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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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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35 views

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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25 views

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 ...
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27 views

Variance in Poker

I am working on a Poker Strategy that involves Game Theory, and my question is about calculating Variance on the table if we assume no one at the table changes their play style. I believe that a ...
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39 views

Poker Chips Shuffling: Top Chip Expected Value

In order to shuffle a pile of n poker chips. They are first separated into two equal piles of size n/2. Next, chips are added by alternating from each side. The side that is chosen to have the bottom ...
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1answer
36 views

Probability of Getting Two Specific Cards in 7-Card Poker Hand, Using Ordinary Deck of 52 Cards?

If we have an ordinary deck of 52 cards, how many possible 7 card poker hands are there that contain exactly one "2" and 1 "King"? Originally, I was thinking of it as $$ \frac{\binom{52}{4}*\binom{48}...
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27 views

Probability in the game of draw poker

Suppose you are playing a game of draw poker and you have 3 aces and two different small cards. If you discard two small cards ,what are your chances of improving your hand on the draw? Improvement ...
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62 views

Texas Hold'em Poker odds with many opponents - impossible to compute?

I'm starting to wonder if it is even possible to analytically calculate the odds of beating multiple opponents in a Texas Hold'em Poker game. Let's start with an example to explain the complexity of ...
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1answer
38 views

Probability for hand with no sets (3+ of a kind / straight flush of 3+ cards) or potential sets (no additional card can make a set) in a card game?

Problem In a gin variant, you win immediately if you are dealt a hand with no sets (3+ of a kind or suited run of 3+ cards) and no "potential sets", i.e. no additional card added to the hand could ...
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1answer
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What is the probability of a poker hand (5 cards) containing at least one club? [closed]

Could this be calculated using the complement of the event? And if so, how?
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What's the probability for a 14-card hand to contain at least one full-house?

(This question is related to my previous question: When drawing 14 cards from a set of 52 cards, is it more likely to have a full house or two consecutive pairs?). Problem: What is the probability ...
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1answer
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When drawing 14 cards from a set of 52 cards, is it more likely to have a full house or two consecutive pairs?

This is a problem that has been bothering me for quite some time now: When drawing 14 cards from a set of 52 cards (standard poker deck), is it more likely to have at least one full house or at least ...
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question about combinatorics but i've never played poker.

I have a questions about combinatorics. my question : You are playing a version of poker where you can see three of your cards and three of your opponents. She has 6♣, 8♣, 10♣ and you have A♦, A♣, A♠....
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Poker Probability with hands of 6 cards

I am trying to answer Question 1(d). A valid hand would be Ace hearts, 10 hearts, 2 clubs, 7 clubs, Ace spades, J spades. My attempts have given me 2 different answers that I am unsure of. What I ...
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1answer
23 views

Types of flops, in relation of held hand

I'm having difficulties on matching the expected total number of flops $50\choose3$ $= 19600$ by splitting them in categories in relation to the held hand, let's say for example it is AS (Ace of ...
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1answer
24 views

Probability Drawing Different Poker Hands

For my year 11 specialist math PSMT, I've been tasked with designing a card game with 5 divisions. The game I designed was "5 Card Draw" (working title), it is played with a deck of 53 cards (standard ...
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1answer
33 views

Probability of drawing a Nothing from a poker hand

I'm trying to figure out the probability of drawing a poker hand of no value from a deck of 53 cards (1 additional joker) the context that it cant contain a joker, and none of the cards can be the ...
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2answers
32 views

Probability of Drawing Three of a Kind and a Joker

In a standard deck of cards plus 1 additional joker (53 cards), I am trying to calculate the probability of drawing a Three of a Kind and a Joker in the same 5 card hand. At the moment I know the ...
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1answer
26 views

Probability of Drawing Different 5 Card Hands from a Deck of 53 Cards (standard deck with 1 joker)

I'm trying to calculate the probabilities for drawing different hands from a deck of 53 cards (standard deck with 1 joker) The hands I am trying to calculate are: A single pair Three of a Kind ...
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2answers
37 views

