# Questions tagged [card-games]

Questions regarding probabilities and combinatorics of card games. The number of cards in the deck, number of players, and other parameters can vary.

108 questions
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### 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. ...
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498 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 ...
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112 views

### Asymptotic value of card drawing game

A deck consisting of $r_0$ red cards and $b_0$ black cards is randomly shuffled. The host turns up the cards one at a time; if it is red, you get $\$1$; otherwise you pay the host$\$1$ (and you're ...
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46 views

### Deck of 5 cards Shuffling Problem but only allowed to choose two adjacent cards

Say I have a deck of 5 cards that are labeled 1, 2, 3, 4, 5. 1 being at the top and 5 being at the bottom. The rules of this game are as follows. You can take only take two adjacent cards (1 2, 2 3, 3 ...
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119 views

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### What is the probability that other players have Hearts or Q of Spades on hearts game?

I'm developing a 4 player Hearts game that has three AIs. So, I need some probabilities to do so. Rules: Initially, 52 cards are distributed among all 4 players. Each of them has 13 random cards. ...
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60 views

### Probability of a straight in a card game I'm designing

I am developing a card game with a friend and I want to calculate the probability of different win conditions being achieved (I am putting together an excel sheet). I have trouble calculating the ...
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36 views

### Card probability (15 cards, 9 unique suits, odds of specific possibilities acros three 5 card hands)

A randomly shuffled deck of cards consists of 15 cards total of 9 suits. We'll designate the suits as A1, A2, A3, B1, B2, B3, C1, C2, & C3. The deck contains one card each from suits A1, A2, B1,...
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22 views

### Calculating probability distributions for card game

I am creating a card game for a project and I need to calculate the probability and distribution when playing the game. I do not know how to go about it, and would appreciate some insight on starting. ...
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29 views

### Probability of picking a card randomly vs always picking the first card?

I shuffle a deck of cards. Each card appears there only once. Now, I need to pick a card randomly. I can do this in two ways: literally, pick a card somewhere in the beginning/middle/end of the deck ...
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146 views

### How to calculate probability for card game

I am creating a card game for a project and I need to calculate the probability and distribution when playing the game. I do not know how to go about it, and would appreciate some insight on starting. ...
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13 views

### Probability of doubles on 2 shuffled deck of cards and gaining doubles

I am not asking for questions on homework or anything related to school or work, I am asking for help with a card game I was playing with my friends. I was playing a card game called Tractor(its a ...
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28 views

### How to shuffle more than 1 deck of cards

I know that after "ruffle shuffling" 1 deck (54 cards) 7 times, every configuration is nearly equally likely. How should I shuffle (for example) 3 decks (162 cards) assuming I can shuffle together ...
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22 views

### Probability of reaching 20 by drawing X cards from a single deck

A Blackjack inspired question i thought of after reading several existing questions, which lead me to this formula http://probability.infarom.ro/blackjack.html which is fairly simple for calculating ...
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31 views

### Calculating probabilities for drawing specific cards from multiple decks?

I've been trying to get an achievement in a game called 'Sentinels of the Multiverse' (for context, its a superhero-themed card game). The achievement requires you to get insanely lucky with your ...
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35 views

### Is bridge a fair game: references/heuristics?

Though not knowledgeable on card games or game theory, I've just learnt the rules of bridge, and I'm starting to wonder whether it can be proven that bridge is a fair game. Of course, to give an ...