Questions regarding probabilities and combinatorics of card games based on C cards decks and P players.

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Number of Unique Ranks of High Card in Three Card Brag

Well the game is called Teen Patti in India. Almost similar to Three Card Brag a British game. There are total $16440$ Unique High Card hands are present. (Considering the suit.) Hand $1 = 5$ Heart, ...
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2answers
36 views

Gambler's ruin (Deck of cards).

A deck of $52$ cards is shuffled, and the cards are turned up one at a time until the first $A$ appears. Show that: $$P(\text{next hand is Ace of spade}) = P(\text{next hand is 2 of club}) = ...
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1answer
50 views

Measure of card shuffling randomness

I've read online that you need to shuffle a deck of cards at least 7 times (depending on the game being played) for the deck to be 'random enough', i.e. that it is nearly impossible to predict the ...
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2answers
35 views

Player position algorithm for cards game

So, in a classic 4 player cards game, which is multiplayer. I want to show each player sitting in the central position on their own respective screen. Opposite sitting players are partners. ...
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1answer
34 views

Probability of Choosing Cards out of a Deck of 60

Similar to the standard 52-card deck questions, I have a question about choosing cards; however, I am working with a 60 card deck and I have 4 players. At the end of each game, 1 player will have 15 ...
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What is the probability of shuffling a deck of cards, & coming up with an order of cards that doesn't have any 2 cards of the same value back to back? [duplicate]

This is a question that I have been struggling with for quite some time. I work with kids at a math tutoring center, and one of the things we do is work on the multiplication facts. We use a ...
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1answer
24 views

Probability of having 2 cards in hand knowing the probability of having 1

Given (per player): 1 deck of 30 cards 15 different cards, so there are always 2 identical cards (let's name them ONE, TWO, ..., FIFTEEN) 1 hand of 5 cards (drawn from the deck) I was wondering ...
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1answer
19 views

Probability that at least one of two drawn cards has greater face value than at least one of your two, if both your two cards are the same?

I have just been messing around with some card odds and have been having a little difficulty. The situation is that both you and your single opponent are dealt two cards. You look at your own cards ...
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37 views

The hardest game of mahjongg

I was playing Mahjongg solitaire the other day. It got me thinking... The board has $2n$ pieces at the beginning and assuming that the game is winnable. The game would be trivial if there would be ...
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38 views

Shuffle Deck $7$ times or$ 8.55$ times$?$

Persi Diaconis showed in $1992$ that in order to shuffle a deck of $52$ cards, you need at least $7$ riffle shuffles. However, in the paper he published, he showed that we needed ...
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1answer
17 views

mean value of multiple card draw

I'm calculating probabilities for a card game that I'm creating. In this game, there are 78 cards in the deck. The cards have the following values: 4 cards have value 1 4 cards have value 2 4 cards ...
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1answer
37 views

Is this the correct way to calculate probability?

I'm trying to create an AI for a game I develop but I run into the problem of trying to figure out how to calculate probability. The probability I'm trying to calculate is what is the probability ...
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67 views

Four of a kind -dilemma

CONDITIONS Imagine, that we have five standard 52-card decks. We will now mix all these five decks into a one (afterwards "big deck", 260 cards in total). Now our task is to turn all the cards open, ...
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0answers
58 views

Is there a better way for calculating the odds for the horserace card game?

horserace card game in progress Game: The 4 aces ("horses") are laid face-up at one end of the table. 6 cards face-up are laid ("race track") in a straight line perpendicular to the aces. The race ...
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2answers
35 views

If I draw two cards, what is the probability that either is an ace?

