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

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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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18 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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131 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
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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
36 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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32 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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74 views

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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30 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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45 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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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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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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42 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 ...
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55 views

Card game questions

I write down 4 numbers on four cards and you should choose one card. After seeing the card you can decide to throw away this card and pick another one without replacement. You can stop anytime you ...
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1answer
59 views

Combinatorics: How many ways are there to distribute zero to thirteen distinct cards to four distinct players?

Other ways to word the question so that it's clear: In a game where players hold a maximum of thirteen cards and a minimum of zero cards, how many possible positions are there? How many possible ...
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Limit probability of winning a card game [duplicate]

As mentioned in this question, the probability of winning, with an $n$-card per $k$ suit deck, a counting-up match card game (where you count through each of $n$ cards in order $k$ times and lose if ...
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Krypto analysis

The game Krypto is where you get 5 numbered cards dealt with you by the dealer and then a sixth card that you must connect the five cards to with mathematical symbols. The values of the first 5 cards ...
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70 views

Probability a blackjack dealer will bust if you know their score and know the exact deck?

If you know the exact cards left in a deck, and the score of the dealer, how can you calculate the exact probability that they will bust? The dealer behaves as follows: If the dealer's score is less ...
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Probability of drawing >18 when drawing 3 cards

I am trying to calculate some probabilities for a card game. Players have to draw 3 cards each time and the cards must add up to a certain value for them to win - the value changes depending on the ...
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Card trick - Count to 13 explanation [duplicate]

I was just shown this card trick. Let me attempt to explain: You begin by shuffling a standard 52 card deck. After it is shuffled decently enough for your audience, lay down the first card face up, ...
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43 views

What is the probability of getting a heart in $n$-th draw without replacement?

You are given a deck of cards. What is the probability of getting a heart at the first draw. What is the probability of getting the same in second draw without replacement? What is the probability ...
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2answers
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Odds of pulling out 10 specific cards out of a deck

What would the formula be to calculate the odds be of pulling all four 2's, all four 3's and at least 2 of the 4 4's from a standard 52 card deck. No order is necessary as long as these ten cards are ...
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46 views

What is the percentage chance of drawing at least 1 of 12 cards when drawing 3 of a deck of 44 cards?

What is the percentage chance of drawing at least 1 of 12 cards when drawing 3 of a deck of 44 cards? I'm not sure how to calculate this. It's related to a game that a play, so it's not homework or ...
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How many possible shuffles can be won perfectly?

It is known that the possible shuffles of a deck of cards is $52!$, or ~$80658175170943878571660636856403766975289505440883277824000000000000$ different combinations. I have become aware of a game ...
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167 views

What is the algorithm to generate the cards in the game “Dobble” ( known as “Spot it” in the USA )?h

In the game Dobble ( known in the USA as "Spot it" ) , there is a pack of 55 playing cards, each with 8 different symbols on them. What is remarkable ( mathematically ) is that any two cards chosen at ...
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Seven-Card Stud with Random Hand Selection

I was recently confronted with a number—$2727707$, actually—that started a short train of thought while I was placed on hold. (This seems to happen quite often: both the observation of unusual ...
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1answer
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Card Probability in Magic: The Gathering

I'm playing with a deck in Magic: The Gathering which can be seen here: http://tappedout.net/mtg-decks/21-05-15-robots/ The deck has sixty cards. I'm trying to find the probability of pulling 5 ...
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31 views

Same card probability in a deck

Working on my first board game design. To simplify, having 4 types of cards: 5 blue ones, 4 red ones, 3 yellow ones, 2 green ones, so 14 cards in total. How can I calulate the possibility that ...
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173 views

Mega-straight flush with a huger hand

Three days ago I asked about the probability of drawing a straight flush when being dealt $26$ out of the $52$ cards of the deck, which Michael wisely solved. Now I'd like to make things more ...
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2answers
126 views

Straight Flush probability with a huge hand.

It's easy to calculate the probability of a straight flush when you're dealt $5$ cards. I'd like to ask for the probability of the same when you're dealt half the deck. I seek $P(\text{straight ...
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How many shuffles are really needed for bridge?

