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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 to correctly simulate splitting in blackjack

I'm writing a probabilistic simulator for blackjack that returns the best action and expected profit for a given hand, dealer up card, and unseen cards (by calculating all possible scenarios, not ...
user448893's user avatar
2 votes
0 answers
33 views

Optimal Strategy for Card Betting Game

I'm mulling over the following question: You are playing a game with two other people where each player initially contributes 10 dollars to the pot, creating a total pot of 30. During each turn, two ...
Mario Diw's user avatar
0 votes
1 answer
42 views

Expected time after first 2 and before first ace

We have a standard deck of cards. Find the expected number of cards after the first $2$ and before the first ace given that the first $2$ appears before the first ace. Let $X$ be the number of cards ...
Kilkik's user avatar
  • 1,952
10 votes
2 answers
604 views

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 ...
Ian Clayman's user avatar
1 vote
0 answers
44 views

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 ...
thefool's user avatar
  • 1,054
0 votes
1 answer
62 views

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 ...
thefool's user avatar
  • 1,054
1 vote
1 answer
46 views

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 ...
Steven Creech's user avatar
0 votes
1 answer
71 views

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 ...
Michelle's user avatar
  • 149
0 votes
1 answer
64 views

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 ...
Phil Freedenberg's user avatar
1 vote
1 answer
90 views

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 ...
Shaun Andrew's user avatar
3 votes
3 answers
530 views

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? ...
ryangosling's user avatar
0 votes
1 answer
40 views

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 {...
fmt's user avatar
  • 3
1 vote
0 answers
48 views

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 ...
Evan Semet's user avatar
2 votes
1 answer
45 views

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 ...
Scott Prager's user avatar
1 vote
2 answers
47 views

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\...
HyperCodec's user avatar
2 votes
4 answers
227 views

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 ...
clement's user avatar
  • 135
-1 votes
4 answers
59 views

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 ...
CrimsonWookiee's user avatar
3 votes
2 answers
222 views

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 ...
mathoverflowUser's user avatar
4 votes
4 answers
178 views

Expected value of number of specific cards in starting hands in a card game

I don't understand what I found when calculating the expected value of a card game. A deck contains 40 cards. 8 of them are red cards and 32 of them are blue cards. At the start of the game, 5 cards ...
ENM's user avatar
  • 49
0 votes
1 answer
48 views

Divide a deck of cards in 2 equal parts. What is the probability of drawing a queen from 1st deck given 2nd deck has at least one queen? [closed]

A deck of 52 playing cards has been dividen into 2 equal parts. What is the probability of drawing a queen from 1st deck given 2nd deck has at least one queen?
Aditya Apurba's user avatar
0 votes
0 answers
36 views

Interesting Card game Problem [duplicate]

Imagine you're at a casino. The game you're playing consists of the following: There are 52 cards, half of them are red, and the other half are black. Croupier mixes the cards and he draws two. If ...
Pabloo's user avatar
  • 1
-1 votes
1 answer
147 views

A Game of Number Cards

In a cards game, there are ten cards, $1$ to $10$. Two players, seated facing each other, randomly choose $5$ cards each. They arrange their cards in ascending order of the number on the cards as ...
Fredrick's user avatar
  • 228
1 vote
0 answers
29 views

Probability that the last card drawn is a spike while randomly drawing the deck of cards [duplicate]

I am playing a card game. The goal is to withdraw randomly a card until there is no more. The symbol of the last card is the winning one, ie: if the last card is a spike, spike wins. Right now there ...
Pistolero81's user avatar
0 votes
0 answers
50 views

Best strategy to win a card game

The contest consists of a series of matches of psychological jujitsu between bots. In each match, 2 bots face off for N = 1024 turns. At the beginning of a match, each bot receives 1024 cards numbered ...
resynel's user avatar
  • 25
2 votes
1 answer
44 views

Scrabble probability of Player A playing a U word?

so I was recently involved in a probability debate with a friend involving Scrabble: I had been selected to be Player 1. It was my turn to play (first play of the game) and I had a q and was looking ...
Kevin Iqbal Rodriguez's user avatar
4 votes
2 answers
78 views

What is the probability of drawing 5 cards of the same type from a deck of 52 cards?

My textbook has the following problem: There is 52 cards in a deck and 13 cards of each type/color. You are drawing 5 cards. Whats the probability of all these 5 cards being the same type? My ...
volticus's user avatar
2 votes
0 answers
82 views

Analysis of the Card Game "Declare"

I was wondering if it would be possible (and feasible) to analyse a card game called "declare" which I recently discovered. Suppose there are 9 players playing with 4 decks of 52 cards and ...
Ninja In The Night's user avatar
1 vote
1 answer
41 views

How can we maximize the expected number of runs in a shuffled deck of cards?

Take a standard deck of cards, with 52 cards, 26 red and 26 black. A run is a maximum contiguous block of cards, which has the same color. So, (𝑅,𝐡,𝑅,𝐡,...,𝑅,𝐡) has 52 runs. (𝑅,𝑅,𝑅,...,𝑅,𝐡,οΏ½...
MrMustache's user avatar
8 votes
1 answer
186 views

Simplifying a binomial sum for bridge deals with specific voids

While trying to get an expression for the number of deals from a generalised bridge deck with nobody being void in any suit I encountered the following subproblem. From a generalised bridge deck with $...
Parcly Taxel's user avatar
1 vote
1 answer
85 views

How many cards until 2 kings or a king and an ace? [closed]

In a card game with a standard deck of 52 cards, dealing stops when either two kings appear or at least one king and one ace appear. What is the expected number of cards that will be dealt? I know ...
DiamondCorp's user avatar
0 votes
2 answers
78 views

From a deck of $52$ cards, we draw $5$ cards. Find the probability that we get at least $4$ face cards if we know that we have an ace and no hearts.

