Mathematics Stack Exchange
Mathematics Stack Exchange

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.

This tag is for questions about probabilities and combinatorics of card games. The number of cards in the deck, number of players, and other parameters can vary.

Related tags: , . could be relevant in some cases.

1182 questions
79
votes
9 answers

What is the math behind the game Spot It?

I just purchased the game Spot It. As per this site, the structure of the game is as follows: Game has 55 round playing cards. Each card has eight randomly placed symbols. There are a total of 50 different symbols through the deck. The most…
Javid Jamae
  • 894
38
votes
10 answers

How to mentally flip a coin?

If you've ever played rock-paper-scissors, and you are reading this on math.stackexchange, you probably know that always playing $1$ of the $3$ choices at random (more precisely: uniformly at random and independently of previous choices) guarantees…
Anonymous
  • 5,857
36
votes
6 answers

Probability of drawing the Jack of Hearts?

You have a standard deck of cards and randomly take one card away without looking at it and set it aside. What is the probability that you draw the Jack of Hearts from the pile now containing 51 cards? I'm confused by this question because if…
J. Zimmerman
  • 842
33
votes
4 answers

Is this math game always winnable?

Kent Haines describes the game of Integer Solitaire, which I find to be excellent for young kids learning arithmetic. I'm sure they will be motivated by this game to get a lot of practice. Kent asks a question about his game, which I find very…
JDH
  • 45,373
31
votes
5 answers

Mathematics behind this card trick

Suppose I have $21$ playing cards. I distribute them in $3$ columns and tell you to choose mentally a card. Then just indicate in which column the card is. I pick up one of the columns which doesn't contain your card, then the column which…
A. Napster
  • 872
30
votes
1 answer

When can we quit a game of War?

Consider the game of War. (The rules are below.) It would be nice to be able to end the game early. Suppose, for example, one player has 50 of the 52 cards. It is very likely that they're going to win. Without knowing what's in their hand,[1] can we…
msh210
  • 3,948
26
votes
1 answer

Winning strategy for game guessing if next number is prime

I've come across an intriguing card game where a deck is used with cards numbered from $1$ to $N$. The game proceeds as follows: the dealer draws cards one by one from the deck and shows the number on each card. At any point in the game, even before…
Daniel P
  • 263
25
votes
5 answers

In a deck of cards, do a queen and a non-queen have equal chances of being the card that follows the first queen?

I encountered the following problem: From a shuffled deck the cards are flipped one by one until a queen shows up. Then again a card is flipped. Is it more likely that this card is the Jack of Spades or the Queen of Hearts? I managed to solve this…
drhab
  • 153,781
25
votes
3 answers

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 solvable games? When I came up with the question, it…
Bruno Stonek
  • 12,973
23
votes
3 answers

Probability of choosing ace of spades before any club

From a deck of $52$ cards, cards are picked one by one, randomly and without replacement. What is the probability that no club is extracted before the ace of spades? I think using total probability for solve this $$P(B)=P(A_1)P(B\mid…
rcoder
  • 4,665
23
votes
2 answers

$4$ cards are drawn from a pack without replacement. What is the probability of getting all $4$ from different suits?

$4$ cards are drawn from a pack without replacement. What is the probability of getting all $4$ from different suits? Here's how I tried to solve: For the first draw, we have $52$ cards, and we have to pick one suit. So, probability for this is…
Pratyush Yadav
  • 933
19
votes
4 answers

In the card game Set, what's the probability of a Set existing in n cards?

Given $n$ randomly drawn Set cards on a table from a standard 81-card deck, how can I determine the probability of one or more Sets existing on the table? First, for those who may not be familiar with the game, here's a simple introduction to Set…
Daniel
  • 435
19
votes
11 answers

What is the algorithm to generate the cards in the game "Dobble" ( known as "Spot it" in the USA )?h

In the game Dobble ( known in the USA as "Spot it" ) , there is a pack of 55 playing cards, each with 8 different symbols on them. What is remarkable ( mathematically ) is that any two cards chosen at random from the pack will have one and only one…
sevanstephan
  • 201
  • 1
  • 2
  • 7
18
votes
1 answer

Probability that at least one of four hands missing at least one suit

Deal each of four players a 13-card hand at random. What is the probability that at least one of the four hands is missing at least one suit? Let $A_i$ mean that player $i$ is missing at least one suit. I can compute the probability that player 1…
Bridge counter
  • 181
18
votes
1 answer

At what rate does the entropy of shuffled cards converge?

Consider a somewhat primitive method of shuffling a stack of $n$ cards: In every step, take the top card and insert it at a uniformly randomly selected one of the $n$ possible positions above, between or below the remaining $n-1$ cards. Start with a…
joriki
  • 242,601
1
2 3
…
78 79