Poker is a card game with several variants (Draw, Texas Hold'em, ...), the common goal being to collect face value patterns such as "four of a kind", "full house" or "straight" or all of a suit ("flush") with five cards. Questions about combinatorics, probabilities, strategies (bluffing and betting).

# Questions tagged [poker]

305 questions

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### Probability of getting two pair in poker

I was looking at this website http://www.cwu.edu/~glasbys/POKER.HTM and I read the explanation for how to calculate the probability of getting a full house. To me, the logic basically looked like you figure out the number of possible ranks and…

Curt

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### Fundamental Theorem of Poker

I've been doing an investigation into the mathematics behind poker, and I have stumbled upon this theorem called 'The Fundamental Theorem of Poker', which is as follows:
"Every time you play a hand differently from the way you would have
played…

Mildwood

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### Probability of a Full House for five-card hand.

So I know this can be solved easily by counting the total ways to make a full house and dividing that by the total possible hands, but I want to know why another way I thought of to solve it is wrong.
My calculation is: $$1 \times \frac{3}{51}…

ToGzGaming

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### Game theory problem: Poker with bluffing

Hope someone can help me with this one. The problem I am talking about can be found in the book titled "Game Theory Evolving: A Problem-Centered Introduction to Modeling Strategic Interaction" by Herbert Gintis. The problem is as follows:
Ollie and…

Rok Dominko

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### Game Theory: Is there an "unexploitable" strategy in No Limit Holdem?

Do "unexploitable" strategy exist in No Limit Holdem? By this I mean frequency-based mixed strategy that has non-negative expected payoff against any other strategy (let's assume the game is completely symmetric, seats are randomly assigned to all…

zero-divisor

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### Probability of an Indisputable winner at Texas Holdem

What are the fraction of hands that can be classified as "indisputable winners" (aka "the nuts") after the river is revealed in Texas Holdem? By "hand" I mean the 2 hole cards you have that no one else can see plus the 5 cards on the table.
An…

user3294068

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### Why is the probability of getting a pair in a five-card poker hand so complicated?

The working-out of this question has really confused me. I know the basics of probability but I don't get the calculations here. I think 13C2 * 4C2 determines the number of possible pairs, and the stuff in the brackets is the number of combinations…

EH86055

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### Probability of drawing an ace or 2 after an ace

From a standard 52 card deck, we draw one card at a time without replacement. After having drawn the first ace, the game continues until either
We draw another ace, or
We draw a 2,
and the game then stop. Which events of the two is more likely,…

wanderlust

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### Why is this not a valid algorithm for counting poker hands?

In my probability class, we had an example asking what is the probability of getting three of a kind when randomly drawing $5$ cards from a typical deck ($13$ denomination and $4$ suits, total of $52$ cards). Three of a kind is defines as getting…

Jroc

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### Combinations: Poker hands, full houses

Reading through my Probability book brushing up on some stuff:
What is the probability that a poker hand is a full house? (A full house is defined as a hand with three cards of one denomination and two cards of another denomination; ex. three Queens…

Matt

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### How is calculated the frequency of a pair, a flush of 2 cards, a straight of 2 cards and a straight flush of 2 cards (52 cards, hand of 2, 3, 4, etc)?

Introduction
Before starting, I would like to specify a few things:
The deck has 52 cards. From 1 (Ace) to 10, J, Q, K, all in four different suits: spades, diamonds, club and hearts. I don't add jokers because that is far beyond my possibilities…

Enderluck

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### Numbering system for poker hands

I figure that this is surely either a solved problem or it is provably impossible. But I'm not able to track down an answer.
There are ${52 \choose 5}$ = 2,598,960 distinct ways to deal five cards from a standard 52 card deck. In poker one would…

mdahlman

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### What is the expected number of suits in a hand of 4 cards?

To find the expected number of suits the formula is
$E(Num Suits) = 1*P(1 Suit) + 2*P(2 Suit) + 3*P(3 Suit) + 4*P(4 Suit)$
For the probability of getting 4 suits I got
${13 \choose 1}^4 {4 \choose 4}/{52 \choose 4}$
For the probability of getting…

Eleanor

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### Probability of royal flush dealt to table of n players

I'm interested in calculating the probability of a royal flush being dealt to ANY of the n players seated at a Texas Hold'em poker game (2 hole cards, 5 community cards). The probability of YOU being dealt a royal flush is readily available on the…

Abovestand

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### Ways of getting three of a kind in a 52 card deck

This question has probably been asked before, but just to be clear here, I am NOT asking for the answer, I know the answer. What i want to know is why my solution is not equivalent to the actual solution.
Three of a kind in a deck means you draw 3…

Riptyde4

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