From a deck of $52$ cards, we draw $5$ cards without returning. Determine the probability that we get at least $4$ face cards (w if we know that we have an ace and no hearts. $A_4 =$ we get $4$ face ...
thefool's user avatar
  • 1,054
-3 votes
1 answer
82 views

Determine the mapping related to a machine which shuffles cards [closed]

A friend of mine told me about this problem. Given a indexed sequence of 13 cards from Ace to King, there is a machine which shuffles them and gives a certain (indexed) output sequence. Now inserting ...
user1170874's user avatar
2 votes
2 answers
96 views

Card matching game

The game setup is as follows: there is a bag with 6 matching pairs of cards (two 1s, two 2s, two 3s, two 4s, two 5s, two 6s). We randomly draw one card at a time, but put matching cards aside as soon ...
blizzy's user avatar
  • 21
0 votes
1 answer
38 views

Probability of dealing a specific blackjack sequence of hands

I'm trying to calculate the probability that a certain scenario will be dealt in Blackjack (known as "21" to some), after a very random shuffle of a pack of 52 cards. Let me describe the &...
Steve's user avatar
  • 3
3 votes
3 answers
295 views

How many possible pairs in a random 5-card poker hand?

This question is from Introduction to Probability, question 32b. I've seen the solution and I understand it clearly. $$\frac{\binom{13}{2}\times \binom{4}{2}\times \binom{4}{2} \times 44}{\binom{52}{5}...
Ron Luu's user avatar
  • 43
-1 votes
2 answers
77 views

Calculating probabilities in a children's card game [closed]

So I want to know how to calculate the probabilities of opening a specfic hand in a 44 card deck in which you draw 5 cards in you 1st turn. Lets say I have 3 copies of Stratos, 3 copies of Faris, 3 ...
Juan Troisi's user avatar
2 votes
1 answer
124 views

Probability of popular 4 playing card flip game.

I recently saw some friends play a game where the goal is to get a series of 4 educated and/or random guesses on 4 playing card flips. Thinking about the probability of winning seemed as simple as ...
NanoSmug's user avatar
0 votes
2 answers
110 views

Card draws and two players game

Let's consider a deck of $52$ cards $(A,K,Q,J,10,9,8,7,6,5,4,3,2)$. Two players each draw $5$ cards without putting them back into the deck. Calculate the probability that the first player draws at ...
Sigma Algebra's user avatar
2 votes
1 answer
82 views

Probability of getting at least $3$ cards of each suit when dealt a $13$-card hand.

A random 13-card hand is dealt from a standard deck of cards. What is the probability that the hand contains at least 3 cards of every suit? Choose one of the 4 suits, within that suit choose 13 ...
IGottaLearnMath's user avatar
0 votes
3 answers
61 views

Probability with card games

I was doing my exercises and I had this one question. If I drew all cards from a deck of 36 cards ( 4 different colors and 9 numbers per color) how big is the probability that the second card is a Ace....
haminta kurti's user avatar
1 vote
1 answer
77 views

Card Game Fair Value

Let's say you have a deck of 4 cards: Ace, King, Queen, Jack. (Worth 40, 30, 20, 10 points respectively) The deck is shuffled and you are given two choices for each card: to view or to discard. If you ...
shrizzy's user avatar
  • 794
4 votes
2 answers
110 views

Distinguishable subsets of the 52-card blackjack deck

I need to find, for $n = 0, 1, . . . , 52$, the number of distinguishable subsets of size n. Blackjack deck has $4$ cards for each value from $1$ to $9$ and $16$ cards of value $10$, color doesn't ...
Monia's user avatar
  • 51
1 vote
1 answer
100 views

Simple Casino War Probability

This question is from QuantGuide(Casino War): You are playing a game with the casino. You and the dealer are each dealt a card from a fair, shuffled deck of 52 cards. If you have a strictly larger ...
Md Kaif Faiyaz's user avatar
0 votes
0 answers
36 views

Average Deviation of Cards

Suppose we draw cards from a standard 52 card deck where each card has a value from 1-13 (Ace being 1 King being 13). What is the average deviation of the value of a randomly selected card? What is ...
shrizzy's user avatar
  • 794
1 vote
1 answer
57 views

Bridge Card Orderings

Let's say 4 players, A, B, C , and D are playing bridge. (Each player is dealt 13 cards and random from standard 52 card deck). What is the number of ways that all cards of two suits are split among ...
shrizzy's user avatar
  • 794
0 votes
1 answer
37 views

Possible card hands

Suppose you have a deck of $20$ cards with $4$ suits and ranks {A, K, Q, J, 10}. Let's say you draw 4 cards at random (without replacement). What is the probability you will have exactly 3 suits? I ...
shrizzy's user avatar
  • 794
26 votes
1 answer
2k views

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 ...
Daniel P's user avatar
  • 263
2 votes
2 answers
160 views

Probability of at least one ace in a hand without using complementary event

While going through the textbook, Discrete Math and its Applications, I found a problem, "what is the probability that a 5-card poker hand contains at least one ace?" It uses a standard deck ...
Blouiser's user avatar
0 votes
2 answers
70 views

Adding a twist to a card game which may probability wise make the game unfair

My friends and I gathered to play a card game the other night. More than 15 people showed up, therefore we had to shuffle two decks of cards so everyone could play at the same time. The game generally ...
Negar Rezaei Nejad's user avatar
2 votes
1 answer
53 views

A chance to get a flush in a poker game, is the same chance as getting two flushes in sequence?

I know this question looks dumb... but I'm going to ask it anyway because I'm really confused. Let's say that getting a flush in a poker game is 7%, and then I get it. After this, suppose that the ...
Nicholas Yamasaki's user avatar

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