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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Probability of card game
In this game, we use a standard shuffled deck of $52$ cards. The suits of each card do not play any part.
Take a card from the deck one by one. If the card's rank is equal to the number of cards you ...
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20 cards with 4 specials split in 2 batches of 10. Whats the probability...
There are 20 cards and inside them there are 4 specials (i.e. hearts) and 16 "others" (i.e. other colors).
We need to split it to 2 players, therefore each of them have 10 card.
What is the ...
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Minimum amount of required chits to award player points
There is a board game for up to four players that has 7 rounds and at the end of each round the game awards the first player 3 points, the second 2, the third 1 and the fourth 0 points.
The points are ...
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Drawing Cards from a Deck [closed]
You have a standard deck of 52 cards. When drawing 3 cards randomly from this deck, answer the following questions:
What is the probability of drawing at least one Ace card (excluding Jokers)?
What is ...
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Probability of finding successive cards of a certain suit in a 13 card hand
A deck of cards contains 52 cards. Player G has been dealt 13 of them. Compute the probability that player G has a. Three successive spades
b. At least three successive spades
c. Three successive ...
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Expected number of cards between first Jack and first queen given first Jack appears before first Queen.
Suppose we draw cards from a standard deck one-by-one. Find the
expected number of cards after the first Jack and before the first
Queen given that the first Jack appears before the first Queen.
My ...
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Expected value of highest card before first ace
For practice, I decided to invent a variation on the problem of the expected number of cards to be drawn until the first ace is found. I would appreciate some feedback and clarification on certain ...
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How to compute probabilities in a card game?
Setting:
I am developing an app for a card game with 4 players.
Every player can see his own hand, but has normally only probabilities, which cards are in the hand of the other players.
Lets take as ...
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French Tarot suits probability
French Tarot is played with a 78-card deck.
The deck includes four suits (hearts, diamonds, spades, clubs).
Each suit contains 14 cards: 1, 2, ..., 10, Jack, Knight, Queen, King.
There are also 21 ...
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Is there a winning strategy in the card removal game?
A and B play a game with blue, red, and green cards. They start with an even number of $n$ blue cards ("stacks"). Player A starts, and the players take turns. Only two moves can be made:
(i) ...
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Count possible outcomes in dealing cards [closed]
our players Blanche, Dorothy, Rose, and Sophia are playing bridge. An outcome is a particular partition of the $52$ cards into
assignment of $13$ cards each to the $4$ players. Leave your answers in ...
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Number of cards between first jack and queen
You pull cards out of a shuffled deck until you get a jack and a queen. Given see the jack first, what is the expected number of cards between the jack and the queen?
I believe this is a conditional ...
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Optimal Strategy for 29 card game
I recently played an interesting card games called 29 and was trying to figure the optimal strategy for the same.
Here's the wiki link for the game
https://en.wikipedia.org/wiki/Twenty-eight_(...
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Probability: Card distribution problem
A deck of 52 cards is equally dealt to 4 players.
Find the number of ways to distribute the cards so that each player has exactly one card from each rank.
[Note: A deck of 52 cards consists of 13 ...
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Group generated by pile shuffles
I can find plenty of questions relating to riffle shuffles, but none about the simple pile shuffle. My question is about the permutations possible on eight cards by pile shuffling.
Eight cards are ...
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Probability of drawing two different suits out of 4 cards.
Given a deck of 40 cards, with 4 suits of 10 cards each and cards numbered from 1 to 10, we draw 4 cards. Let the random variable N be the number of different suits.
I am asked to compute $P(N=2)$.
...
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" How many ways are there to choose four cards of different suits and different values from a deck of 52 cards ? "
"How many ways are there to choose four cards of different suits and different values from a deck of 52 cards ? "
I solved this question in this way :-
"So, for the first card we have ...
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Draw 5 cards from a deck of 52 without replacement, what is the probability that those 5 cards are in ascending or descending order?
Need help double checking the answer for this one:
Firstly, calculate the probability of getting 5 distinct cards. This would be:
52/52 * 48/51 * 44/50 * 40/49 * 36/48 = p
Now, the probability of the ...
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Expected number of cards to draw before first ace using stopping times?
Consider the classic combinatorial problem that asks how many cards we should expect to have to draw on average before we see our first ace. There are several solutions. My first instinct was to write ...
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2 dice -> 9 cards
Alice has two standard dice with labels 1 thru 6. When she rolls them and adds their labels, she gets a distribution over integers in [2, 12]. Bob has nine cards, each labeled with some real number. ...
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Standard Deviation of 26 Cards
What is the standard deviation for 26 cards drawn from a standard deck (each card's value ranges between 1 and 13)? Assume selection is with replacement.
I saw someone approach this problem by summing ...
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Sum of Variance
I came across the following question.
What is the variance of 26 cards (assuming cards values are between 1 and 13)?
The answer for the question involved finding the variance for 1 card and ...
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Choosing $m-1$ consecutive cards
You have a deck of n cards with face values $1,...,n$, out of which you pick m cards u.a.r. without replacement. You want to know what is the probability that there are at least $m-1$ cards whose face ...
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Probability of drawing cards with both required and negative conditions
Question: How do you check for a drawn card being any card other than a certain card when drawing cards WITHOUT replacement, but also apply conditions on the rest of the cards. To make things more ...
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Why the probabilities are not adding up?
I have this problem
Question: Four cards are drawn at random from a pack of 52 cards. Find the probability that two are kings and two are queens.
Answer: $$
P(E) = \frac{\,^4C_2\cdot \,^4C_2}{\,^{52}...
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What is the probability of getting a 3-of-a-kind in a 7 card poker hand?