I thought to solve this problem as follows: $P_{atLeast} = P_{AceFirstOnly} + P_{AceSecondOnly} + P_{BothAces}$ The actual solution: $P_{atLeast} = P_{AceFirst} + P_{AceSecond} - P_{BothAces}$ Why ...
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1answer
25 views

deal five cards to six players from a deck of 48 distinct cards

How many ways are there to deal five cards to six players from a deck of 48 distinct cards? I know that $13^4 * 48$ divided by 2 (to remove duplicate hands) is the total number of possible 5 cards ...
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1answer
29 views

Probability about a deck of cards

"What is the probability of drawing either an ace or a diamond in a single draw from a fair deck of cards?" For this question would I need to subtract the ace of diamonds in my calculation because it ...
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1answer
26 views

Draw at least 2 of the same card, and 1 of another card

I'm trying to work out some statistics for a game I'm working on, but can't wrap my head around some of the statistical concepts. To make a generic case along the lines of what I'm trying to do: ...
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2answers
51 views

Choosing cards at random without replacing

Out of 52 cards we choose two without replacing them. Are events {we have at least one heart} and {we do not have any figures} independent? I have managed to solve that with use of binomial ...
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2answers
28 views

Probability Deck of Cards

In a hand of 13 playing cards from a deck of 52 whats the probability of drawing exactly one king. My approach would be $${4 \choose 1}*{48 \choose 12}/{52 \choose 13}*{2}$$ I divided by 2 because I ...
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0answers
34 views

Expected payout of an optimal hand in Poker

Expected payout of a hand I created a video poker hand evaluator and I am not getting the optimal hand and I know my mistake is because of the way I am calculating the expected payout. Above is a ...
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2answers
181 views

How many 5-cards poker hands are there containing at least 3 of the 4 suits?

How many 5-cards poker hands are there containing at least 3 of the 4 suits? I don't how know how to properly handle this question. There 13 ranks of each card, and 4 suits My Attempt: Begin with ...
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1answer
39 views

Ways to get a full house, how is my method wrong?

In how many ways can you deal a "full house"? (Three cards of one rank and two cards of another rank.) What is wrong with this approach? ${13 \choose 2}$ ways to choose 2 ranks out of 13 ${4 ...
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1answer
36 views

Two pair problem, what is wrong with this reasoning

What is the probability that you are dealt a "two pair"? (Two pairs of cards where each pair contains two cards of the same denomination, with the fifth card of a different denomination. Note that we ...
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1answer
71 views

Number of permutations for card decks in “Skat” and “Doppelkopf” games

In the card game Skat, you play with a deck of $32$ cards and each of the three players gets $10$ cards. This means that there are $32! \approx 2.63 × 10^{35}$ possible permutations of the card deck. ...
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Independence of removing a spade and picking an ace.

In this video, around 8:00, it is stated that if a spade is removed from a deck of cards, the probability of picking an ace stays the same. I don't understand why. I tried to simplify with three ...
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2answers
40 views

Probability red cards in game

There are 16 cards (4 red, 4 blue, 4 green, 4 yellow and have numbers 1-4) and 4 player. a) I want to calculate the probability that 2 player have 2 red cards and 2 player have 0 red cards. How can I ...
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Ideal Card Game

I have invented a very interesting card game. All the cards from 2 to 10 (in four colours) are divided evenly between the two players (the deck is shuffled before dealing the cards, of course). Now ...
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1answer
42 views

Probability that one player has three aces? (Solution check)

There are 20 cards (4 colors with 5 cards types each, e.g. ace). Each of the 4 players randomly receives 5 cards. What is the probability that one player has three aces after the drawing? ...
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1answer
228 views

Fine the value of k such that this game is fair (E(X) = 0)

From an ordinary deck of 52 cards, cards are drawn at random and with replacement until three aces are drawn. If it takes more than ten draws to obtain the three aces, the player loses k dollars; ...
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Asymptotic value of card drawing game

A deck consisting of $r_0$ red cards and $b_0$ black cards is randomly shuffled. The host turns up the cards one at a time; if it is red, you get $\$1$; otherwise you pay the host $\$1$ (and you're ...
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2answers
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guess the color of the next card, what is the payoff of this game?

There are 26 red cards and 26 black cards on the table which are randomly shuffled and are facing down onto the table. The host turns up the cards one at a time. You can stop the game any time (even ...
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1answer
71 views

Highest card expectation puzzle

There is a deck of 100 initially blank cards. The dealer is allowed to write ANY positive integer, one per card, leaving none blank. You are then asked to turn over as many cards as you wish. If the ...
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3answers
88 views

Probability of 4th card drawn to be a king?

