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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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Your friend starts first. What is the probability that you win?

Imagine you’re playing a game of cards with a friend. You decide to keep it a simple game: taking turns, you both take a card from a standard $52$-card deck (first your friend takes a card, then you,...
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1answer
33 views

Dual 52 card deck, pair of exact card match (position and rank) probability

Suppose we have 2 well shuffled decks and alternately draw 1 card from each deck without replacement, placing the cards in a 2 deep 52 wide pattern, and looking for exact card matches between the 2 ...
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2answers
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Six-card hand with $2$ cards of each suit - did I calculate this correctly?

Suppose you have a deck of $36$ cards - $3$ different suits, $12$ cards per suit. If you draw a $6$-card hand, what is the chance of a hand with $2$ cards of each suit ($2-2-2$)? I would do $$\frac{\...
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2answers
62 views

A simple model for the card game Dominion

This problem is inspired by the card game Dominion. We play a card game. At the beginning, we get one card "Copper". At each round, we draw a card uniformly at random form cards that we already have....
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0answers
38 views

Card Expected Value with Option to Skip Cards

In a normal deck of cards, you can either reveal the top card or guess whether that card is black. If you reveal the top card, you get to see what the card is and the game continues with one less card ...
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1answer
27 views

3 cards are drawn at random from a pack of well shuffled 52 cards.find the probability that all the 3 cards are of the same suit.

Three cards are drawn at random from a pack of well shuffled $52$ cards. Find the probability that all the $3$ cards are of the same suit. My two attempts: $\displaystyle\frac{ {13 \choose 3} }{ 52 }...
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0answers
27 views

Drawing self-improving cards: get good or remove bad first?

Suppose there is a single player card game in which there is a deck of $n$ cards. A card is either red, green or blank. Initially, the deck consists of $r_0$ red, $g_0$ green and $b_0$ blank cards ...
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1answer
33 views

combinatoric problem: probability of different wins (outcomes) in the some way similar to the the BINGO game

In game, we randomly generate four grids (cards) $3\times 5$ (row × col), with each column containing 3 numbers randomly selected without replacement from 18 possibilities: first columns from ...
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1answer
62 views

Estimate number of cards needed to be drawn from deck before full house

Imagine we have a well-shuffled deck of cards and we keep drawing cards until there is at least one full house in the drawn cards. How many cards will we draw on average? I would be interested in both ...
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1answer
19 views

How many 5-card hands from a standard 52-card deck contain exactly 1 king and exactly 1 heart?

Is my solution correct? There are two cases: Case 1: (the chosen heart is not a king) So there are $3 \choose 1 $ ways to choose the king, and $12 \choose 1 $ ways to choose the heart, and then $...
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1answer
26 views

What is the probability that only one of the cards will have the matching suit?

A group of 4 friends are playing a card game using a standard deck of 52 cards. Each friend receives one card from the deck, and the next card is flipped up. Only one of the friend has a card that ...
2
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1answer
14 views

Indicator Random Variables for Card Game (2 Red in a row)

Working through some practice problems in Introduction to Probability, Blitzstein. (I found similar problems to this one but want to make sure I understand this concept.) You have a well-shuffed 52-...
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2answers
37 views

Probability of Infection in Who Goes There / The Thing (the game)

In the game Who Goes There, you are fighting for survival with other players (up to 6 can play) and fending off The Thing, an alien who infects and attacks your camp. To be infected, you take an ...
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0answers
15 views

Calculating probability distributions for card game

I am creating a card game for a project and I need to calculate the probability and distribution when playing the game. I do not know how to go about it, and would appreciate some insight on starting. ...
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0answers
27 views

Probability of picking a card randomly vs always picking the first card?

