# 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 ...
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### 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 ...
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### 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 ...
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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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1 vote
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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 ...
• 1,054
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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 ...
• 1,054
1 vote
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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 ...
1 vote
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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 ...
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? ...
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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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### 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 ...
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### 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?
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### 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 ...
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### 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 ...
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1 vote
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### 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 ...
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 ...
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### 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 ...
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### 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 ...
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### 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 ...
1 vote
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### 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,𝐵,𝑅,𝐵,...,𝑅,𝐵) has 52 runs. (𝑅,𝑅,𝑅,...,𝑅,𝐵,�...
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### 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 ...
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