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

learn more… | top users | synonyms

1
vote
1answer
33 views

How many draws to have a 90% chance of getting the ace of spades?

You have a standard 52-card deck, and you want to take the minimum number of draws from a random/shuffled deck such that you have a 90% chance of drawing the ace of spades. How would you find the ...
6
votes
0answers
57 views

When can we quit a game of War?

Consider the game of War. (The rules are below.) It would be nice to be able to end the game early. Suppose, for example, one player has 50 of the 52 cards. It is very likely that he's going to win. ...
0
votes
1answer
69 views

Another card game probability calculation

The game: dealer and multiple players, lets say 6 players, 1 dealer. Each participant received 2 cards. Hands: each hand consists of 4 cards, the player's two cards and the dealer's two cards. ...
0
votes
0answers
23 views

52 card deck hi-low rtp probability and combinations

I am new to the world of card games and I am doing research on a hi-low card game using 52 cards = 1 deck without joker. How to come up with the proper RTP (Return to Player). Here is a sample of a ...
2
votes
1answer
39 views

Probability of running out of cards in draw poker

Seven players sit down for a hand of draw poker. If a player has a one-pair hand, she will call the first-round bets, thus participating in the draw; and all players drawing to one pair will want to ...
2
votes
0answers
19 views

Sufficient number of riffle shuffles for randomizing a deck of n cards.

It has been proven previously that for a deck of $52$ cards, $7$ randomized riffle shuffles are enough to randomize the deck to the point that any further riffle shuffles will not meaningfully get the ...
0
votes
0answers
26 views

7th Sea 2e: Grouping dice results into sets of 10 vs doing the same with Tarot cards.

Note: While an interesting problem on its own, it also struck me as an excellent example of how marvelous the human brain is, as it is able to almost effortlessly negotiate a task that (at least to ...
3
votes
2answers
76 views

3 people dealt 3 cards, probability that nobody recieves 3 of a kind

If $3$ people are dealt $3$ cards from a standard deck, determine the probability that none of them is dealt three of a kind? Here is my attempt: The total number of hands is $${_{52}\mathsf ...
1
vote
1answer
66 views

Probability that two cards will be higher than a third

I'm currently creating a game for class. I know that the probability of one card being higher than another is $8$ out of $17$. What I'm trying to determine is the probability of the following: A ...
1
vote
0answers
28 views

How to calculate the probability of getting at least one of each card in a given set from a deck?

I am trying to calculate the probability of getting a particular straight after drawing $x$ cards from a deck. Say, for this example, that the straight I am attempting to obtain is "2-3-4-5-6". I know ...
1
vote
1answer
51 views

Probability of getting a straight after drawing 20 cards?

Here is the question I am trying to solve: "Say you draw a 7 from a deck of 50 cards, what is the probability that after drawing 19 more cards from the deck, you will have the cards required to form ...
0
votes
6answers
56 views

Finding the expected value for card problem

You have 4 cards, 2 black and 2 red. You play a game where during each round you draw a card. If it's black, you lose a point. If it's red, you gain a point. You can chose to stop at any time. ...
4
votes
2answers
83 views

In a Zener card test using a 25 -card pack and no replacement, what is the expected score?

The Zener cards were invented by Karl Zener and used by J B Rhine in his experiments on extrasensory perception (ESP) at Duke University in the 1930s. They comprise cards of each of five types, ...
6
votes
0answers
55 views

At what rate does the entropy of shuffled cards converge?

Consider a somewhat primitive method of shuffling a stack of $n$ cards: In every step, take the top card and insert it at a uniformly randomly selected one of the $n$ possible positions above, between ...
6
votes
1answer
115 views

perfect riffle shuffle problem

A perfect riffle shuffle, also known as a Faro shuffle, is performed by cutting a deck of cards exactly in half and then perfectly interleaving the two halves. There are two different types of perfect ...
0
votes
2answers
51 views

Expected number of cards we end up with in game

Suppose that we have $N$ distinct cards arranged in no particular order. If the first card of the pack is less than the second card of the pack, we keep both cards. Otherwise we discard the second one ...
5
votes
2answers
48 views

Help With a Card Game

Intro A friend of mine is trying to create a real time card game where players try to match images on cards in their hand to another card that is in play. Example: Player 1 plays a card with images ...
4
votes
2answers
49 views

Probability of a run of $n$ cards of the same color?

