0
votes
0answers
21 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 ...
0
votes
1answer
35 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 ...
7
votes
1answer
131 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 ...
2
votes
2answers
67 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 ...
0
votes
0answers
26 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 ...
1
vote
2answers
36 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 ...
2
votes
2answers
47 views

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 $\binom{52}{13}$ ...
0
votes
2answers
31 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 ...
6
votes
3answers
275 views

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? ...
0
votes
1answer
60 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 ...
2
votes
3answers
92 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 ...
1
vote
2answers
425 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.?
14
votes
5answers
3k 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 ...
2
votes
2answers
294 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 ...
1
vote
1answer
77 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 ...
4
votes
2answers
134 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 ...
1
vote
2answers
136 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 ...
1
vote
1answer
100 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 ...
0
votes
3answers
56 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). ...
2
votes
1answer
89 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 ...
0
votes
1answer
63 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 ...
0
votes
1answer
48 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 ...
1
vote
2answers
297 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 ...
-1
votes
2answers
96 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 ...
1
vote
1answer
85 views

probability problem related to card shuffling [duplicate]

You have five cards numbered 1,...,5. You shuffle them, so that at the end every permutation of them is equally likely to show up. What is the probability that no card 'i' will end up in the i-th card ...
1
vote
1answer
51 views

What are the chances that 2 arbitrary ranked cards can be found adjacent to one another in a shuffled pack of cards

What are the chances that 2 arbitrary ranked cards can be found adjacent to one another in a shuffled pack of cards. Ranks being the face value of the cards (ace, two, three, etc), adjacent being ...
1
vote
2answers
41 views

What is the Probability that the Lowest Card out of 4 Cards is X?

If I have four different value cards, what is the probability that the lowest card (ace, lowest -> king, highest) is some value X? Here is what I have so far: I know that the lowest value card ...
1
vote
2answers
89 views

What's the expected position of the second card in a deck of 108 cards

Suppose we have a deck of cards from two sets of cards (104 or 108 cards). What is the expected position of the second, let's say, spade ace ? Any idea ? I am trying to figure out something for a ...
0
votes
2answers
29 views

What are the odds of drawing 23 cards and there is at least one ace?

So my friends dad asked him this question and he asked it to me. None of us know the answer, and while I tried to solve it, I'm not to sure if my math behind is right. I solved it a number of ways ...
0
votes
1answer
106 views

Card game probability question?

A person selects 2 cards without replacement from a standard deck of cards. What is the probability that he select a heart, given that he has selected a face card? So my solution is P(getting a ...
2
votes
3answers
204 views

Probability of winning the game 1-2-3-4-5-6-7-8-9-10-J-Q-K

A similar question to mine was answered here on stackexchange: Probability of winning the game "1-2-3" However, I am unable to follow the formulas so perhaps someone could show the ...
1
vote
1answer
1k views

Drawing 3 cards of same suit and 2 of a different suit

What is the probability of having 3 cards of the same suit and $2$ cards of the same suit (but a different suit than the first three) in a $5$ card hand from a standard $52$ card deck? What is the ...
0
votes
1answer
157 views

Pulling Cards in Consecutive and Ascending Order

A deck of cards contains 6 cards numbered from 1 to 6. If three cards are randomly selected one-by-one from the deck, what is the probability that the numbers on the cards drawn are consecutive and in ...
0
votes
0answers
59 views

Optimizing a population to maximize probability of achieving certain samples.

Preface: I'm reasonably comfortable with mathematics on the whole, but I don't know too terribly much about probability theory, or optimization. I play Magic: The Gathering, and am trying to apply a ...
4
votes
2answers
171 views

Probability in a deck of cards to have two jacks in a row

In a deck of $36$ cards ($9$ cards per color, $4$ colors) what is the probability to have $2$ jacks (or more) that follow each other?
0
votes
1answer
174 views

Probability question involving playing cards and more than one players

I've been struggling with this problem for a while, so I have to ask you guys for a little mental push. My problem involves a full deck of playing cards and 4 players, but I'll simplify it to 4 cards ...
3
votes
3answers
198 views

Probability of winning the game “1-2-3”

Ok, game is as follow, with spanish cards (you can do it with poker cards using the As as a 1) You shuffle, put the deck face bottom, and start turning the cards one by one, saying a number each time ...
13
votes
2answers
343 views

A card game with no decisions

A friend showed me a mindless card game he plays, in which the initial state of the deck completely determines whether he wins or loses. The game is played as follows: Shuffle a standard $52$ card ...
2
votes
1answer
2k views

Find the probability of having 3 cards of the same suit and 2 cards of the same suit in a 5 card hand from a standard 52 card deck? (Method)

I'm trying to understand why my method doesn't work to answer the question: What is the probability of having 3 cards of the same suit and $2$ cards of the same suit (but a different suit than the ...
0
votes
1answer
54 views

Odds of being dealt 4 particular cards out of 106 in a 6 card hand

I was playing a card game called Mille Bornes with my daughter. She dealt a hand while I was getting a cup of coffee in the other room. I came back and we started playing. She immediately played the ...
0
votes
1answer
157 views

Probability of hitting a 'bomb' in a memory-like game

I came across a casino-like game a few days ago where there is a playing field of face-down cards of 5x5 cards. Out of these 25 cards, 5 are 'bombs'. The player bets a fixed amount of money at the ...
2
votes
3answers
1k views

Probability of having exactly 1 pair from drawing 5 cards

I have an exercise as follows: There is a collection of cards consisting of 52 cards (13 types and 4 colours each type). We draw 5 cards from the collection. Then what is the probability of having ...
2
votes
1answer
258 views

Probability question involving sets of cards

I have an infinite deck built out of sets of 10 cards (in other words 10*n cards). The sets are identical so one '2' is identical to another '2'. A player draws 6 cards. If he draws: any '1' AND a ...
5
votes
3answers
2k views

Dealt 3 cards. Odds of being dealt any pair?

This is not to aid a gambling habit. I am simply curious how to do this math. You get dealt 3 cards. What are the odds of having any pair? (We can exclude 3 of a kind) Total number of hands = ...
0
votes
0answers
51 views

Number of elementary shuffling operations to produce deck with no $k$ cards in same order?

The requirement for "suitably shuffled" is that no $k$ cards appear in same order in $D$ and $D'$. Elementary shuffling operations are defined, very simply, as : Interleaving. Split deck in ...
6
votes
3answers
96 views

Removing a card while preserving “shuffled-ness”

Suppose you have a deck of numbered cards (possibly with multiple copies of each number), perfectly shuffled, and you want to extract certain cards without disturbing the "shuffled-ness" of the ...
4
votes
1answer
98 views

How to calculate the role of chance (vs strategy) in a card game?

I recently played two different card games with a friend: 500 Rum and Lost Cities (modified to use a regular deck of cards). We started arguing about which game was more subject to chance. I realized ...
1
vote
3answers
124 views

Pick a card from a set with the help of a dice

Some days ago i was playing "Settlers of Catan", an homemade version. In this game there is an event where a players pick, randomly, a card from another player. So here is the problem: can we use the ...
3
votes
3answers
186 views

Calculate Probability : A bridge deck of Cards

From a bridge deck of $52$ cards, we draw $13$. What is the probability that we have $5$ spades in our hand? I think that there are $\dfrac{52!}{13! \cdot 39!}$ ways we can choose $13$ cards. ...
2
votes
1answer
283 views

Probability involving cards, using negative binomial and hypergeometric distributions

I'm working on the following problem, and I don't really know how to approach it! It has 3 subsets: You randomly take one card at a time from a deck, with replacement. How many 'draws' are needed to ...