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]
365 questions
23
votes
6 answers
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
- 419
15
votes
2 answers
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
- 243
- 1
- 7
10
votes
1 answer
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
- 101
9
votes
3 answers
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
- 91
7
votes
2 answers
Generating random numbers in your head
I'm a poker player, and often at the poker I table I want to be able to randomize to make a decision (call 1/2 of the time, raise 1/3 the time, etc). I can't flip a coin or pull out my phone at the table, so I'd like an easy way of generating that…
weissguy
- 422
7
votes
1 answer
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
- 81
7
votes
3 answers
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
- 735
7
votes
2 answers
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
- 1,272
6
votes
0 answers
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
- 87
6
votes
2 answers
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
- 63
5
votes
1 answer
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
- 235
5
votes
3 answers
Texas Hold'em Poker odds - calculating opponent's odds
Scenario: we have reached River, i.e. there are 5 cards on the table, and three of them are hearts. I have no heart on my hand, and there are 6 remaining players other than me. What is the probability, that (at least) one of them will have (any) two…
5
votes
1 answer
Probability of poker pair - what's wrong with this?
Thanks to others here, I know the correct way to calculate the probability of one pair in 5-card poker is
P(one pair) = $C(13, 1) * C(4, 2) * C(12, 3) * [C(4, 1)]^3 / C(52, 5)$ = 0.4225690276...
Why doesn't the following work? The answer comes out…
kotm16
- 53
5
votes
1 answer
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
- 110
5
votes
2 answers
Probability of a flush given that the first two cards are of the same suit.
there. I'm looking to write probability of a flush (suppose it contains royal flush, straight flush, etc.) given that the first two cards are of the same suit.
Here is the solution, let $F$ be the event that a flush appears, $T$ be the event that…
Jamie Carr
- 413