# Tagged Questions

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

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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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### 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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### 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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### Five cards are chosen from a standard deck with replacement. Find joint PMF of number of queens, kings and others.

Five cards are randomly chosen from a standard deck, one at a time with replacement. Let $X$, $Y$, $Z$ be the numbers of chosen queens, kings, and other cards. (a) Find the joint PMF of X, Y, Z. ...
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### Is this statement true?

If you shuffle a pack of cards properly, chances are that exact order has never been seen before in the whole history of the universe... If it is, what is the explanation. I find it hard to believe.
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### Card Matching: expected value of correctly predicted cards with partial feedback

A standard deck of cards is shuffled, and the cards are dealt face down one by one. Just after each card is dealt, you name any card (as your prediction). Let $X$ be the number of cards you predict ...
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### Playing card game probability problem!

So the problem is stated below: A card game of 52 cards are dealt between 4 people (including me), each receiving 13 cards. 4 of the cards are Aces; one is called Ace of Spades and the other Ace ...
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### How to calculate the probability of busting in Black Jack?

Is there a formula to calculate the probability of busting in the Black Jack game after you are dealt two cards? I want the game to be just between the dealer and me. I do not want to know what the ...
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### Probability of no king, queen or jack before the first ace occurs?

A deck of cards is shuffled well. The cards are dealt one by one, until the first time an Ace appears. Find the probability that no kings, queens, or jacks appear before the first ace. (Introduction ...
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### Probability that a random 13-card hand contains at least 3 cards of every suit?

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? (Introduction to Probability, p.36) My solution: ...
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### Combinatorics: Number of possible 10-card hands from superdeck (10 times 52 cards)

I have the following problem from book "Introduction to Probability", p.32 A certain casino uses 10 standard decks of cards mixed together into one big deck, which we will call a superdeck. Thus,...
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### What are the best $3$ pocket cards in Omaha poker?

In Texas Hold'em poker, the best $3$ pocket cards are AA, KK and QQ respectively. I've been trying to find the best $3$ pocket cards in Omaha poker, where you have to use exactly $2$ pocket cards out ...
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### Probability of getting the same 10 cards after a 104 card shuffle

Consider this situation: You have two standard decks merged together (104 cards). You give 10 cards to 4 players. What is the probability that the next time you deal (after the deck is randomly ...
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### Can the probability of a trump poverty be calculated without making case distinctions?

The card game Doppelkopf is played with four players. Every player receives 12 of the 48 cards. The 48 cards consist of 26 trump cards and 22 other. A trump poverty is what we call the scenario that a ...
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### When does it become impossible to lose a game of FreeCell?

After spending more time than I should playing FreeCell, I've been wondering about the following: At what point in the game does it become impossible for someone to lose? "losing" probably isn't ...
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