Problem: Out of a pack of 52 playing cards, 3 cards are drawn one after the other without replacement. If a fourth card is drawn, what is the probability that it is a king? One of my friends has ...
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1answer
44 views

Getting probability of a certain hand in card game (french tarot)

I am trying to figure out the odds of a certain situation in the card game French Tarot, specifically what are the odds of the 'attacker' being out of the same suit of the 'R' that a defender has ...
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3answers
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5 cards are drawn one at a time without replacement from a deck of 52.

Calculate the probability of landing a straight flush. A royal flush is considered a straight flush. I can't be sure, but I think the answer changes depending on the first card you choose. Like if ...
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4answers
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Is the probability of picking an Ace as the second card of a deck the same if the deck is shuffled after the first card?

Here's the situation: You have a deck of 52 cards that is already shuffled. You pick the first card, and the first card is not an Ace. Is the probability of drawing an Ace as second card the same if ...
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1answer
38 views

Probability that in bridge game the Players N,E,S,W have a,b,c,d spades respectively.

There are 52 cards in bridge and 13 cards of each suit. The formula for numerator is: $${13\choose a}{39 \choose 13-a}{13-a\choose b}{26+a\choose 13-b}{13-a-b\choose c}{13+a+b\choose 13-c}$$ But i ...
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1answer
23 views

Probabilty of Drawing Specific Cards

If I have a deck of randomized cards and I draw 5 cards, what is the probability that I will draw at least one 2 and at least one 3. In other words, I am looking for any hands of the form x2xx3, ...
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0answers
185 views

The mathematics of a drinking game called Spoon

This question is about the drinking game Spoon. It was asked on reddit.com/r/math : http://www.reddit.com/r/math/comments/3i9790/drinking_game_turned_mathematical/ The question is whether the person ...
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3answers
1k views

With a standard deck of 52 cards, how many different 25 card spreads are available?

With a 52 card standard deck, if you need to deal 25 cards, how many different spreads are possible? For example, with a 2 card spread: ...
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1answer
51 views

Probability that a random bridge board does not contain a sequence?

Two cards with adjacent values and the same suit produce a SEQUENCE. For example, the heart-ten and the heart-jack form a sequence. The order of the values in bridge is $$23456789TJQKA$$ -What is the ...
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2answers
56 views

Binomial Coefficient Probability Question

completely stuck in this probability question. I know to use Hypergeometric probability but im not sure about what numbers i should be using. Any help would be great. A regular deck of 52 playing ...
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Casino game trente et quarante (probabilities)

I am currently working on side bets for the game 30 and 40 (known mainly in Europe) explained on this page : http://wizardofodds.com/games/trente-et-quarante/ If I try to sum-up the rules of the ...
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find minimum number of card which is needed to perform trick

some one ask you to choose number between $1$ and $n$ both inclusively then he shows you some card having one of more element and asks whether the card contains your chosen number or not after showing ...
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1answer
79 views

Probability a card can win a trick with a trump suit

I'm working on the AI for a card game that uses a standard deck of 52 cards consisting of 13 cards in 4 (spades, clubs, diamonds, hearts) suits. Each player starts with 13 cards in their hand. ...
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3answers
133 views

Probability of picking a card one out of 52 times.

Let's say we have a standard deck of 52 cards. What would be the probability of choosing the 2 of diamonds? Obviously, it would be $\frac{1}{52}$. If we were to randomly choose another card from ...
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1answer
26 views

Does the expectation for a blackjack hand become even in certain situations?

Particularly, when the player hand and the the dealer up card show the same value, shouldn't the odds of winning be about even at 50% (assuming infinite decks)? I ask this also because in some tables ...
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1answer
54 views

Probability, drawing cards from 5 packs.

Firstly apologies for the vague post title. Apart from probability I don't really know what sub category this question falls within. If I have a pack of cards and I draw one card from it the chance ...
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2answers
112 views

Two cards are drawn at random from a standard deck of $52$ cards and not replaced.

Two cards are drawn at random from a standard deck of $52$ cards and not replaced. What is the probability that the first card is a face card and the second card is a seven? What is the answer to this ...