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

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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
34 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 ...
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3answers
738 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 ...
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1answer
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
517 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
241 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
251 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
735 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
248 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
458 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 ...
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2answers
387 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
94 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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2answers
4k 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
237 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
63 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
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1answer
188 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 ...
3
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1answer
330 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
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 = ...
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0answers
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
108 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
117 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
923 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
170 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
413 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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3answers
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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
399 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 ...
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1answer
195 views

A card is drawn from 52 cards. What is the probability that the second card is a face card?

A card is drawn from 52 cards. What is the probability that the second card is a face card? I hope the question is clear. I believe the answer to be as follows... Two cases - Case 1: First card ...
2
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1answer
124 views

Probability of cards without combinatorics

5 cards are dealt from a well shuffled standard deck of cards. What is the probability of getting 2 kings and 2 jacks? I started by evaluating each choice in turn. Probability that the first card is ...
10
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1answer
1k views

Losing at Spider Solitaire

Spider Solitaire has the property that sometimes none of the cards in the final deal can "go" and so you lose, regardless of how much progress you have made beforehand. You would have known that you ...
5
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1answer
137 views

Derangements with repetitive numbers

Hi to all i have a very simple problem Lets assume that i have a well shuffled deck of 52 cards. I start drawing the top card always and when the card matches it's rank i lose. J=11 Q=12 K=13 If ...
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2answers
160 views

Poker, number of three of a kind, multiple formulaes

I wanted to calculate some poker hands, for a three of a kind I infered, 1) every card rank can form a 'three of a kind' and there are 13 card ranks, 2) there are $\binom{4}{3}$ ways to choose three ...
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1answer
394 views

Game Theory Matching a Deck of Cards

Moderator Note: This question is from a contest which ended 1 Dec 2012. Suppose we have a deck of cards labeled from $1$ to $52$. Let them be shuffled in a random configuration, then made ...
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2answers
132 views

Probability doubt for a card game

I'm creating AI for a card game, and I run into problem calculating the probability of passing/failing the hand when AI needs to start the hand. Cards are A, K, Q, J, 10, 9, 8, 7 (with A being the ...
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2answers
125 views

Poker probability conundrum

You deal your friend five cards from a standard shuffled deck. He looks at his hand and says either "Oh! I have at least one $X$!" or "I don't have any $X$s," where $X$ is the name of a rank. Your ...
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1answer
53 views

Poker communication problem

You've been dealt five cards from a standard deck, and you wish to communicate the exact contents of your hand. The catch is that you're only allowed to make utterances of the form "I have an $X$" or ...
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2answers
68 views

Cards and numbers

There are $10$ cards on which numbers from $1$ to $9$ are written. Number $8$ is written twice, other numbers - only once. Cards are pulled in the random order. What is the probability that $9$ ...
0
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1answer
345 views

Conditional probability within a poker hand

Given a 5 card poker hand from a standard deck, I'm looking to calculate the probability of getting: all 1 suit, 2 different suits, 3 different suits or 4 different suits, with the additional ...
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2answers
8k views

Probability for #suits in 5 card poker hand

Given a 5 card poker hand from a standard deck, I'm looking to calculate the probability of getting: all 1 suit, 2 different suits, 3 different suits or 4 different suits. All one suit is ...
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1answer
75 views

Please help me will the following probability question

Consider a game that involves flipping over cards from a standard 52 card deck. What is your probability that a) at least one of the first two cards is a spade b) draw a king of diamonds in 5 pick. ...
3
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1answer
57 views

What are the chances that a particular suit shows up at least once in the first two cards?

A standard deck of 52 cards. It seems obvious that the probability of getting a particular suit (say diamonds) on the first try is 13/52. After that, if we do not get diamonds, our chances are 13/51. ...
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1answer
199 views

Probability with cards

Consider a game with 24 cards with 4 suits and 6 ranks: 2,3,4,5,6,7 and lets say 5 cards are dealt to 4 people (jim, joe, mary, fred) also the other four cards are unused. I am trying to find out the ...
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2answers
5k views

How to calculate a fullhouse after dealing 5 cards?

In case you are not familiar with a fullhouse, it is when you have XXXYY (three of a kind + a pair). I am not that good calculating odds, but after time I manage ...
3
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1answer
115 views

non-intuitive results in random sampling

I play a card game (Magic The Gathering) that involves creating a deck of cards that can loosely be split into two categories: land and spells. You are permitted to play only one land per turn, and ...
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3answers
149 views

Consider a card game-parity

Consider a card game where the deck consists of 63 distinct cards. The deck is created in the following manner: each card consists of some number of symbols, where no two symbols are the same. There ...
2
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1answer
149 views

Expected length of a game of Kings

The game of Kings is a drinking game played with a standard 52-card deck. The rules are irrelevant to the nature of this question; we only wish to calculate the expected length of a game of Kings. The ...
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2answers
1k views

Probability with card game

I need help calculating the chances of winning this strange game that I'm going to explain right now: ...
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1answer
104 views

Calculate the average number of cards of a certain suit in my opponent's hand

Let's suppose that I am playing a card game with 3 other friends. One of my friends is on my team while the other 2 people are on the opposing team. The cards have just been shuffled and dealt so ...
5
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1answer
4k views

The probabilty of a new arrangement of 52 cards deck?

I just read this article, it claims that if you just shuffle a 52 card deck, you will mostly be creating an arrangement that no human have ever seen before. But this doesn't seem right since every ...
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1answer
96 views

A probability problem [duplicate]

Possible Duplicate: Card probability problem The following question was asked on a closed online forum. I think the correct answer is 1/2, however the ...