Questions tagged [card-games]

Questions regarding probabilities and combinatorics of card games. The number of cards in the deck, number of players, and other parameters can vary.

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Odds calculation when drawing 3 cards.

I would like some feedback on some of my thinking. Situation : I pull 3 cards consecutively from a standard 52 deck. Question 1 : What are the odds of pulling a flush? (all same suit). i am trying to ...
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Probability In Playing Card Questions

Find the probability that a specific player gets 4 kings and another specific player gets exactly 2 Aces in a hand at whist, given that there are 4 players and 52 playing cards. Here's what i did: ...
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What is the probability of a 4 of a kind being the flop and turn in a 5 player game of Texas Holdem? [closed]

What is the probability of cards 11, 12, 13 and 14 forming a 4 of a kind (e.g. 4 fives) within in a random shuffled deck of playing cards? The 10 cards dealt before this can be any 10 cards as long as ...
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36 cards were distributed equally to 6 people. Prove that there is a person who has at least 4 cards of the same suit

36 cards were distributed equally to 6 people. It is known that for any two people there are at least two suits, such that they have equal cards of these suits. Prove that there is a person who has ...
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Good examples of zero-sum perfect information game?

I am trying to come up with some good examples of zero-sum perfect information game. What I have on the list are: Tic-Tac-Toe Connect 4 Chees Any thing more? One more question, for connect-4, this ...
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Can someone help me estimate values of stochastic variables in my study of a card game?

Background: I'm trying to analyze a variant of Open-Face Chinese Poker, a card game where players essentially try to arrange drawn cards in special combinations to earn points. Normally, each hand ...
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Number of $5$-card hands where all $4$ suits are present

A standard $52$-card deck consists of $4$ suits and $13$ ranks. Find the number of $5$-card hands where all $4$ suits are present. I tried to solve it like this: ...
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expected value of 7 cards game

hi i am trying to find a question about calculating the expected value of a card game. The overall game should be like this: (1) you have 7 cards with number 1- 7 printed on each , and they are all ...
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Probability of all 4 of at least 1 of the 13 denominations in hand of 13 cards. [closed]

Compute the probability that a hand of $13$ cards contains all $4$ suits of at least $1$ of the $13$ denominations. I am able to understand how to start this question. Can someone help me out? The ...
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1answer
46 views

Expected value of card game

You have a deck of $52$ cards, and you keep taking pairs of cards out of the deck. If a pair of cards are both red, then you win that pair; if a pair of cards are both black, then I win that pair; if ...
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how much would you be willing to pay for this card game?

suppose there are 12 cards with number 1 - 12 on each card. All cards are faced down and are listed one by one in front you. You get to pick one card, if the card has 1 on it, you get $1. If it's 2, ...
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The winning probability in a card game

Suppose that I am playing a card game with my friend - a $1$ vs $1$ card game. All cards in standard card deck (52 cards) are shuffled randomly, then two cards are drawn to each person respectively. (...
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Is there an optimal strategy for this game of card?

This game is based on the concept of minimizing resource wastage. The Game Cards which do not have numbers are not used e.g. ace, king, queen, joker. For the remaining cards, regardless of the color ...
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1answer
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What is the name of this non-linear optimization problem?

I'm using a JavaScript library ( jsLPSolver ) to solve optimization problems to do with building a deck of magic the gathering cards. Currently my problem are linear, as the library can only solve ...
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Dealing cards to 4 people

I and three friends are playing a game of Open Face Chinese Poker involving a standard deck of 52 cards. Player X got a Queen Fantasy land which means the next time the game is played, he will get the ...
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even or odd card game

There are cards numbered $1,2,\ldots,2n$ where $n$ is odd. The deck is shuffled. The top two cards are drawn. If the sum is even the even player gets a point and if the sum is odd the odd player gets ...
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Number of straight flushes and three-of-a-kinda with three cards

The two questions involve drawing 3 card combinations (thus non-repeating) from a standard 52-card deck with the following conditions. 3 cards in a "ladder-type" ascending order from the ...
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1answer
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What is the probability that a person is dealt 13 cards of the same suit out of the 26 cards he is dealt to, from a shuffled 52 cards deck?