I shuffle a deck of cards. Each card appears there only once. Now, I need to pick a card randomly. I can do this in two ways: literally, pick a card somewhere in the beginning/middle/end of the deck ...
4
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1answer
55 views

Expected value of a card game with 6 cards

A deck contains 3 cards with +1 value and 3 cards with -1 value. The dealer shuffles the cards and deals them face up one by one. After each card is dealt, you have the option of stopping the game. ...
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0answers
48 views

How to calculate probability for card game

I am creating a card game for a project and I need to calculate the probability and distribution when playing the game. I do not know how to go about it, and would appreciate some insight on starting. ...
0
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1answer
27 views

Drawing Cards and Expected Value

In many strategic board games, there is a stack of cards with events. I'm interested in the number of cards that need to be drawn until you can expect a certain card or a combination of certain cards ...
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2answers
59 views

Probability of winning/losing a lonely card game when you shout an integer progressively each time you draw

Take a standard face-down 52-deck of cards, including 13 ranks of four suits (for simplicity, assign value 1 to 13 from ace to King). Draw the cards one by one, shouting the integers from 1 to 13 (and ...
1
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1answer
36 views

What is the probability of obtaining a total of 6 for the two cards?

Consider the experiment of drawing two cards from a deck in which all picture cards have been removed and adding their values (with ace = $1$). What is the sample space? What is the probability of ...
0
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1answer
39 views

exercise on combinations (poker deck)

I have to count with 3 extractions without repetition from a deck of 52 cards (flop in texas holdem), How many possible combinations of 3 cards that have an Ace? How many possible ...
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0answers
10 views

Probability of doubles on 2 shuffled deck of cards and gaining doubles

I am not asking for questions on homework or anything related to school or work, I am asking for help with a card game I was playing with my friends. I was playing a card game called Tractor(its a ...
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1answer
48 views

Probability of each player withdrawing 4 aces given 3 cards each on a 40 card deck?

Let's say there is a deck of 40 cards with 4 aces (just take any 12 non-ace cards of a regular deck for instance) We deal three cards for each player (so 40-12=24 remain undealt) what is the ...
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1answer
43 views

profitability of drawing 2 of the same card in 60 draws

Edit: Python code added. Question corrected Right, i am trying to figure out my chances of drawing certain cards in MTG, so that is my frame. I have 4 of the same card and 56 fillers (60 in total) I ...
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0answers
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How to shuffle more than 1 deck of cards

I know that after "ruffle shuffling" 1 deck (54 cards) 7 times, every configuration is nearly equally likely. How should I shuffle (for example) 3 decks (162 cards) assuming I can shuffle together ...
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1answer
93 views

What is the minimum amount of moves it takes to finish this game?

This is a follow up question from this post which I asked. The previous question was answered by Barry Cipra, and I was suggested to create this follow up question. The Game: Two players have $...
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2answers
137 views

Prove that this card game between 2 people always ends in a finite amount of moves.

Update: Bram28 and Barry Cipra have given very good answers! I've also fixed a lot of my examples because of the better solutions. Also, as per Barry Cipra suggestion, I've created a follow-up ...
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1answer
15 views

How do I count how many ways to place 8 cards of only 2 ranks (suits ignored) into 16 possible positions?

I have a need to generate all combinations of placing 8 standard playing cards of only 2 distinct ranks, (suits are ignored), into 16 possible positions. For example, suppose we had A A A A 2 2 2 2 ...
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4answers
1k views

A magic trick - find out the fifth card if four is given

Here is a magic trick I saw. My question is how the magician and his partner did it. Given the simple French deck of cards, with $52$ cards. A person from the audience chooses randomly five cards ...
0
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1answer
93 views

Optimal Double Up for Poker Game Reward in DanMachi Memoria Freese

I am trying to figure out the optimal times to double up my poker game reward in the casino in Danmachi Memoria Freese. Here is the details to figure it out. This poker version uses joker as wild ...
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2answers
30 views

Draw two cards at random without replacement. What is the chance of not getting all kings? [closed]

I am at a loss for how to solve this problem. Can someone please help and link the steps below? Thank you so much!
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1answer
177 views

Random Bridge Hand w Cards of exactly two suits

Question: What is the probability that a random bridge hand contains cards of exactly two suits? My Attempt At A Solution Bridge hands consist of $13$ cards, and a suit contains $52$ cards, so the ...
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0answers
20 views

Probability of reaching 20 by drawing X cards from a single deck

A Blackjack inspired question i thought of after reading several existing questions, which lead me to this formula http://probability.infarom.ro/blackjack.html which is fairly simple for calculating ...
2
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3answers
337 views

Deck of 52 cards, 3 card rank/order repeat pattern probability.

