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7
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2answers
98 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
27 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
68 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
99 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
29 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
40 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
44 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
43 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
27 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
votes
3answers
59 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
64 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
106 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
22 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
63 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
244 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
35 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
votes
2answers
31 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
75 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
vote
2answers
86 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
77 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
votes
4answers
121 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
613 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
167 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. ...
0
votes
0answers
33 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 ...
1
vote
2answers
85 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
36 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 ...
1
vote
0answers
42 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
votes
4answers
61 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
votes
2answers
33 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. ...
3
votes
3answers
129 views

What's the probability of a straight in $5$ card poker given $5$ and $7$ of hearts?

Using a standard $52$ card deck, if you are given the $5$ and $7$ of hearts from it, what is the probability that you end up with a straight if $3$ additional cards from that same deck are given to ...
1
vote
1answer
40 views

Help understanding the Expected Value equation when applied to poker

I don't play or follow poker, (just thought I'd declare that), but found it interesting from speaking to a few people that do that their way of calculating the Expected Value, $E(x)$, didnt account ...
3
votes
2answers
47 views

Is it possible to get the largest conceivable score in Hearts?

I should explain the necessary rules: in the four-player game of Hearts, the object is to get as few points as possible. The points you receive are determined by the cards you pick up through a hand: ...
0
votes
0answers
51 views

Overall probability of winning a card hand, given the probabilities of what the other player has

I am creating a program that deals out the cards for Texas hold em, and I have calculated the probability with two players, given the 5 community cards, and the 2 cards in my hand, what the ...
3
votes
3answers
92 views

Card Game Probability 13 Card Hand

Me and my friends play a four person poker style card game. Each person is dealt 13 cards, and it is a standard trump card game. Now, as the standard, a five card flush beats a five card straight, but ...
1
vote
1answer
115 views

Deck of Cards Probability Question - Probability of Getting At Least 2 Queens

There was actually another question like this but the final answer a person mentioned was incorrect and I was confused as to how he got it. Can any answers explain how they got there? I'd like to ...
1
vote
0answers
69 views

Poker Hand Probabilities in Doomtown Reloaded

The short version of my question is as follows: What is the best way to compute the probability of different hand ranks after redraw in poker? Can this easily generalise to a non-standard deck? ...
4
votes
3answers
102 views

How many perfect shuffles are needed to go back to initial state?

The other day, in a popular-science book, I saw: Given 32 cards ($c_i$ for $i=0..31$), cut the deck into two parts and shuffle them the American way (riffle shuffling). The deck now looks like: ...
1
vote
3answers
116 views

Draw 4 cards where: 3 cards same suit and remaining card of different suit

Four cards are drawn from a standard 52-card deck without replacement. Find the probability that exactly 3 cards are of the same suit and the remaining card is of a different suit. What I did: ...
0
votes
1answer
41 views

Chances of a shuffled deck being sorted only by color

QUESTION (TL;DR) Let's assume you are handed a deck of 52, standard cards which are already shuffled. You take the the deck and mindlessly shuffle it for a few minutes. After the shuffle, you turn ...
1
vote
1answer
67 views

Counting number of two pair hands in poker (not standard)

I was doing number counting problem and wanted to check if my result was correct. Problem description: From a standard deck of cards(52 cards, 4 suits, 13 numbers in each suit) there are 5 cards ...
4
votes
2answers
188 views

Probability of a minimum sum of card values when drawing cards from a custom deck

Apologies if this question has been answered -- I tried searching for an answer but wasn't sure what terminology to use. Suppose I have a deck of cards, consisting of $n_1$ ones, $n_2$ twos, etc. ...
0
votes
0answers
133 views

Game theory: Bidding strategy during an auction in a card game

I'm trying to create a mathematical model for the auction process in a card game called Pitch. The specific question I'm interested in solving is: Let $p_i$ represent the probability of a specific ...
0
votes
1answer
64 views

A Probability Game of Bridge Problem and Its Puzzling Correct Answer

In my effort to work on my probability and combinatorics skills before the semester starts, I have come across this problem: What is the probability that a bridge hand will contain 13 cards of the ...
7
votes
1answer
158 views

The Day Camp Stacking Game

My friend works at a day camp as a counselor and he told me about an interesting game he plays with his group of kids. You have a perfectly shuffled, regular $52$-card deck and a group of $2 \leq n ...
2
votes
1answer
105 views

Minimum number of out-shuffles required to get back to the start in a pack of $2n$ cards?

So I'm stuck on this problem. If you perform a faro out-shuffle (i.e. a perfect "riffle shuffle" where the top and bottom cards stays in place) on a pack of 52 cards ($n=26$), you can get back the ...
2
votes
2answers
191 views

Probability of Getting a “Perfect Score” in the Card Matching Game Concentration

A person is playing the card matching game concentration. There are 40 cards, 20 pairs total. All the cards are shuffled and placed at random face down. A turn consists of two moves and a move is ...
0
votes
1answer
45 views

Straight in 52cards+2Joker

I have 52card (ace to king) + 2Joker I'm supposed to compute how much straights of 5 cards I can make, excluding the straight flushes (straights with all cards being the same color) My reasoning is : ...
1
vote
3answers
44 views

How Many Hands Having 3 Cards of a Kind are There?

The conditions are as follows: Standard 52-card deck, 4 suits. 5-card hand. There must be three of a kind, but only this (i.e., no 4 of a kind or full house). I know this has been asked already, ...
0
votes
0answers
50 views

Optimal strategy in a simple card game

So some friends and I are playing this simple card game. We choose 15 random cards from a normal deck of card and lay them on a table in a pyramid shape. 5 cards in the bottom row, 4 in the next row ...
1
vote
2answers
63 views

How to get the number of ways of getting a five card hand that is a straight flush from a standard deck of cards

I do not get the result at this page, ex. 13-7: Suppose that Aces can be either high or low; that is, that {Ace, 2, 3, 4, 5} is a straight, and so is {10, Jack, Queen, King, Ace}. The number of ...