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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
34 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
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1answer
130 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
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1answer
50 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 ...
2
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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 ...
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1answer
40 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
23 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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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 ...
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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
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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
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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 ...
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0answers
69 views

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
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? ...
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0answers
145 views

What is the chance 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
73 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 ...
2
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2answers
58 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 ...
0
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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
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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 ...
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2answers
418 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
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 ...
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0answers
181 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 ...
2
votes
2answers
292 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 ...
2
votes
1answer
71 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
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 ...
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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 ...
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2answers
135 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
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). ...
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1answer
43 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 ...
2
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1answer
88 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 ...
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2answers
296 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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0answers
25 views

what calculation/algorithm should I consider for finding the winner(s) of a series of games

first of all I'm not in any way a mathematician, so be kind ;) Our current routine: The game is a card game. At the end of each round cards still in your hand are summed up and make your points. The ...
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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 ...
5
votes
1answer
540 views

I don't understand why this card trick works

So a friend of mine showed me a very interesting card trick that I don't quite understand. You have 52 normal cards from any regular deck you can buy anywhere. The Ace is worth 1 while 2 through 10 ...
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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 ...
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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 ...
4
votes
1answer
111 views

Solitaire Solvability

Is there a fairly straightforward procedure for determining if a given game of Solitaire (say Klondike) is solvable? One of my students would like to write a Solitaire game and give an "always ...
0
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1answer
120 views

Probability for fullhouse in POKER - 54 cards

I need to calculate the probability to get fullhuose in a poker game, using 54 cards - included 2 jokers. I know that I have 13 kinds of cards, but I need 2 out of 4, then I have 12 kinds and I need ...
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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 ...
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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
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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
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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 ...
3
votes
0answers
30 views

Algorithm to Create All “Spot it!” Cards [duplicate]

"Spot it!" is a fun card game, played with 55 cards, each having eight symbols. There are more than 50 symbols in all. There is always one, and only one, matching symbol between any two cards, and ...
2
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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
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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
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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 ...
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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?