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1answer
21 views

Black Jack card game probability

If a dealer deals us two cards from a standard deck, without replacement, what is the probability that our first card is an ace? In addition, what is the probability that our second card has a value ...
2
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2answers
57 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
41 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
59 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
46 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
1k 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
174 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
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2answers
195 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
62 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
1
vote
1answer
64 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
1answer
74 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
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2answers
84 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
70 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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3answers
48 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). ...
1
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1answer
42 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
votes
1answer
83 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
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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
45 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
161 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
21 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
80 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
175 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 ...
1
vote
1answer
74 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
46 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 ...
2
votes
1answer
59 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
votes
1answer
94 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 ...
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
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2answers
74 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
27 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
80 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
votes
3answers
186 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
739 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
88 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
54 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
155 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
150 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 ...
5
votes
3answers
270 views

Game Theory: Is there an “unexploitable” strategy in No Limit Holdem?

Do "unexploitable" strategy exist in No Limit Holdem? By this I mean frequency-based mixed strategy that has non-negative expected payoff against any other strategy (let's assume the game is ...
3
votes
3answers
182 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 ...
8
votes
4answers
210 views

Modify the rules of Gomoku (Five-in-a-row) or Connect Four type games to enforce the fairness among players

One colleague and me were discussing this problem during lunch today, and I did a little bit digging for several hours after returning to my office. Fact: For an $(m,n,k)$-game, there does not exist ...
12
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2answers
307 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 ...
5
votes
1answer
78 views

AI strategies for losing positions [closed]

I have a card game that I am analyzing with Maple. Actually, it's a series of card games, one for every parameter k, where k is a natural number (representing the number of ranks of cards used in the ...
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 ...
1
vote
1answer
207 views

24 Game with $31,41,59,26,53$ and an additional number.

We have got five numbers $31,41,59,26,53$,please add a positive integer $n$,as small as possible,which we can find a way to manipulate these numbers with addition, subtraction, multiplication, or ...
0
votes
1answer
47 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
145 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 ...
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3answers
807 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
209 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 ...
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3answers
1k 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
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0answers
49 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 ...