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0
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1answer
186 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
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
votes
1answer
316 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
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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 = ...
0
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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 ...
6
votes
3answers
106 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
113 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 ...
4
votes
1answer
906 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: ...
2
votes
3answers
162 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
379 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. ...
10
votes
3answers
4k views

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 ...
2
votes
1answer
386 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 ...
1
vote
1answer
180 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
votes
1answer
117 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
votes
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
votes
1answer
136 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 ...
2
votes
2answers
154 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 ...
3
votes
1answer
385 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 ...
1
vote
2answers
129 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 ...
2
votes
2answers
123 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 ...
0
votes
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 ...
2
votes
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
votes
1answer
337 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 ...
3
votes
2answers
7k 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 ...
-1
votes
1answer
74 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
votes
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. ...
0
votes
1answer
196 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 ...
3
votes
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
votes
1answer
113 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 ...
4
votes
3answers
147 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
votes
1answer
145 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 ...
8
votes
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: ...
0
votes
1answer
103 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
votes
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 ...
1
vote
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 ...
1
vote
1answer
110 views

Newly Invented Card Game Hand Ranking

What would single-deck 2-card poker rankings/probability be for the following hands. (Deal 2 cards) Hands Royal Flush - Ace King Suited Pair Straight Flush - Any consecutive suited Flush - Any ...
3
votes
1answer
73 views

A card game with a long path

I recently played an online card game in which the cards were spread on the table. The goal was for me to pick up as many as possible, subject to the following rule: After picking up the first card, ...
1
vote
2answers
603 views

Why is this term required for a probability about drawing cards from a deck

Five cards are drawn from a standard deck (not replaced). Determine the probability of drawing exactly 3 hearts and 2 diamonds. The expression for the probability is: ...
0
votes
2answers
610 views

Deal combinations in solitaire game 'Klondike'

It seems that the solitaire card game 'klondike' presents some head scatching when trying to work out odds for winnable games etc, but I would image a 'simpler' question is 'how many different deal ...
1
vote
2answers
3k views

What are the probabilities of getting a “Straight flush” in a poker game?

I'm not a pretty much fun of Poker, but I'd like to study that game. What are the probabilities of getting a Straight flush in a Poker game considering this factors? Number of playersHow are cards ...
10
votes
2answers
19k views

What is the probability that a solitaire game be winnable?

By "solitaire", let us mean Klondike solitaire of the form "Draw 3 cards, Re-Deal infinite". What is the probability that a solitaire game be winnable? Or equivalently, what is the number of ...
1
vote
2answers
204 views

Help calculating the probability of dealing a custom deck of cards

Imagine a deck that consists of two types of cards. There are 2 type A cards and 9 Type B cards, totaling 11 cards. Assuming that 1 card will be dealt to 5 players. What are the probabilities that ...
1
vote
2answers
478 views

non-routine application of inclusion-exclusion

What are the circumstances when inclusion-exclusion can't be routinely applied, and some adjustments have to be made ? This question arises from a problem of finding the probability of getting a ...
1
vote
1answer
2k views

A bridge hand void in one suit

A bridge hand consists of 13 cards from a standard deck of 52 cards. What is the probability of getting a hand that is void in exactly one suit, ie consisting of exactly 3 suits ?
1
vote
2answers
378 views

A question in Probability, aces drawn from two halves of a shuffled deck

"A deck of cards is shuffled and then divided into two halves of 26 cards each. A card is drawn from one of the halves, it turns out to be an ace. The ace is then placed in the second half-deck. The ...
-1
votes
3answers
142 views

From a mathematical point of view is it optimal in no limit texas hold em to play with more money than less?

I noticed the other time a friend of mine went to a casino and bought in 100 dollars for a 1-2 table. Other players had heavier buy ins. I have received two opposing arguments. One says that buying in ...
10
votes
1answer
340 views

Algorithm for a deck manipulation

Let's say you have a randomised deck of $N$ different cards. An $M$-action ($M\le N$) is defined as follows: you look at the top $M$ cards of the deck, put as many of them as you choose on top of the ...
2
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2answers
193 views

Very simple poker holdem question

N holdem hands (just 2 cards from a standard 52 cards deck)  are dealt to N players How to compute the probability that: -exactly k players have a pair ( Two cards of the same value e.g.: 7, 7). ...
1
vote
1answer
64 views

Completely stuck: probability of handing out cards a certain way

After handing out 5 cards to each player, what is the probability that, given that Mr. A has exactly 1 ace, none of the other 3 players have more aces than Mr. A? I figured the probability of ...
0
votes
2answers
190 views

Conditional Probability [closed]

In a $13$ card hand, given that a person has one ace, what is the probability that person has more than one ace? In a $13$ card hand, given that a person has the ace of spades, what is the ...