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3
votes
3answers
208 views

How do you calculate the odds getting a single pair in Texas Hold 'Em?

Given that I am dealt one card, what are the odds that I will then make a pair either from the next card dealt to me or from the river of 5 cards played out? I'm thinking something like: given I have ...
7
votes
1answer
452 views

Bulgarian Solitaire: Size of root loops

I first learned of Bulgarian solitaire from one of Martin Gardner's books a while ago and have since investigated it somewhat. Google-searching has revealed that surprisingly little work has been done ...
7
votes
3answers
1k views

Failing to guess each card in a deck

Consider the situation from this video. Cards from a normal playing deck are dealt out one at a time while the player guesses what the number of the card is not (suit is ignored). To be clear, the ...
3
votes
1answer
114 views

The maximum number of straight making ranks

Poker nerd question here... I'll start out with some definitions of standard poker terms: A flop is 3 cards chosen from a 52 card deck. For example: 789 (suits are irrelevant to this question). If ...
4
votes
3answers
357 views

A combinatorial card problem

Suppose you have a standard bridge deck of 52 cards. We will say you "have a pair" if you have two consecutive cards in the deck with the same rank (2,3,4,5,6,7,8,9,10,J,Q,K,A). If a deck is ...
23
votes
5answers
10k views

What is the math behind the game Spot It?

I just purchased the game Spot It. As per this site, the structure of the game is as follows: Game has 55 round playing cards. Each card has eight randomly placed symbols. There are a total of 50 ...
7
votes
2answers
262 views

Combinatorial Card Flip Game

Recently, I've been given an interesting type of problem that I am having a difficult time proving. The problem revolves around a game, with the rules as follows: "You have a deck containing n cards ...
7
votes
1answer
226 views

Proving a certain type of poker game can always be won

Ok, so I just finished a Discrete Math class where we learned about all types of proofs and counting and graphs, etc. So I know the basics, but never thought I'd need to use it in the real world (not ...
3
votes
2answers
2k views

Probability in a game of Contract Bridge

in a game of contract bridge, partner and me together have 11 cards in a suite. The remaining 2 cards in the same suite can be distributed amongst our opponents as either 1-1 or 2-0. What is the ...
2
votes
1answer
195 views

How many games should we play to determine the better player statistically significantly?

We are playing a game with my friend and trying to determine who is the better player. The game has an luck element to it. The current score is 9-7. The following questions have risen: 1) How many ...
6
votes
4answers
538 views

Mental card game

Each of n persons draws a card from a shuffled deck of $k$ cards numbered from $1$ to $k$. There are at least as many cards as persons. The winner is the person who is holding the largest card. If ...
7
votes
1answer
2k views

Counting how many hands of cards use all four suits

From a standard 52-card deck, how many ways are there to pick a hand of $k$ cards that includes one card from all four suits? I know that for any specific $k$, it's possible to break it up into cases ...