According to the Gilbert-Shannon-Reeds model (which apparently models reality well), one should riffle shuffle seven times to achieve a suitably randomized $52$ card deck. However, it occurs to me ...
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Combinatorics while drawing cards

He have a deck with $52$ cards and $4$ suits, $H$,$D$,$C$,$S$, from which you take $26$ cards. There are some combinations that, when taken with the same suit, give a prize. Let's those combinations ...
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Optimal way to decide Blackjack play with a soft score

I am designing a Blackjack AI such that it would try to play optimally each hand against the dealer. When I'm having a hard score the algorithm is easy: as long as my risk of busting is lower than ...
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135 views

What are the chances of winning Higher/Lower?

Given the game 'higher/lower': A deck of cards of size N is uniquely ranked. The deck is shuffled, lain in a row, and the first card is turned over. You have to guess whether the next card to be ...
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14 Cards of 52, calculate p_Royal Flush, Straight Flush, a Pair

14 cards are dealt of the 52-card deck (1 card is to be discarded, so the final hand will consist of two 5-card poker hand and one 3-card poker hand) Task is to calculate probability of getting Royal ...
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Collection all cards in a cardgame

Imagine we have a cardset of 140. Every card has 1/140 chance of being drawn every time. When a card is drawn, it is shuffled into the deck of cards again. This would be like when you buy a set in a ...
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$3$-player card game probability question

Three people, (call them $C$, $D$, and $E$), decide to play a card game for fun. They use an ordinary fair deck of $52$ cards, shuffled well immediately before each hand is drawn, and randomly draw ...
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Probability of getting A to K on single scan of shuffled deck

Let us say we have a regular 52-card well-shuffled deck. We scan through the deck (first to last) till we find an Ace. Then we continue (from that Ace) till we find a 2. Then we scan (from the 2) ...
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Getting $5$ in a row of same color card “mystery”

I was wondering why this is the case... If you take a standard well shuffled deck of $52$ cards and draw cards randomly without replacement until you get $5$ of the same color (red or black) in a row ...
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At time n, randomly choose a natural number ≤n. How long is it until a single number is chosen three times?

To clarify, the number ≤n is chosen uniformly at random at each step, and n chooses from the natural numbers beginning with 1. I wish to determine the expected value of $n$ at which a natural number ...
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Why can I not include unused cards into a second binomial coefficient?

In trying to count the number of 13-card hands where there is at least one ace and no J, Q, K, we can see one way is $$ \sum_{k=1}^4 \binom{4}{k}\binom{36}{13-k} = 9722433280. $$ However, I cannot ...
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In the card game “Projective Set”: Compute the probability that $n$ cards contain a set

In the game of Projective Set, it turns out that any seven cards contain a projective set. For fewer than 7 cards, how can we determine the probability that one or more sets exist (in terms of the ...
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In the card came “Projective Set”, show that 7 cards do always contain a set. [duplicate]

In the game of Projective Set, it turns out that any seven cards contain a projective set. How can one prove this? And for fewer than 7 cards, how can we determine the probability that one or more ...
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1answer
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Probability to get the same cards in a card game two times

I want to calculate the probability to get a set of cards two times in a card game, respectively how many two times I would have to play to get it with a specific probability. The card game is ...
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Playing Cards: Formula for match probability with card draw rules

This is a simplification of a larger problem I have been working on, calculating probabilities based upon a characteristic, with rules for selection based upon a second characteristic. I believe if I ...
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1answer
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Circular list from the 2nd element of the result of repeatedly perfect shuffling a magnitude ordered list of natural numbers less than an even number.

Start with a magnitude ordered list of the natural numbers that are less than a chosen even number greater than 0. {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11} Repeatedly 'Perfect Shuffle' this list, ...
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Propability of M-faced dice rolling a greater result than an N-faced dice ( M<N) and expected value of the absolute difference?

Hello I have a game-mechanic which goes like this: Two-sides are rolling numbers. The defender rolls between [1,Armor_Value] , attacker rolls between [1,Damage_Value]. If the attacker_roll> ...
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Does discarding cards face down affect the distribution of the remaining cards? [closed]

You have a deck of $N$ cards, $Y$ of which are labelled "A". $N$ and $Y$ are known. Does discarding $n$ cards face down from the top of the deck affect the probability that the next card drawn is ...
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Unknown Card Monty Hall

I'm trying to understand this problem better and whether or not it is defined as a variant of the classic Monty Hall problem. Let's say there are X cards in a deck of cards. A copy of this deck of ...
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How do you calculate the odds that the odds will be right?

So in this instance I have a standard deck of 52 cards and am playing a high/low game with it (ie turn over the top card, guess if the next card is higher or lower) and maintain a record of all the ...