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

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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
576 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
107 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
106 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
204 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
371 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
147 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
142 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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104 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
49 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
107 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
68 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
59 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
517 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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2answers
193 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 ...
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1answer
3k 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
102 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
61 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 ...
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1answer
157 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 ...
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1answer
271 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
57 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
148 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 ...
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2answers
39 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 ...
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1answer
288 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 ...
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0answers
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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 ...
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4answers
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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 ...
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2answers
2k 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 ...
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1answer
614 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 ...
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2answers
252 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?
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1answer
263 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 ...
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3answers
821 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 ...
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3answers
286 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 ...
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4answers
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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 ...
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2answers
409 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 ...
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1answer
100 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 ...
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1answer
5k 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 ...
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1answer
244 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 ...
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1answer
65 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 ...
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1answer
202 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
2k 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 ...
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1answer
363 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
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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 = ...
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53 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 ...
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3answers
109 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 ...
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1answer
124 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 ...
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1answer
978 views

Analytically solving (calculating Nash equilibrium for) 3-player extensive form games

Let's say we extend the popular half-street Kuhn poker variant to 3 players. The rules would be as follows: ...
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3answers
208 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 ...
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3answers
496 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. ...
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Can you explain this card trick?

Can you explain the card trick that is explained here? Edit: Here's a summary of the trick as explained in the video: Start by asking a spectator to pick any three cards they like out of a ...
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1answer
420 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 ...