA, KK and QQ respectively. I've been trying to find the best $3$ pocket cards in Omaha poker, where you have to use exactly $2$ pocket cards out ...
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3answers
149 views

What's the probability of a straight in $5$ card poker given $5$ and $7$ of hearts?

Using a standard $52$ card deck, if you are given the $5$ and $7$ of hearts from it, what is the probability that you end up with a straight if $3$ additional cards from that same deck are given to ...
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3answers
107 views

In Texas Hold'em poker, is the ranking according to chance of beating 1 opponent's hand the same as according to beating multiple opponents?

In Texas Hold'em poker, you can rank hands according to the probability of beating one randomly generated opponent's hand. However, no one can compute the exact probabilities of beating $8$ random ...
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0answers
83 views

Poker Hand Probabilities in Doomtown Reloaded

The short version of my question is as follows: What is the best way to compute the probability of different hand ranks after redraw in poker? Can this easily generalise to a non-standard deck? ...
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0answers
32 views

How do they calculate players' chances of winning in 9-handed Hold 'em or Omaha poker with hidden information?

So Omaha poker is a card game where each player is dealt 4 private cards, and then 5 community cards are dealt in the middle, and each player makes the best possible 5 card poker hand by using 2 cards ...
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1answer
84 views

Counting number of two pair hands in poker (not standard)

I was doing number counting problem and wanted to check if my result was correct. Problem description: From a standard deck of cards(52 cards, 4 suits, 13 numbers in each suit) there are 5 cards ...
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3answers
84 views

Poker game full house

I'm dealing with an exercise which deals with the poker game. I need to calculate the probability of getting a full house. Full house is getting 3 cards of the same type and 2 cards of the same ...
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1answer
57 views

poker probability texas holdem

I get a few percent off from simulation results when I verify these probability calculations, so I am hoping someone spots it. When there is a suited pair on the flop in texas holdem and nine seats ...
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2answers
54 views

Poker blind interest equation

I'm trying to find the equation that will calculate my blinds for me based on number of players and target length of a tournament. I have most of it. I'm only missing one part. Given a starting blind ...
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2answers
91 views

Poker probability question [Texas hold'em]: Do chances to get a certain hand with the flop decrease with number of opponents?

In a basic Texas hold'em game if I had 2 6's I understand what the probability of getting a 6 on the flop is. My question is... I say no matter how many players are in the game that the odds are the ...
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1answer
46 views

Poker Return on 100 Hands

Just looking for a bit of validation of a theoretical problem I’ve been working on. It may be completely unoriginal, but take 100 hands of poker. For arguments sake, say the difference between the ...
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1answer
431 views

10-hand card is dealt from a well shuffled deck of 52 cards

A 10-hand card is dealt from a well shuffled deck of 52 cards. What is the probability that the hand contains at least two cards from each of the four suits?
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0answers
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Probability and Statistics: Bowling Night Poker

Let me build this up a bit. There's five people on my bowling team, including myself. None of us are especially good at bowling; our averages range from about 120 to about 155 (Mine is the 155, ...
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1answer
25 views

What is the probability of getting three “top cards” in the same suit and two cards in another suit (but both in the same suit)?

Jack, Queen, King and Ace are the top cards. What is the probability of getting three top cards in the same suit and two cards in another suit (but both in the same suit)? This has stumped me for ...
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1answer
52 views

Clarification for this combinations/permutations problem?

I've been going through a list of poker hands and their descriptions, and then attempting to calculate their probabilities by first calculating the number of possible hands for the given hand. I ...
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2answers
268 views

Probability of getting two pair in poker

I was looking at this website http://www.cwu.edu/~glasbys/POKER.HTM and I read the explanation for how to calculate the probability of getting a full house. To me, the logic basically looked like you ...
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2answers
181 views

Probability of poker cards using combinations, its a poker question [closed]

Choose two cards from a regular 52 card deck, what is the probability of getting atleast one face card from the two card hand drawn? (Without replacement) What is the probability that the first card ...
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1answer
58 views

Probability one pair poker

Which is the probability to obtain one pair in poker? I'm interested in the case when I decide which is the pair. I know the probability for one pair is: $$\frac{C^{4}_{13}\cdot4\cdot ...
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1answer
41 views

Probability of intersection of two events in poker game

Here, can anyone explain in "Pr[A3|A1(Intersection)A2] = 11/50", how do you interpret A(intersection)B here? I mean if A1 is the event that the first card is heart, and A2 is the event that the ...
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3answers
564 views

What is the probability of of drawing at least 1 queen, 2 kings and 3 aces in a 9 card draw of a standard 52 card deck?

The title problem is just one specific example of a more generalized problem that I'm trying to solve. I'm trying to write an efficient algorithm for calculating the probability of at least k ...
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1answer
2k views

What is the probability of of drawing at least one king and one ace in a five card poker hand?

The title problem is just one specific example of a more generalized problem that I'm trying to solve. I'm trying to write an efficient algorithm for calculating the probability of at least k ...
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2answers
130 views

Poker hand probabilities

I am very bad at probability problems in math. There is a homework question such that: During a game of poker, you are dealt a five-card hand at random. With the convention that aces may count ...
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1answer
98 views

Texas Hold'em Probability Question

In a game of Texas Hold'Em you are dealt: 4 of hearts and 5 of hearts The flop: 2-club, 6-spade, K-Diamond. Define set S1 as 7-card hands that contain the 5 revealed cards AND contain a straight ...
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2answers
43 views

How many possible deals in straight poker.

Each player is dealt 5 cards. 5 players how many deals are possible? I know that for one player there is 2598960 possible outcomes i.e. 52 C 5, I need to know how I can do this for the next four ...
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3answers
247 views

Recommended math background for game theory

I recently got interested in some game theory applications to poker. I want to try some of them out programmatically, but a lot of the math is a bit confusing. I learn math on my own fairly quick and ...