A magician friend hit me with this one: given a shuffled deck, what is the probability that it contains at least one run of at least $n$ cards of the same color — for example, four reds or four blacks ...
0
votes
0answers
24 views

What are the odds (average card sample distribution)?

In a card game, how would I compute content of statistical sample of random hand drawn from the deck? I know how to use hypergeometric distribution, but that is good for getting answer in style: ...
0
votes
2answers
49 views

$16$ cards. What is the conditional probability, that initially John took this card of boy? [closed]

John and Jane are taking the cards from the well mixed pack of $16$ cards. In pack of cards are $4$ aces (A), $4$ kings (K), $4$ queens (Q) and $4$ boys (J). First John take one card from the top of ...
0
votes
3answers
44 views

John and Jane are taking the cards from a well mixed pack of $16$ cards. What is the probability that she takes a boy? [closed]

John and Jane are taking the cards from a well mixed pack of $16$ cards. In the pack of cards are $4$ aces (A), $4$ kings (K), $4$ queens (Q) and $4$ boys (J). First John takes one card from the top ...
-1
votes
2answers
42 views

John and Jane are taking the cards from the well mixed pack of $16$ cards. What is the probability that John in the hands has card of boy? [closed]

John and Jane are taking the cards from the well mixed pack of $16$ cards. In pack of cards are $4$ aces $(A)$, $4$ kings $(K)$, $4$ queens $(Q)$ and $4$ boys $(J)$. First John take one card from the ...
-1
votes
1answer
28 views

Card Game Probability, the 15th card

Playing a card game in which 2 52 card decks are combined to create the pile and from this pile each player is dealt 14 cards. One rule of the game is if any player is dealt 3 doubles (a double being ...
1
vote
2answers
21 views

you need to draw 1 card with 4 cards left and 2 draws

I was wondering what are the odds of drawing the 1 card you need when you have 4 cards left and two draws. I instinctively think 50/50 as you have two draws, but then I think it's a 1/4 + 1/3 == > ...
0
votes
1answer
30 views

Number of Unique Ranks of High Card in Three Card Brag

Well the game is called Teen Patti in India. Almost similar to Three Card Brag a British game. There are total $16440$ Unique High Card hands are present. (Considering the suit.) Hand $1 = 5$ Heart, ...
0
votes
2answers
43 views

Gambler's ruin (Deck of cards).

A deck of $52$ cards is shuffled, and the cards are turned up one at a time until the first $A$ appears. Show that: $$P(\text{next hand is Ace of spade}) = P(\text{next hand is 2 of club}) = ...
2
votes
1answer
54 views

Measure of card shuffling randomness

I've read online that you need to shuffle a deck of cards at least 7 times (depending on the game being played) for the deck to be 'random enough', i.e. that it is nearly impossible to predict the ...
1
vote
2answers
43 views

Player position algorithm for cards game

So, in a classic 4 player cards game, which is multiplayer. I want to show each player sitting in the central position on their own respective screen. Opposite sitting players are partners. ...
-1
votes
1answer
37 views

Probability of Choosing Cards out of a Deck of 60

Similar to the standard 52-card deck questions, I have a question about choosing cards; however, I am working with a 60 card deck and I have 4 players. At the end of each game, 1 player will have 15 ...
2
votes
0answers
21 views

What is the probability of shuffling a deck of cards, & coming up with an order of cards that doesn't have any 2 cards of the same value back to back? [duplicate]

This is a question that I have been struggling with for quite some time. I work with kids at a math tutoring center, and one of the things we do is work on the multiplication facts. We use a ...
0
votes
1answer
27 views

Probability of having 2 cards in hand knowing the probability of having 1

Given (per player): 1 deck of 30 cards 15 different cards, so there are always 2 identical cards (let's name them ONE, TWO, ..., FIFTEEN) 1 hand of 5 cards (drawn from the deck) I was wondering ...
0
votes
1answer
24 views

Probability that at least one of two drawn cards has greater face value than at least one of your two, if both your two cards are the same?

I have just been messing around with some card odds and have been having a little difficulty. The situation is that both you and your single opponent are dealt two cards. You look at your own cards ...
2
votes
0answers
42 views

The hardest game of mahjongg

I was playing Mahjongg solitaire the other day. It got me thinking... The board has $2n$ pieces at the beginning and assuming that the game is winnable. The game would be trivial if there would be ...
4
votes
0answers
49 views

Shuffle Deck $7$ times or $8.55$ times?

