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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Probability of getting a specific set of rolls atleast once after n dice rolls.

I am trying to calculate average number of turns it will take to win in Catan given a set of hexes. I am stuck at calculating probability of an event given n rolls. Each roll uses 2 6-sided dice. You ...
45 views

Multiset definition of "all" [closed]

The multiset $\{n,n,n\}$ is a multiset containing elements that are all $n$. It does not contain non-$n$ elements. The empty multiset $\{\}$ also does not contain non-$n$ elements. Is it also a ...
68 views

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 ...
119 views

How do I measure how "random" a deck of cards is? [closed]

I'm doing a project on shuffling cards and I've come across an interesting problem. At some point I need to look at a deck of cards and be able to "measure" how random the deck is. I'm using ...
41 views

probability of drawing at least 3 cards of the same number among 4 [closed]

The question is the following: You draw 4 cards from a deck of cards, what is the probability that you get at least 3 of the same number. (I'd appreciate calculations as I need to generalise this for ...
47 views

How to calculate chances of beating two opponents with one card?

SETUP: Standard 52 card deck. Game is O-hell. Trump game where any card from one arbitrary suit beats any other card from another suit. 3 players, A, B & C. A has the lead. Each player has one ...
111 views

Puzzle: Good card of 2021*2021 cards of 2021 colors

Assume there are 2021 kinds of colors, and for each color, we dye 2021 cards with this color. Now we put these 2021*2021 cards in a straight line. We define a card as "good" card, if the ...
29 views

Probabilities of repeated card draws

I draw from a deck of 40 cards 9 cards (edit: without replacing them). 3 of the cards in the decks are a Joker. What is the chance I drew at least 1 Joker? My initial thought was: "Easy!, the ...
64 views

Probability of everyone having 4333 distribution in bridge hand with given information

In a game of bridge, there are $4$ players, each is dealt a hand of $13$ cards coming from $4$ suits each of which has $13$ cards in that suit. We say that a player has a 4333 distribution if they ...
72 views

Is this weird solitaire card game a real game or just a multi-generational prank?

I have a question about a weird, unknown (and possibly impossible) game a friend of mine has taught me. It is a solitaire game that's played with a regular deck of 52 cards but it is suspiciously ...
30 views

Arrangements of a standard deck of $52$ playing cards if the denominations of the cards are ignored, so that only the suits are distinguished?

I am struggling to see why my solution is wrong for this question. My solution: Number of arrangements of length $k$ is $4^k$ and, since the maximum length is $52$ we have that the total possible ways ...
43 views

Proability with card games of sequence of length 2

Consider the following two-player card game using a standard deck of cards. • Players A, B each choose a length-two sequence of colours (e.g. RB, BR). • Cards are then revealed from a standard deck of ...
146 views

Provably Unwinnable Spider Games

I would like to know what fraction of Spider Solitaire games (played with 104 cards and four suits) are provably unwinnable. It seems various people have various ideas about what constitutes an ...
96 views

Probability with card deck flips

Here is my problem : we flip cards from a 52-card standard well-shuffled deck until the first club appears. I am looking to calculate the probability that the next card at the $k+1$th flip is also a ...
42 views

Draw n cards k times. Probability that we got exactly all red cards at least once?

We have a standard deck of 52 cards, that has 26 red and 26 black cards. We draw n cards from the deck at the same time, then return them and reshuffle. We repeat that k times. The question: What is ...