Questions regarding probabilities and combinatorics of card games based on C cards decks and P players.

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Can the probability of a trump poverty be calculated without making case distinctions?

The card game Doppelkopf is played with four players. Every player receives 12 of the 48 cards. The 48 cards consist of 26 trump cards and 22 other. A trump poverty is what we call the scenario that a ...
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54 views

When does it become impossible to lose a game of FreeCell?

After spending more time than I should playing FreeCell, I've been wondering about the following: At what point in the game does it become impossible for someone to lose? "losing" probably isn't ...
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4answers
72 views

Probability of 5 card hand

You have a $5$ card hand from randomly shuffled standard deck of $52$ cards: $X$ - Event that hand exactly contains $1$ spade $Y$ - Event that hand exactly contains $1$ ace How do I calculate $P(X ...
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38 views

Probability - 5 card hand

Question is : You have a 5 card hand from randomly shuffled standard deck of 52 cards. P - Event that hand exactly contains one spade. Q - Event that hand exactly contains one ace. Calculate : a. ...
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3answers
187 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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1answer
52 views

Help understanding the Expected Value equation when applied to poker

I don't play or follow poker, (just thought I'd declare that), but found it interesting from speaking to a few people that do that their way of calculating the Expected Value, $E(x)$, didnt account ...
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2answers
56 views

Is it possible to get the largest conceivable score in Hearts?

I should explain the necessary rules: in the four-player game of Hearts, the object is to get as few points as possible. The points you receive are determined by the cards you pick up through a hand: ...
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3answers
301 views

Card Game Probability 13 Card Hand

Me and my friends play a four person poker style card game. Each person is dealt 13 cards, and it is a standard trump card game. Now, as the standard, a five card flush beats a five card straight, but ...
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1answer
300 views

Deck of Cards Probability Question - Probability of Getting At Least 2 Queens

There was actually another question like this but the final answer a person mentioned was incorrect and I was confused as to how he got it. Can any answers explain how they got there? I'd like to ...
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103 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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3answers
121 views

How many perfect shuffles are needed to go back to initial state?

The other day, in a popular-science book, I saw: Given 32 cards ($c_i$ for $i=0..31$), cut the deck into two parts and shuffle them the American way (riffle shuffling). The deck now looks like: ...
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3answers
459 views

Draw 4 cards where: 3 cards same suit and remaining card of different suit

Four cards are drawn from a standard 52-card deck without replacement. Find the probability that exactly 3 cards are of the same suit and the remaining card is of a different suit. What I did: ...
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1answer
119 views

Chances of a shuffled deck being sorted only by color

QUESTION (TL;DR) Let's assume you are handed a deck of 52, standard cards which are already shuffled. You take the the deck and mindlessly shuffle it for a few minutes. After the shuffle, you turn ...
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1answer
160 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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2answers
244 views

Probability of a minimum sum of card values when drawing cards from a custom deck

Apologies if this question has been answered -- I tried searching for an answer but wasn't sure what terminology to use. Suppose I have a deck of cards, consisting of $n_1$ ones, $n_2$ twos, etc. ...
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370 views

Game theory: Bidding strategy during an auction in a card game

I'm trying to create a mathematical model for the auction process in a card game called Pitch. The specific question I'm interested in solving is: Let $p_i$ represent the probability of a specific ...
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1answer
101 views

A Probability Game of Bridge Problem and Its Puzzling Correct Answer

In my effort to work on my probability and combinatorics skills before the semester starts, I have come across this problem: What is the probability that a bridge hand will contain 13 cards of the ...
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1answer
170 views

The Day Camp Stacking Game

My friend works at a day camp as a counselor and he told me about an interesting game he plays with his group of kids. You have a perfectly shuffled, regular $52$-card deck and a group of $2 \leq n ...
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1answer
200 views

Minimum number of out-shuffles required to get back to the start in a pack of $2n$ cards?

So I'm stuck on this problem. If you perform a faro out-shuffle (i.e. a perfect "riffle shuffle" where the top and bottom cards stays in place) on a pack of 52 cards ($n=26$), you can get back the ...
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2answers
397 views

Probability of Getting a “Perfect Score” in the Card Matching Game Concentration

A person is playing the card matching game concentration. There are 40 cards, 20 pairs total. All the cards are shuffled and placed at random face down. A turn consists of two moves and a move is ...
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1answer
48 views

Straight in 52cards+2Joker

I have 52card (ace to king) + 2Joker I'm supposed to compute how much straights of 5 cards I can make, excluding the straight flushes (straights with all cards being the same color) My reasoning is : ...
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3answers
51 views

How Many Hands Having 3 Cards of a Kind are There?

The conditions are as follows: Standard 52-card deck, 4 suits. 5-card hand. There must be three of a kind, but only this (i.e., no 4 of a kind or full house). I know this has been asked already, ...
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83 views

Optimal strategy in a simple card game

So some friends and I are playing this simple card game. We choose 15 random cards from a normal deck of card and lay them on a table in a pyramid shape. 5 cards in the bottom row, 4 in the next row ...
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2answers
137 views

How to get the number of ways of getting a five card hand that is a straight flush from a standard deck of cards

I do not get the result at this page, ex. 13-7: Suppose that Aces can be either high or low; that is, that {Ace, 2, 3, 4, 5} is a straight, and so is {10, Jack, Queen, King, Ace}. The number of ...
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probability in cards that 4 people each get queen and king?