Obviously, the denominator in the probability formula is $\binom{52}{7}$. For the numerator I was thinking it would be $\binom{13}{1}\binom{4}{3}\binom{48}{4}$, but this gives a probability of about 7....
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Conditional probability after drawing the first card of any color
My card deck has $2n$ cards, $n$ black and $n$ red. I keep drawing cards (without replacing) until I reach the first black card. What is the probability that the next card is again black?
Surprisingly ...
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Who is the winner in the Low-High card game?
Recently, I do watch a Low-Card game in Korean Game show called Running Man. Here is the link. Basically, the game is like this.
There are 20 cards in the table, numbered from 1 to 20.
There are 4 ...
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Five cards from a standard deck are lined up in a row. How many of these line ups contain exactly one queen?
Five cards are dealt off of a standard 52-card deck and lined up in a row. How many such line ups are there in which exactly one of the 5 cards is a queen?
My attempt at a solution:
The queen could be ...
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Introductory probability question involving permutations of cards
I'm struggling with the following introductory probability problem:
Bob randomly chooses 8 cards from a 52-card deck. What is the probability that all the aces are contained in his choice?
The ...
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Riffle Shuffle - Example
Small question: In the paper by Bayer and Diaconis "TRAILING THE DOVETAIL SHUFFLE TO ITS LAIR", the authors claim that the number of ways to riffle shuffle a certain ordering of cards $\pi$ ...
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Probability of getting 2 cards with the same color
You have two decks of cards: a 52 card deck (26 black, 26 red) and a 26 card deck (13 black, 13 red).
You randomly draw two cards and win if both are the same color. Which deck would you prefer?
What ...
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Picking cards from a 65-card deck
A special deck has 5 suits of 13 cards each, making a total of 65 cards.
We are dealing a 6-card hand from this deck. In how many ways one can pick a "well-suited" hand (defined below)?
A ...
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Expected number of cards fixed in a deck after a certain operation, Paul Zeitz, 3.1.28, pg 69, Art and Craft of Problem Solving
Problem: Given a standard deck of 52 cards, extract 26 of the cards at random in one of the $(52 C 26)$ possible ways and place them on the top of the deck is the same relative order as they were ...
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Probability of two consecutive pairs in a hand of cards out of X identical playing card decks
I play a game that involves standard decks of playing cards, and scales with the number of players. 4 players use two decks of standard playing cards, 6 players use three decks, etc.
One sequence of ...
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Expectation of time for an ace to appear [duplicate]
This question appears in Zhou's A Practical Guide To Quantitative Finance Interviews.
What is the expected number of cards that need to be turned over in a regular 52-card deck in order to see the ...
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Odds of getting a 3 card straight from 3 cards out of an 8 deck set
Title says it. Combine 8 decks, shuffle, deal three cards. What are the odds that these three cards make a straight. Not just looking for the answer as I believe I found that online. Really I'd like ...
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In MTG Arena Jump In! Events, How do I maximize my long term rare/mythic rewards? [closed]
Introduction:
Magic the Gathering: Arena is a online collectible card game where you build a deck of cards and battle other players based on the physical trading card game of the same name. In the ...
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Probability that the next card is the ace of spades
Say I have a standard $52$ count deck of cards in random order, and that I start flipping cards from the deck over until a king appears, which is card #$19$. What's the probability the next card is ...
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Making card configurations in Sagemath
I'm following SageMath's tutorial on Combinatorics and one of the exercizes is to calculate the set of Four of a Kind hands (in card games a hand containing four cards of the same value is called a ...
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You draw 5 cards out of deck of N cards, needed to calculate probabilty of picking 2 marked cards.
So, there is a deck of N cards ($N-2$ are blank, and $2$ are marked), you draw $5$ cards with each attempt, what is probability of picking 2 marked cards with the first and each new try? (The deck ...
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How can I solve this challenging card counting problem?
A deck of 52 cards is shuffled and evenly split amongst 13 people(4 cards each). What is the probability that one of them has exactly 2 aces and 2 others have exactly 1 ace each?
I feel like a good ...
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Probability the 13th card dealt is the first king dealt?
The problem:
A player is randomly dealt 13 cards from a standard 52-card deck. What is the probability the 13th card dealt is the first king dealt?
I understand the solution which is based on the ...
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Dobble Algorithm for three or more matches.
I've played Dobble and asked myself it is possible to have instead of pairs, $n$ cards having one symbol in common, for example for $n=3$ if you take any three cards they only have one symbol in ...
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What is the probability of getting a King, Queen, Jack and Ace of same colour, and a Single pair of same colour in a hand of six cards?
What is the probability of getting a King, Queen, Jack and Ace of same colour, and a single pair of same colour in a hand of six cards?
I am working on a casino game however to determine house edge ...
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Probability of being dealt a perfect hand in bridge
Let's say a perfect hand is said to contain 13 cards all of the same suit.
What is the probability of this?
My logic is that there are 4 possible perfect hands (all from clubs, hearts, spades, ...
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Tetrahedral pancake problem game.
I am currently playing around making a little puzzle game and was looking for some input from people better at maths than me. It is based on the pancake problem.
You have a stack of $8$ "pancake&...
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Variance of cards without replacement
So let's say that we label a deck of cards as 1-13. There is a 1-13 of hearts, diamonds, spades, and clubs. What is the variance of the sum of picking 3 cards (without replacement)?
If this was with ...
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Is there a way to prove the 'Austrian deal' part of the 'Einstein' card trick?
I watched this video the other day.
You have between 4 and 8 cards.
Look at the bottom one and memorise it.
Move the top card to the bottom; do this 8 times in total (like the number of letters in ...
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Most physically efficient way to reorder cards
I have a deck of say, $100$ cards, in a physical stack in front of me. I have also (by computer) generated randomly a permutation of these cards in whatever form is convenient. My question is, how do ...
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