Probability of full house when a player already has 2 cards of the same value (ex 5 of hearts/clubs) when drawing next 3 cards (total 5)

I am having trouble trying to calculate the probability of getting a full house when a player already has 2 cards in their hand. For example, if they have a 5 of hearts and 5 of clubs, then they can ...
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1answer
54 views

Conditional poker probability. [closed]

In event space for a standard pack of 52 playing cards. Assume there are no wild cards. Consider 5-card hands. Compute the conditional probability of a straight flush given that the first two cards ...
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2answers
95 views

Probability of getting full house in five-card poker with cards missing

Missing cards from the deck: $\heartsuit3$, $\spadesuit$King, $\heartsuit$King, $\clubsuit$king and $\spadesuit2$ a) If I draw $5$ cards randomly what are the chances of getting a full house ? b) ...
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1answer
70 views

Poker combinatorics

I have a problem solving the following: Out of a $52$-card deck, I'm missing all my kings and one card of number $2$. Now if I pull five cards randomly, what is the chance to get $4$ of a kind? ...
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1answer
19 views

Probability of getting a particular card in Poker

Suppose, I am playing a poker match. I have a pair of 5 in hand and see that the there is no 5 in the first 3 drawn cards. What is the probability that there will be at least one 5 in the next two ...
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1answer
48 views

Poker probability with missing cards [closed]

I have a deck with 52 cards where I miss the following cards:♤2 ♤King ♡King ♢3 ♧5 and I need to : a) find the possibility to get a four of a kind; b) if another card goes missing, what card should ...
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36 views

In a 52 deck card, you draw 4 cards without replacement, what are the odds of picking exactly 2 different suits and a 5?

In a standard 52 card deck, what are the odds of picking exactly: 2 Different suit a 5 Picking two different suits: (52/52) * (39/51) Picking a 5: (1/52) 0.76 * 0.019 = 0.014 What to do with the ...
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2answers
42 views

In poker, What is the probability of the first player receiving a royal flush?

In the game of poker, five cards from a standard deck of 52 cards are dealt to each player. Assume there are four players and the cards are dealt five at a time around the table until all four ...
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95 views

In poker, What is the probability of the first player receiving a royal flush (the ace, king, queen, jack, and 10 of the same suit)

In the game of poker, five cards from a standard deck of 52 cards are dealt to each player. Assume there are four players and the cards are dealt five at a time around the table until all four ...
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3answers
139 views

In a 52-deck card, draw 6. Probability of getting 3 different suits, an 8 and a face card?

A standard deck of cards has 52 cards. If order does not matter, what are the chances of getting 3 cards of different suits, an 8 and a face card? I thought like this: P(first card being a different ...
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1answer
59 views

Full House Probability: Why is my answer incorrect?

For the probability of a full house, I did: 52/52 * 3/51 * 2/50 * 48/49 * 47/48 = 3/20825 I was off by a factor of 10 or in other words: ...
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1answer
43 views

Poker and a conditional probability question

This problem is from the book, "Introduction to Probability" by Hoel, Port and Stone. It is problem 24 on page 48. Problem: Find the probability that a poker hand of $5$ cards will contain no cards ...
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1answer
41 views

Ranking 5 Deck Poker Hands

I'm trying to create a poker game that uses 5 decks, and have run into a problem calculating how many possible combinations of suited 4 of a kinds there are. Suited 5 of a kind seems easy enough. To ...
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3answers
78 views

A poker deck has $52$ cards, $13$ ranks ${A,2,…,10,J,Q,K}$ and $4$ suits {diamond, club, heart, spade}.

