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

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1answer
137 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
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1answer
41 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
174 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
186 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 flush}...
2
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0answers
41 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 ...
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0answers
51 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
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0answers
64 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
651 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 ...
1
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1answer
20 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
94 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 ...
13
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2answers
240 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
102 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
167 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
33 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
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2answers
108 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
156 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
44 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
228 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
60 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
69 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> ...
-2
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1answer
33 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
79 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
197 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
280 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
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1answer
56 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
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1answer
131 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 ...
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4answers
438 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 6=...
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1answer
212 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, Z. ...
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
361 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 ...
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2answers
336 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
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1answer
436 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 ...
1
vote
4answers
332 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. (Introduction ...
4
votes
2answers
2k 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: ...
10
votes
2answers
589 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. Thus,...
0
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0answers
51 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 ...
2
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3answers
167 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
45 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
56 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
75 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
41 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
195 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
56 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
58 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: ...
3
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3answers
469 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 ...
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1answer
376 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 ...
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0answers
120 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
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3answers
126 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: $...
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3answers
682 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: (4C1)(...
1
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1answer
173 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 ...