Articles of card games

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 dice (six faces) to pick the card randomly? Until the opposite player has less than seven cards, […]

Probability of picked cards to be smaller than the largest picked card

I have an assignment for my algorithms module that requires us, amongst other things, to find the equations for the following question. Edit – Question Updated You have n cards with pairwise different integer values from 1 to n , shuffled randomly on a pile. You pick cards from the pile, one after another, and […]

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 exactly 1 pair (pair means same colour or same type)? Thanks for any indication.

Minimum number of out-shuffles required to get back to the start in a pack of $2n$ cards?

So I’m stuck on this problem. If you perform a faro out-shuffle (i.e. a perfect “riffle shuffle” where the top and bottom cards stays in place) on a pack of 52 cards ($n=26$), you can get back the original order in 8 shuffles. Call $8$ the order for $n=26$. That’s easily seen if you write […]

How many cards do you need to win this Set variant

I enjoy the card game Set, and have come up with a few variants based on the concept of assigning card “values” to stacks of cards (that is, each stack of cards is considered equivalent to a particular card) as follows: A stack containing a single card is equivalent to that card A stack containing […]

Straight Flush probability with a huge hand.

It’s easy to calculate the probability of a straight flush when you’re dealt $5$ cards. I’d like to ask for the probability of the same when you’re dealt half the deck. I seek $P(\text{straight flush})$ of any suit. We have $52$ cards, and $26$ are dealt. A straight flush is $5$ consecutive cards of the […]

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 would lose had you seen the final ten cards before the game started. I wonder if we can calculate […]

In the card came “Projective Set”, show that 7 cards do always contain a set.

This question already has an answer here: In the card game “Projective Set”: Compute the probability that $n$ cards contain a set 2 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 matching symbol . […]

Mental card game

Each of n persons draws a card from a shuffled deck of $k$ cards numbered from $1$ to $k$. There are at least as many cards as persons. The winner is the person who is holding the largest card. If everyone is honest, how can they mutually determine the identity of the winner, without any […]