I know that to the probability of drawing 13 cards and having them in the same suit from a deck can be found by $\frac{4}{(52!/13!\cdot 39!)}$, but what about from drawing 26 cards? I originally ...
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Is dealing cards till a particular one is seen the same as dealing till the last one

Question comes from Introduction to Probability, by J. Blitzstein. A deck of cards is shuffled well. The cards are dealt one by one, until the first time an ace appears. Find the probability that no ...
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You draw three cards from a standard deck of 52. What is the probability that you draw two clubs and a face card that could be any suit?

I am not sure how to properly interpret this question. For example, if I randomly select three cards and get an Ace of clubs, a Queen of clubs, and a three of diamonds, would this outcome belong to ...
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Picking colored balls randomly.

I created this post yesterday but I have a further enquiry that I will post here. In 13 balls we have: 5 Blue 4 Red 4 Green We randomly select 6 balls without replacement, what is the probability of ...
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1answer
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Number of ways to arrange 4 identical decks of cards

Let's say we have 4 identical decks of cards, and each one has 10 cards (therefore we have 4 units of the first card, 4 units of the second card and so on). In how many ways can we arrange these 40 ...
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Taking two draws, what is the probability that $x$ aces are in the first draw if there were $w$ aces in both of them together?

I have some doubts about my answer to this question, and I hope someone can help me figure it out. Considering two consecutive, independent draws with replacement card by card, where you draw $n$ ...
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Expected value of the minimum of 3 cards

Is this question it is shown that the probability of a minimum is: https://stats.stackexchange.com/questions/220/how-is-the-minimum-of-a-set-of-random-variables-distributed $1-[1-F_X(x)]^n$ I have a ...
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1answer
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Card Game Probability Difficulties

Construct a $30$ card deck including $w$ doubles in the following manner: 1) Remove all jokers, face cards, and spades, from both our permanent deck and a spare, temporary deck 2) Select $...
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Deck card probability distribution with missing cards

Given a deck of cards (standard 52 deck), we know that there are some cards missing. Some of the cards that are missing we know exactly what they are (e.g. an Ace, a Two are missing). Other cards ...
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Probability of having1 King and no Queens in 6 cards pick

Lets say we have a deck of 36 cards (4 suits x 9 values). What is the probability that if you pick 6 random cards there will be at least 1 King and totally no Queens? I know that the probability of ...
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Odds of an Unwinnable Game of Rummikub

I was playing the game Rummikub with my family the other day and the tiles were drawn in such a way that the game could not end. Here are the rules: There are 106 tiles in the game which at the game'...
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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 ...
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Card game - probability [duplicate]

In the card game ($32$ cards, $3$ players receive $10$ cards each, $2$ remain), $A$ = "The remaining ones contain $2$ aces" $K$ = "I get at least one king". In total there are $4$ aces and $4$ ...
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What is the probability of a least one person having 4 hearts given this circumstances?

$4$ people $(A,B,C,D)$ receive $13$ cards each from a normal $52$ deck cards. If $A$ and $B$ have combined $9$ hearts, what is the probability of either $C$ or $D$ alone having the other $4$ hearts in ...
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1answer
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Pull 3 cards from a deck - Odds

i've been looking for help for some days for this,I have a few simple questions. Could you fill in the blancs where needed? situation : i Pull 3 cards from a normal deck of 52 cards, simultaniously. ...
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1answer
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Probability of specific cumulative sum when drawing cards

I have a question regarding the probability of reaching a specific cumulative sum when drawing cards. Let's say we have a regular deck of 52 playing cards and we want to know what the chance is of ...
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1answer
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Probability of winning high-low with full deck

I play a game on a site I use that's a version of the casino game of "High Low." A standard 52-card deck is shuffled, and the top card is revealed. The player guesses whether the next card on the top ...
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Are there any real & decent mathematics video games?

