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

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1answer
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Do the last three remaining cards in a game of Set always form a set?

Question (brief introduction to the game Set is given after the question) When a game of Set gets to a point that there are only three cards left on the table, and all other cards were already ...
5
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2answers
249 views

Variable triples vs. single quad card game. Who has the advantage?

$2$ people decide to count wins on a card game using a well shuffled standard $52$ card deck. Community (shared) cards are drawn one at a time from the deck without replacement until there is a winner ...
0
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1answer
59 views

I don't understand why this card trick works!

So My math professor did a card trick with me where he gave me a set of normal 52 cards and let me shuffle them however I like, he even said that i can arrange them however I would like. Next, he ...
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2answers
86 views

Standard playing card deck without jokers: Deal 13 cards. What is the probability at least 1 suit is not present?

Similar questions: What is the probability that 13 cards drawn from a standard deck has at least one card from each suit? Deal 4 cards from a deck. What is the probability that we get one card from ...
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2answers
42 views

first card club and second card ace?

Larsen and Marx Suppose that two cards are drawn—in order— from a standard 52-card poker deck. In how many ways can the first card be a club and the second card be an ace? I think there are ...
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2answers
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Picking cards sequentially vs consecutively

We have a pack of 6 cards over the table. Cards are: {A, A}, {B, B}, {C}, {D}. There are 3 players (Papa, Pepe, Popo) sat around the table. Cards are all upside down, so the players cannot see which ...
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For given range of opponent cards, which must I hold to be at least equally likely to win a showdown?

(What I need at least are the names of the concepts I need to learn so I can google them. Not expecting the reader to do the legwork for me.) The game is No-limit Texas Hold'em. Nine handed table, ...
2
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1answer
73 views

Probability on card suits in a standard deck

Let's say we have a standard deck of 52 cards with 13 cards each of the standard suits of spades, clubs, diamonds, hearts. Let's say we have p players and each player is dealt q cards where pq<52. ...
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0answers
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Find most varied match assignments for a 4-player card game

I'm a programmer and confronted with a particularly hard (at least for me) problem I couldn't find an answer for. This is not a school task or anything. It is something I need personally. I've ...
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0answers
40 views

Big Two's classification according to game theory

Is the game Big Two, as described in https://www.pagat.com/climbing/bigtwo.html, classified as: a game of perfect or imperfect information? deterministic or stochastic? EDIT: I am fairly certain ...
3
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0answers
45 views

How to punish a riffle shuffle?

It is common knowledge that for a deck to be considered randomly sorted, at least seven riffle shuffles should be used. However, in my experience, very few people will take the time to complete seven ...
1
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1answer
102 views

Probability that duplicates are still in the deck after X card drawn

Deck has 30 cards, out of which 5 cards have duplicates (20 cards are unique, 5 cards have 2 copies each). If you draw X cards from the deck (without returning), what is the probability that there ...
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1answer
50 views

Combination: Selecting at least two cards, at least one from two non-exclusive sets.

I'm trying to figure out probabilities of certain hands for a game I've been considering. An example is the probability of having a card that is an Ace or King and a card that is a Heart or a Diamond,...
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2answers
392 views

Probabilities playing bridge

Being very bad with probabilities, I would greatly appreciate help for the following problem. The first bid of my partner indicates that, among his $13$ cards, he handles $6$ hearts and a maximum of $...
1
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1answer
46 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 ...
12
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0answers
215 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
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1answer
81 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. ...
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0answers
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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
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1answer
41 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
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0answers
23 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 ...
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0answers
32 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
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2answers
82 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 C}_3\...
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1answer
68 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
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1answer
53 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 ...
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1answer
53 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 ...
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6answers
78 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. What'...
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2answers
94 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, ...
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0answers
60 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
133 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
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2answers
56 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 ...
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2answers
53 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 {...
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2answers
52 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 ...
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0answers
32 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
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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
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3answers
49 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 ...
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2answers
44 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
29 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
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2answers
26 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 == > 50/...
0
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1answer
34 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
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1answer
52 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}) = \frac{1}{...
2
votes
1answer
86 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 ...
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2answers
45 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
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1answer
41 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
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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
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1answer
31 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
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1answer
27 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
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0answers
45 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
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0answers
52 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 $\frac{3}{2}\log_2n$...
0
votes
1answer
23 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
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1answer
43 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 ...