The card-games tag has no wiki summary.
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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 ...
2
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3answers
76 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
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4answers
102 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
202 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
49 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 ...
1
vote
1answer
40 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 first ...
1
vote
1answer
73 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
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1answer
25 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
65 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
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3answers
108 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 ...
1
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1answer
98 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
120 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
39 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
85 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
68 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 ...
2
votes
0answers
288 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:
...
1
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3answers
80 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
74 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
381 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
159 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
73 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
63 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 ...
9
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1answer
258 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
88 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
69 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
175 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
85 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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votes
2answers
53 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
43 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
65 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
101 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
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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
51 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.
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3
votes
1answer
51 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
170 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
793 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
87 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
125 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
99 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
463 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
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1answer
83 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
558 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
86 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
88 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
69 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, ...
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2answers
111 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:
...
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2answers
235 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 ...
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2answers
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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 ...
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2answers
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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 ...
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2answers
92 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 ...
