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

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3
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1answer
28 views

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 ...
1
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0answers
30 views

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, ...
0
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1answer
38 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
31 views

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 ...
0
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1answer
26 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 ...
4
votes
0answers
49 views

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 ...
0
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2answers
119 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 ...
3
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0answers
25 views

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 ...
3
votes
1answer
42 views

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 ...
0
votes
1answer
29 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 ...
0
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0answers
169 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 ...
2
votes
2answers
119 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 ...
1
vote
0answers
26 views

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 ...
1
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0answers
27 views

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 ...
1
vote
0answers
35 views

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 ...
2
votes
1answer
76 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 ...
0
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0answers
43 views

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 ...
1
vote
1answer
13 views

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 ...
0
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0answers
66 views

$3$-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 ...
9
votes
2answers
172 views

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) ...
2
votes
1answer
82 views

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 ...
9
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2answers
153 views

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 ...
1
vote
1answer
29 views

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 ...
0
votes
2answers
90 views

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 ...
4
votes
1answer
115 views

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 ...
1
vote
1answer
35 views

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 ...
0
votes
1answer
57 views

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 ...
1
vote
1answer
45 views

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, ...
1
vote
1answer
57 views

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> ...
-1
votes
1answer
28 views

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 ...
0
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3answers
63 views

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 ...
3
votes
2answers
87 views

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 ...
3
votes
2answers
133 views

How to calculate the probability of a hand in a game where cards are dealt one by one?

I wanted to ask a question about finding the chance of a specific hand in a specific game, but then I thought that it would be interesting to have a more generic question related to it. So I will try ...
0
votes
1answer
28 views

Determining the order of cards in a deck of shuffled cards

Once a deck of cards is shuffled, can the order of all of the cards for that specific shuffle be determined by only knowing perhaps the order(sequence) of $4$ of the cards in the deck? How many ...
1
vote
1answer
74 views

Winning strategy for solitaire?

I'm talking about the Klondike solitaire, turning three cards at once to the waste and placing no limit on passes through the deck. I know there isn't always a winning strategy, a counterexample can ...
4
votes
4answers
306 views

Encode order of playing cards (data compression)

Suppose we have a deck of cards, shuffled in a random configuration. We would like to find a $k$-bit code in which we explain the current order of the cards. This would be easy to do for $k=51 \cdot ...
0
votes
1answer
52 views

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, ...
0
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2answers
32 views

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. ...
2
votes
1answer
88 views

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 ...
1
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2answers
122 views

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 ...
0
votes
1answer
151 views

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 ...
0
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4answers
160 views

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. ...
4
votes
2answers
765 views

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: ...
6
votes
0answers
212 views

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. ...
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0answers
40 views

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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2answers
112 views

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 ...
1
vote
1answer
37 views

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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0answers
51 views

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 ...
0
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4answers
65 views

Probability of 5 card hand

You have a $5$ card hand from randomly shuffled standard deck of $52$ cards: $X$ - Event that hand exactly contains $1$ spade $Y$ - Event that hand exactly contains $1$ ace How do I calculate $P(X ...
0
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2answers
35 views

Probability - 5 card hand

Question is : You have a 5 card hand from randomly shuffled standard deck of 52 cards. P - Event that hand exactly contains one spade. Q - Event that hand exactly contains one ace. Calculate : a. ...