Persi Diaconis showed in $1992$ that in order to shuffle a deck of $52$ cards, you need at least $7$ riffle shuffles. However, in the paper he published, he showed that we needed ...
0
votes
1answer
22 views

mean value of multiple card draw

I'm calculating probabilities for a card game that I'm creating. In this game, there are 78 cards in the deck. The cards have the following values: 4 cards have value 1 4 cards have value 2 4 cards ...
0
votes
1answer
41 views

Is this the correct way to calculate probability?

I'm trying to create an AI for a game I develop but I run into the problem of trying to figure out how to calculate probability. The probability I'm trying to calculate is what is the probability ...
4
votes
0answers
90 views

Four of a kind -dilemma

CONDITIONS Imagine, that we have five standard 52-card decks. We will now mix all these five decks into a one (afterwards "big deck", 260 cards in total). Now our task is to turn all the cards open, ...
2
votes
0answers
64 views

Is there a better way for calculating the odds for the horserace card game?

horserace card game in progress Game: The 4 aces ("horses") are laid face-up at one end of the table. 6 cards face-up are laid ("race track") in a straight line perpendicular to the aces. The race ...
2
votes
2answers
37 views

If I draw two cards, what is the probability that either is an ace?

I thought to solve this problem as follows: $P_{atLeast} = P_{AceFirstOnly} + P_{AceSecondOnly} + P_{BothAces}$ The actual solution: $P_{atLeast} = P_{AceFirst} + P_{AceSecond} - P_{BothAces}$ Why ...
0
votes
1answer
32 views

deal five cards to six players from a deck of 48 distinct cards

How many ways are there to deal five cards to six players from a deck of 48 distinct cards? I know that $13^4 * 48$ divided by 2 (to remove duplicate hands) is the total number of possible 5 cards ...
0
votes
1answer
34 views

Probability about a deck of cards

"What is the probability of drawing either an ace or a diamond in a single draw from a fair deck of cards?" For this question would I need to subtract the ace of diamonds in my calculation because it ...
0
votes
1answer
32 views

Draw at least 2 of the same card, and 1 of another card

I'm trying to work out some statistics for a game I'm working on, but can't wrap my head around some of the statistical concepts. To make a generic case along the lines of what I'm trying to do: ...
3
votes
2answers
54 views

Choosing cards at random without replacing

Out of 52 cards we choose two without replacing them. Are events {we have at least one heart} and {we do not have any figures} independent? I have managed to solve that with use of binomial ...
2
votes
2answers
41 views

Probability Deck of Cards

In a hand of 13 playing cards from a deck of 52 whats the probability of drawing exactly one king. My approach would be $${4 \choose 1}*{48 \choose 12}/{52 \choose 13}*{2}$$ I divided by 2 because I ...
0
votes
0answers
40 views

Expected payout of an optimal hand in Poker

Expected payout of a hand I created a video poker hand evaluator and I am not getting the optimal hand and I know my mistake is because of the way I am calculating the expected payout. Above is a ...
0
votes
2answers
223 views

How many 5-cards poker hands are there containing at least 3 of the 4 suits?

How many 5-cards poker hands are there containing at least 3 of the 4 suits? I don't how know how to properly handle this question. There 13 ranks of each card, and 4 suits My Attempt: Begin with ...
2
votes
1answer
41 views

Ways to get a full house, how is my method wrong?

In how many ways can you deal a "full house"? (Three cards of one rank and two cards of another rank.) What is wrong with this approach? ${13 \choose 2}$ ways to choose 2 ranks out of 13 ${4 ...
2
votes
1answer
38 views

Two pair problem, what is wrong with this reasoning

What is the probability that you are dealt a "two pair"? (Two pairs of cards where each pair contains two cards of the same denomination, with the fifth card of a different denomination. Note that we ...
0
votes
1answer
79 views

Number of permutations for card decks in “Skat” and “Doppelkopf” games

In the card game Skat, you play with a deck of $32$ cards and each of the three players gets $10$ cards. This means that there are $32! \approx 2.63 × 10^{35}$ possible permutations of the card deck. ...
1
vote
1answer
28 views

Independence of removing a spade and picking an ace.

In this video, around 8:00, it is stated that if a spade is removed from a deck of cards, the probability of picking an ace stays the same. I don't understand why. I tried to simplify with three ...