A standard deck of 52 playing cards is well shuffled and drawn 1 card at a time without replacement. What is the probability that the ranks of the 3 most recently drawn cards (starting at drawn card ...
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2answers
102 views

Probability of getting 4 aces while drawing 6 cards.

Drawing 6 cards from a standard deck of 52 cards, what is the probability of getting 4 aces? This answer explains how to calculate the odds of a getting any 4-of-a-kind in a 5-card draw. I was hoping ...
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1answer
47 views

Compute the Probability that a hand of 3 cards will contain a king and an ace of the same suit [closed]

This is a problem for my Homework and I see Inclusion-Exclusion method but I still cannot understand it. Can someone please help me. Thanks EDIT: I tried doing it this way, and I am not sure if this ...
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0answers
26 views

Calculating probabilities for drawing specific cards from multiple decks?

I've been trying to get an achievement in a game called 'Sentinels of the Multiverse' (for context, its a superhero-themed card game). The achievement requires you to get insanely lucky with your ...
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0answers
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card war game probability

The "card war" game is played with 2 players and 8 decks (52 cards each, 416 total), the purpose of any player is to score a higher value card, where the values are ordered: ace < two < ... &...
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2answers
34 views

Impact of standard vs random blind choice of card

I have no idea if there is a better way to word this problem, so please feel free to suggest improvements. Here is the scenario: Jack shows Jill ten playing cards, face down. One of those cards is a ...
10
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2answers
133 views

Cards game and probabilities

From a standard 52-cards deck we randomly pull out 2 cards. One is black and the other is a 4. We choose one of the two cards. What is the probability: The card we pick is a 4 The card ...
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0answers
30 views

Is bridge a fair game: references/heuristics?

Though not knowledgeable on card games or game theory, I've just learnt the rules of bridge, and I'm starting to wonder whether it can be proven that bridge is a fair game. Of course, to give an ...
2
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1answer
56 views

Card shuffling and harmonic numbers

Below is a simple proof of one connection between card shuffling and harmonic numbers. I'm interested in references for this if it's already known, as well as alternative methods of proof. (Can the ...
0
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1answer
36 views

Two Simultaneous Cumulative Hypergeometric Distributions

Suppose we have a standard 52 card deck from which we draw five cards. What are the chances of drawing one or more Aces and one or more Kings? How do I calculate this? I know that we can calculate ...
0
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1answer
107 views

Card counting techniques to guess that last card in the deck

I think this is very well known task, but somehow I can't find much information about memorization techniques for cards. You have a deck of 52 cards and they take out one card out of it (51 left). ...
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1answer
97 views

A game involving binomial probabilities

Consider the following tables: Given a number of independent trials $n=2,3,4\ldots$ each of these tables represents the list of all the possible $\binom{k+n-1}{n}=\binom{n+2}{n}=6,10,15\ldots$ ways (...
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1answer
61 views

Shuffle Tracking in Blackjack

I'm a professional card counter, i developed a software that let me count cards in Blackjack very easily, and now i'm trying to implement an algorithm that lets me see all the probabilities of one ...
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2answers
133 views

Probability question about cards being dealt and probability of getting a particular suit [closed]

In this card game, the entire standard deck of $52$ cards is dealt out to $4$ players. What is the probability that (a) one of the players receives all $13$ spades? (b) each player receives $...
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2answers
40 views

Poker Hand Probability

You draw 4 cards from a standard deck of cards without replacement. Find the probability you get: A Straight (4 consecutive cards, Ace can count as either highest or lowest) The solution that's ...
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3answers
47 views

Finding a King and a Queen in 3 Cards

I'm looking at a problem for a card game where you already have a king in hand and need to find a king and a queen when drawing 3 cards. Right now I'm looking at something like: $3! \times \frac{3}{...
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2answers
78 views

what is the chance of a deck of cards not having adjacent suits or numbers?

For example, if we have an Ace of spades, the next card cannot be an Ace nor spades. Edit: Assuming that we pick one particular shuffle amongst all possible ones