A poker deck has $52$ cards, $13$ ranks $\{A,2,...,10,J,Q,K\}$ and $4$ suits {diamond, club, heart, spade}. If $5$ cards are dealt, what is the probability that there is an ace of diamonds? Here is ...
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1answer
40 views

Fullhouse probability for first and third person [duplicate]

my goal is to calculate the probability of first and third person getting a fullhouse at the start of the game (5 people and 52 cards). I understand that for the first person it would be: $$\frac{\...
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1answer
57 views

Poker probability question - multiple players

I'd like to ask for help with a task that I've been given. The task goes like this: In a poker game (52 cards), 5 players are given 5 cards each. What is the probability that both the first and the ...
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1answer
47 views

Conditional Probability in 7-card Poker

For 7 card poker (Texas Hold 'Em) .. how would you find the probability of getting a straight, given that someone else has a straight flush? I'm not sure if the answer is to use Bayes' theorem. If ...
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0answers
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Game Theory Poker - Nash equilibrium: Choose between bet or raise and range of hands

I would like to understand how we choose the best action and how we compose the range for it. I have some notion on zero-sum games and minmax strategies. And I know software that does this for texas ...
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Find General Formula for Combinations about Blackjack

I was recently thinking about the following combination problem for pokers and I got stucked. Consider blackjack games, where Ace is either 1 or 11. Card 2~9 is just 2~9 and card 10, J, Q, K are ...
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3answers
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Does a player having one hand increase the likelihood of other players also having that hand?

Say a deck of cards is dealt out equally to four players (each player receives 13 cards). A friend of mine said he believed that if one player is dealt four-of-a-kind (for instance), then the ...
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1answer
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Reconfiguring this poker equation to solve for a different variable

I'm working on a poker problem where I'm trying to calculate how much of the pot I want to bet (as a percentage). I'll give the nuts and bolts of my request first and then an explanation of it's usage ...
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1answer
139 views

Conditional Probability with Poker Hands

I am trying to answer this question: Draw $5$ cards at random from a standard deck of $52$ cards. Find: $\text{a) } P(\text{full house} \mid \text{full-house or three-of-a-kind}) $ $\text{b) }P(\...
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2answers
67 views

How many possible poker hands with missing cards and too many of other cards?

The problem: You got a deck with 52 cards. Two cards are missing: heart 10 and 9. But you also got some extra cards: you got 2 diamond 7 and 6 to make up for the missing cards. This is what the deck ...
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2answers
39 views

How many chips would you risk for a bet

Say you have a total of c chips, and I present to you a game with a probability $p$ of winning, and payout $k:1$ (where $p > 1/(k+1)$, so this is a +EV bet). How many chips would you risk to take ...
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Counting poker hands: full house, straight, $4$ of a kind, straight flush

A deck of cards contains $52$ cards. There are $13$ different kinds of cards, with four cards of each kind. (Among the terms commonly used instead of “kind” are “rank,” “face value,” “denomination,” ...
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1answer
34 views

Checking understanding using multiple ways to calculate a 2 pair in 5 card hand of poker

In order to get a better understanding of basic probabilities, I have been trying to calculate poker hand probabilities in as many ways as I can think - for example calculating the numerator for a 2 ...
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4answers
89 views

Combinatorics with playing cards

I have a question that I can't seem to find the answer to: What are the odds of pulling 3 cards from a normal deck of playing cards (52 cards, 4 suits, 13 different values) and at least 2 of the ...
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1answer
49 views

If I am dealt Q♢ K♢ 7♠ 3♢ 5♠ and hold the Q♢ and K♢, how do I calculate the number of possible hands that yield 1 pair of Jacks or Better?

For example, If I am dealt Q$\diamondsuit$ K$\diamondsuit$ 7$\spadesuit$ 3$\diamondsuit$ 5$\spadesuit$ and hold the Q$\diamondsuit$ and K$\diamondsuit$, how do I calculate the number of possible ...
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1answer
122 views

How to calculate the optimal amount to bet?

Suppose each player is randomly and secretly assigned a number between $1$ and $6$ and then a communal dice is rolled four times. After each roll, you can place a bet or fold. After the fourth bet is ...
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1answer
82 views

Finding the number of ways of dealing a poker hand

A man is dealt a poker hand (consisting of 5 cards) from an ordinary pack of 52 playing cards. Find the number of ways in which he can be dealt a "straight" (a straight is five consecutive values ...
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0answers
43 views

probability for full house and other combinations in bet on poker game

We are trying to calculate probabilities(and odds) for "bet on poker" game on which we are working now. To calculate probabilities and odds for each hand we used https://github.com/cookpete/poker-odds ...

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