Personally, I like to play video games from time to time, especially arcade games (e.g. Tetris, pinball) or fast-paced games like Super Hexagon, which is known to be quite challenging. However, for ...
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Probability of drawing a particular set of cards

I have a deck of 60 cards, all of which can be assigned to one of three categories (A, B, C). There are 30 cards in category A; 22 in category B; and the remaining 8 in category C. I intend to draw 7 ...
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Card game probability 3 players

I don’t know how to handle this 3 players case, may anyone give a hand? Thanks! When playing card game, there are 3 players playing 32 cards, each receive 10 cards, 2 remind on the table. Overall ...
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If a deck of cards is divided into 4 hands, what is the probability that the north and east hands have the same number of spades

Suppose we deal four 13-card bridge hands from an ordinary 52-card deck. What is the probability that the North and East hands each have exactly the same number of spades? The solution I got was $$\...
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Probability of getting at most 2 hearts in a 5 card hand, using a normal 52 cards deck?

I think I know how to do it, but I am not 100% sure and also maybe there is a better way of doing it. My solution $$\binom{13}{0} \times \space \binom{39}{5} + \binom{13}{1} \times \space \binom{39}{...
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Four cards are randomly chosen without replacement from an ordinary deck of 52 playing cards.

Four cards are randomly chosen without replacement from an ordinary deck of 52 playing cards. What is the chance of all chosen cards not being aces? I found a similar problem here but the provided ...
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How many hands of five cards contain cards from exactly three suits?

I have been trying to solve this but I stink at this kind of math. What I have is (4 choose 3)(13 choose 2)(13 choose 2)(13 choose 1)=316,368. Is this answer right or wrong? Thank you!
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Count the number of combinations of a pair if the deck is a pinochle deck.

the problem goes like this, A pinochle deck consists of 48 cards. There are six denominations (or values) of the cards: 9, 10, Jack (J), Queen (Q), King (K) and Ace (A). There are two of each ...
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Probability of Drawing certain Suits from a Deck of Cards

Let's say I have a standard deck of 52 playing cards, and I need to find a card of a specific suit (lets say spades, for example) and the deck must be sufficiently randomized afterwards. One way to do ...
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Finding the distribution of a card game where replacement happens until you recieve the card you want

Here is a card game. At the beginning of the game, you choose what rank of card you will be taking. Every round, 5 cards are dealt. Any that match the rank you chose are kept, the rest are shuffled ...
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In a game of bridge with a deck of 52 cards, Determine the probability of having a hand containing exactly 4 kings, 4 queens, and 5 hearts?

In my attempt i'm not sure if i am under counting by having 13C2 instead of 13C1 and 12C1. Thanks. My attempt: [(13C2)(4C4)(4C4)(11C5)(4C1)]/52C13.
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Calculating odds of someone holding x clubs in a 4-player game given that he holds the club Ace, at least 4 clubs, and you hold 3 clubs

In the context of a Bridge game: I have 3 clubs in my hand and I want to find how many clubs my partner has. Before any card has been played (i.e. from the bidding alone), I know he holds at least 4 ...
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3answers
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Counting bridge deals if we only distinguish face cards

Bridge is a game of four players in which each player is dealt 13 cards from a standard 52 card deck. Bridge players (such as myself) are interested in the number of possible deals, where each player ...
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A game of skat.

Anne, Ben and Feline play a game consisting of 32 distinct cards. The cards are shuffled at random. Anne receives 12 cards, Ben and Feline receive each 10. Anne’s hand contains precisely two Jacks, ...
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2answers
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What is the probability of drawing at least 1 ace, at least 1 king, and at least 1 queen, in a 5 card poker hand from a standard 52 card deck?

I use the following terms to define the different events: A = draw at least 1 ace B = draw at least 1 king C = draw at least 1 queen I use the following expression to define the problem: P(A∩B∩C) =...
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Can anyone improve on my 'rule of thumb' for determining how likely you are to be successful in a game of Solitaire ( Klondike version)?

In a standard game of Klondike Solitaire, seven cards are initially exposed in the tableau. I have developed a simple rule of thumb which will indicate how likely you are to have a successful outcome ...

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