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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What's Wrong With My Math - Odds of 3 Cards of the Same Suit When Drawing 10 Cards
I'm designing a game with a custom deck. The deck has 5 suits (hearts, spades, clubs, diamonds and crosses) and 5 ranks (1 to 5) for 25 cards total. I'm trying to calculate the odds of revealing 3 ...
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From 52 cards, we draw N times with the return of 1 card each. Expected value of the number of different cards that were drawn. Solution verification
From a deck of 52 cards, we draw N times with the return of one card each. Calculate the expected value of the number of different cards that were drawn.
To calculate the expected value of the number ...
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From 52 cards, we draw N times one card with the return. Calculate the probability that each card in the deck will be drawn at least once.
From a deck of 52 cards, we draw $N$ times one card, with the return. Calculate the probability that each card in the deck will be drawn at least once.
I know that it looks a bit like Coupon ...
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Probability of Shuffling a Deck of Cards a Single Time from New Deck Order
I have the following question about shuffling a deck of $52$ playing cards. Most people are astounded by the fact that $52!$ is a really big number, and they say that because it is so big that ...
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How to calculate the number of possible combinations of different suits when choosing 5 cards from a standard deck of 52? Without order/repetition
The above question is something I was thinking about during my probability class- it's not part of the class, or maybe I'm not understanding correctly, but I'm having trouble figuring out how to go ...
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In Texas Holdem what is the probability that the best hand is on the table?
The brute force method would involve calculating the probability of a royal flush on the table (i.e., the five community cards are A, K, Q, J, T suited). Follow this by calculating the probability ...
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What is the probability of getting 2 chosen ranked cards (any suit). Before the dealer, when the cards are dealt alternately starting from the player?
The player chooses two ranked cards. 52 cards are dealt alternately to the player and dealer, ending up with 26 cards each. What is the probability the player matches the two cards (any suit) before ...
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Probability of choosing 4 cards whose sum is 5 from a deck of 40 cards
Let's say we have a deck of cards excluding face cards, so cards from Ace to 10.
Which of these is the correct way of computing the probability that the sum of 4 randomly chosen cards is equal to 5?
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Probability of four cards from one suit and 3 from two other suits
I'm looking for the probability of drawing 10 cards from a deck of 52 and getting 4 cards of one suit and 3 in two other suits. My first thought was that this is $\frac{{13 \choose 4} \times 4 \times {...
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Combinatorics Pigeon Hole Poker Game
Suppose I shuffle a standard 52 card deck deck and give you 25 cards at random from it. You are then tasked with making 5 poker hands from these cards such that each card is in exactly one hand. The ...
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Hypergeometric-like distribution but where non-successes are replaced?
I'm working on a card game and say the deck has C cards where the player draws 3 cards every turn, picks a card, and the rest are shuffled back into the deck. They can do this N times. There are X of ...
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How would I calculate the probability of n consecutive ties in war?
Assuming each player is given a random $26$ cards of $13$ ranks ( $4$ suits/possible cards for each rank ) out of a $52$-card deck, the basic probability of $n$ consecutive ties would be $\left(1/13\...
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Each of A, B, and C draw a card without replacement from a 52-card deck. What is the probability that A's face value is higher than the rest?
Case 1: All three cards have equal face values. There are 13 such cases since there are 13 different ranks.
Case 2: Two cards have equal face value and the third card has a lower value. Initially, I ...
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Probability of drawing 2 specific cards out of 4, with 3 attempts
Related to a game I play with friends: Say there are 4 unique cards, for ease of explanation, let's say the Ace of each suit. I want to get the Ace of hearts and the Ace of diamonds, but don't care ...
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Two questions around some new card game based on prime factorization.
I have been developing a card game called "Infinity", which involves a unique play mechanic based on card interactions. In this game, each card displays a set of symbols, and players match ...
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