Questions tagged [card-games]
Questions regarding probabilities and combinatorics of card games. The number of cards in the deck, number of players, and other parameters can vary.
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How can you measure how "shuffled" a deck of cards is?
A few days ago I asked for some methods of measuring how shuffled a deck of cards was. Predictably there were a lot of suggested methods, which got me thinking, which is the best one? I think it'd be ...
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Asymptotic value of card drawing game
A deck consisting of $r_0$ red cards and $b_0$ black cards is randomly shuffled. The host turns up the cards one at a time; if it is red, you get $\$1$; otherwise you pay the host $\$1$ (and you're ...
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Can War be Infinite?
War is a card game played by two players, each of which has half of a deck of cards. At the same time, the players take the top card from their deck, and place it face up in front of them. The player ...
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Deck of 5 cards Shuffling Problem but only allowed to choose two adjacent cards
Say I have a deck of 5 cards that are labeled 1, 2, 3, 4, 5. 1 being at the top and 5 being at the bottom. The rules of this game are as follows. You can take only take two adjacent cards (1 2, 2 3, 3 ...
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Is a perfect game of Set always possible?
For anyone not familiar with the game of Set, I'll refer you to the description on this question.
My question is this: The game ends when there are no more cards remaining in the deck and there are ...
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Estimate number of cards needed to be drawn from deck before full house
Imagine we have a well-shuffled deck of cards and we keep drawing cards until there is at least one full house in the drawn cards. How many cards will we draw on average? I would be interested in both ...
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5 cards from a 52 card deck, what is the probability that the sum of cards is greater than 48
The problem states:
$5$ cards are dealt from a standard $52$ card deck. What is the probability that the sum of the values on the five cards is $48$ or more?
It is assumed of course that the value ...
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Conditional Probability 5 card hand
We have a 5 card hand from a standard deck. What is the probability that the hand is all Spades, given that it has at least two Spades?
I know the formula for conditional probability is:
$P(A|B) = \...
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Matrices with special properties and their relation to an interesting problem about cards.
For $k\in \mathbb{N}$, $A$, an $n$ x $n$ matrix has the following properties:
Every entry belongs to the set $\{0,1,2,...,k \}$, and,
Every individual row and column adds up to $k$.
Question: Can we ...
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Largest subset of $S^n$ without a loop for each element for a particular 3-element commutative magma $S$.
Let $S$ be the $3$-element commutative magma with the operation that gives the same element when the operands are the same, and the excluded element when the operations are different (i.e. $S=\{\{a,b,...
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An improbable Euchre game -- A 9$\spadesuit$ kind of evening
Setup
During a game of cutthroat euchre (3 players instead of 4), my girlfriend won the game by playing as her last card, the 9$\spadesuit$. Given that euchre is played with a deck consisting of ...
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Probability of a run of $n$ cards of the same color?
A magician friend hit me with this one: given a shuffled deck, what is the probability that it contains at least one run of at least $n$ cards of the same color — for example, four reds or four blacks ...
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Shuffle Deck $7$ times or $8.55$ times?
Persi Diaconis showed in $1992$ that in order to shuffle a deck of $52$ cards, you need at least $7$ riffle shuffles.
However, in the paper he published, he showed that we needed $\frac{3}{2}\log_2n$...
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Four of a kind -dilemma
CONDITIONS
Imagine, that we have five standard 52-card decks. We will now mix all these five decks into a one (afterwards "big deck", 260 cards in total). Now our task is to turn all the cards open, ...
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How many possible shuffles can be won perfectly?
It is known that the possible shuffles of a deck of cards is $52!$, or ~$80658175170943878571660636856403766975289505440883277824000000000000$ different combinations.
I have become aware of a game ...
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