A 52 card deck is shuffled and then dealt out to 4 people (each person gets 13 cards). What is the chance that each person gets an a Queen AND King? My attempt: I know theres $\binom{52}{13}$ ...
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50 views

randomly choosing from a deck of cards

Suppose I have a deck of 26 black and 26 red cards. I randomly choose 26 cards from this deck and I look at the first two cards. What is the probability that both cards are black? I think the ...
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Finding the 'best' way in a card-arrangement-game

Let $n\ge 2\in\mathbb N$. Suppose that we have a card on which $1$ is written, a card on which $2$ is written, $\cdots$ , and a card on which $n$ is written. Now these $n$ cards are arranged from left ...
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3answers
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Card Problem from Gardner

The following problem is from aha! Insight by Martin Gardner. On a draw of $n$ cards from a deck without replacement, what is the probability that seven of the $n$ cards all have the same suit? ...
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1answer
317 views

On the probability of obtaining 27 sets in the card game Set

For people not familiar with the card game Set, see its entry on Wikipedia and/or one of the related questions here on Math SE. It might be faster to just play the game a couple of times though, see ...
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3answers
96 views

Weird Card Game Problem

I feel like I know what game this is mimicking but I cannot put my name on its title: There are two players in the game (one is Even, the other is Odd). Even starts off with 30 blank cards, and Odd ...
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2answers
71 views

Interesting combinatorics question

As a child I had a deck of cards which consisted of maybe 50 cards. On each card there were 6 objects. Players had to pick 2 cards from the deck, and the player who first spotted the difference ...
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1answer
125 views

Probability of getting all four aces playing with 13 people

There are thirteen people sitting on a table. The dealer deals them a card each from his full deck(52 cards). He repeats this until all of his cards have been used. What is the probability that one of ...
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3answers
7k views

Probability of 5 cards drawn from shuffled deck

Five cards are drawn from a shuffled deck with $52$ cards. Find the probability that a) four cards are aces b) four cards are aces and the other is a king c) three cards are tens and ...
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2answers
7k views

Playing Cards probability problem

From a pack of 52 playing cards, three cards are drawn at random.Find the probability of drawing a king , a queen and jack.?
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5answers
8k views

Probability Discrepancy in drawing 2 cards from a Deck of 52

A colleague and I are having a hard time figuring out this probability question and was wondering if anyone could provide an explanation / insight into it. The question is simple: what is the ...
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0answers
203 views

Card combinatorics problem

Suppose we have a standart deck of cards. It is fixed and can have maximally 52 cards, but may be less. Also we have several subsets of this deck, each subset consist either of all cards of the same ...
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2answers
658 views

What's the probability of a 5 card hand is dealt 4 Kings, given that the hand has the King in Spades and Hearts?

What's the probability of a 5 card hand is dealt 4 Kings, given that the hand has the King in Spades and Hearts? Here's my attempt: E= KKKK_ F= KK_ _ _ so $P(E) = 48/(\phantom{}_{52}C_5)$ and ...
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1answer
140 views

How many 13-card hands contain seven cards of one suit?

How many 13-card hands contain seven cards of one suit? (My intuition is $\displaystyle \frac{13!}{7!6!} \cdot 4$) I may be wrong. please correct me
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1answer
122 views

Card game: How much will you pay to gamble?

You turn over the cards 2 at a time, if they are both red, you keep the cards, if they are both black I keep the cards. If one is red and the other is black then neither you nor I get a card. If you ...
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2answers
234 views

Is it possible to be “too good” at Spider Solitaire?

There was a similar question here: Losing at Spider Solitaire However, what I'm asking is different. The game has a rule that it would not deal the next ten cards, unless there is already a card in ...
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2answers
465 views

Probability and Snap

I have a question about a modified (/simplified) version of the card game Snap: There are 20 playing cards, such that each card has a number from 1...10, so there are 2 cards with each number. The ...
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1answer
171 views

Card game question with conditional probability

If I have a standard deck of 52 cards with ace being 1 and jack being 11, queen 12, and king 13. I know the expected value of any card I draw to be 7. However, how does this change with each ...
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1answer
144 views

Card game question

In a game where we have a normal 52 card deck. Two cards are delt out at a time, if both are red, then I keep the two cards. If both are black, you keep the two cards. If its one of each, then it gets ...
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3answers
136 views

One card is dealt to each of the 6 players. What are the odds of having a game where nobody has a trump card vs only one person having a trump card?

The trump is picked last by picking one card from the remaining deck. A player has a trump card if it's of the same type as the trump card (ex. picked trump is 2 of clubs, player has 10 of clubs). ...
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1answer
52 views

Expressing game mechanic in mathematical form

I have encountered a game mechanic that takes repeated arithmetic to figure out, so I was wondering if it could be made simpler by finding an equation to solve. In this game, there are resources that ...
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1answer
113 views

Probability of picked cards to be smaller than the largest picked card

I have an assignment for my algorithms module that requires us, amongst other things, to find the equations for the following question. Edit - Question Updated You have n cards with pairwise ...
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1answer
70 views

Probability randomly picked card is smaller than another picked card

Given a set of m cards that have values pairwise different with range 1 to m, what is the probability that after shuffling the card, and picking two of them, the first one is larger than the second ...
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1answer
61 views

Probability of a hand containing more clubs than spades in an incomplete deck

The problem: A deck is missing a number of cards. It has S spades, C clubs, and E red cards, for a total of M cards. A side point is that C = S + 1. A hand of N cards is dealt. A) What is the ...
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2answers
671 views

What is the probability of having same cards given two decks?

A practical question. Given two decks of cards (52 cards) if i pick 15 cards randomly from one deck and then 5 cards from another deck, what is the probability that exactly 3 cards, between two picked ...
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239 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 ...