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Questions tagged [poker]

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).

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A little help with confidence interval estimation (for poker database analysis)

I'm a poker player, and I do a lot of database study to understand the frequencies of different profiles of players, to figure out how often they're bluffing and folding in different situations. I'll ...
MD Arshaq's user avatar
0 votes
2 answers
123 views

Does Nash Equilibrium say anything about odds?

Edited after good comment from @lulu I'm struggling with the concept of a Nash Equilibrium. I'm getting confused by comparing the prisoners dilemma with a game like rock-paper-scissors. The prisoners ...
Cdl's user avatar
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34 views

Calculating Probabilities of hands in Texas Hold 'em

My question is how to calculate different probabilities of hands in Texas Hold 'em. I know how to do this for 5 card hands as this is much simpler. Wkipedia gives all the answers: https://en.wikipedia....
Charles6Se's user avatar
1 vote
0 answers
63 views

Probability of a winning hand in Texas hold'em poker

Please correct me if I'm wrong. I'm new to probability and I have a question. Essentially say pre flop you receive an ace and a king. Convention says that it is a toss up roughly 50-50 that you win. ...
hawkeye_pierce's user avatar
0 votes
1 answer
65 views

In Texas Holdem what is the probability that the best hand is on the table?

The brute force method would involve calculating the probability of a royal flush on the table (i.e., the five community cards are A, K, Q, J, T suited). Follow this by calculating the probability ...
Phil Freedenberg's user avatar
1 vote
0 answers
49 views

Combinatorics Pigeon Hole Poker Game

Suppose I shuffle a standard 52 card deck deck and give you 25 cards at random from it. You are then tasked with making 5 poker hands from these cards such that each card is in exactly one hand. The ...
Evan Semet's user avatar
2 votes
4 answers
228 views

Each of A, B, and C draw a card without replacement from a 52-card deck. What is the probability that A's face value is higher than the rest?

Case 1: All three cards have equal face values. There are 13 such cases since there are 13 different ranks. Case 2: Two cards have equal face value and the third card has a lower value. Initially, I ...
clement's user avatar
  • 135
1 vote
1 answer
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Poker: Proof that running the deck multiples times from Turn to River doesn't change EV. How do you prove the same but for Flop to River instead?

There's this scenario that occurs in Texas hold 'em poker where two players will be all-in before the river card is dealt, and they agree to "run it twice". We'll start with the simplest ...
Muji's user avatar
  • 31
0 votes
1 answer
96 views

In a 52 card deck, what is the probability of getting a run of exactly 3 cards of the same suit in a 4-card hand?

In a 52 card deck, what is the probability of getting a run of exactly 3 cards of the same suit in a 4-card hand? So, treat aces (A) as a 1 so that A, 2, 3, 4 is a 4-card run (not a 3-card run), while ...
ClassyClass's user avatar
5 votes
3 answers
93 views

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,...
Martin Smartly's user avatar
1 vote
1 answer
110 views

What is the probability of a flush in 7 card poker

Problem: What is the probability of getting a flush (5 cards of the same suit) in 7 card poker? Note: For purposes of this question, a straight flush or a royal flush counts as a flush. Answer: Let $...
Bob's user avatar
  • 4,064
1 vote
1 answer
62 views

What is the probability of getting exactly one pair in poker?

Problem: What is the probability of getting exactly one pair in poker? Answer: Let $p$ be the probability we seek. \begin{align*} p &= \dfrac{ 13 {{4} \choose {2}} (48)(44)(40)}{ {{52} \choose {...
Bob's user avatar
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1 vote
1 answer
73 views

Number of poker deals with a specific suit configuration?

I'm trying to calculate the number of poker deals with the following suit configuration: Pocket: 2 spades Flop: 1 spade, 2 other cards of unmatched suit The order of the cards within a round of ...
Steven's user avatar
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1 vote
1 answer
40 views

Solve this generalized discrete optimization problem

How can this class of problem be solved in general? Six friends get together to play poker. To start, each player buys fifty \$1 chips from the banker with a \$50 bill. At the end of the game, the ...
Phil Freedenberg's user avatar
0 votes
2 answers
105 views

Calculating number of variants of variants with a generating function?

Imagine you are choosing 2 cards each from different 2 different suits (13 cards in each) and the ordering of suits does not matter. The goal is to calculate the number of possible combinations of ...
Steven's user avatar
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0 answers
22 views

Equivalent of multiset coefficient with a different number of items per group?

I'm trying to calculate the size of non-equivalent poker hands with a given suit configuration (additional context here). from a related question: Lets write $[x_1, y_1][x_2, y_2]\ldots$ for number ...
Steven's user avatar
  • 15
0 votes
1 answer
44 views

Calculating the number of non-equivalent hands for a given suit configuration?

I'm trying to implement this paper to index non-equivalent poker hands. I have all of the indexing implemented for a given suit configuration. But how can I calculate the size of a suit configuration ...
Steven's user avatar
  • 15
0 votes
0 answers
36 views

I'm trying to calculate the Probability of a Full House hand, where 7 cards are drawn and the deck is less than its maximum size.

Frankly I've seen questions similar to this answered on this site but they don't paint a clear enough image. Though I must confess that I'm a total novice to probability and combinatorics so I might ...
Peter's user avatar
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1 vote
1 answer
50 views

In this simple playing card game, is the expected probability constant?

I came up with a simple game using a standard 52-card deck. This is a 1-on-1 game involving a player and a dealer. The rules are as follows. Player makes a bet. One card is dealt to the player. One ...
wzq31757's user avatar
0 votes
1 answer
81 views

What is the number of 7 card poker hands which contain 3 of a kind and the other 4 are not the same?

Im solving this problem in two ways but i don't know which is correct, because they give different results. First Way I calculate the number of hands for the 4 possible forms of accepting hands: (...
Nick Tsiodras's user avatar
3 votes
0 answers
57 views

Why is an online poker article claiming that Straights happen more often than Three of a Kinds in a short deck?

Six Plus Hold'em is a variant of Texas Hold'em in which a short deck is used. A short deck is a deck in which all cards from 2 to 5 are removed from a standard 52-card deck, leaving only 36 cards. Due ...
a9g9's user avatar
  • 31
2 votes
0 answers
76 views

Probability of drawing 2 sets of triplets plus one pair from a poker deck.

If I consider a poker deck with $13$ ranks of $4$ cards each, what is the probability of obtaining 2 triplets and 1 pair (eg. AAA77733) in the following two scenarios: (A) when drawing 8 cards? (B) ...
Qrious's user avatar
  • 21
2 votes
0 answers
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poker expectation clarification

I ran across a passage in "The Mathematics of Poker" explaining bluffing strategy. Here is a paraphrased version. Two players are playing heads-up ($1$ vs $1$) poker. They're on the final ...
nezam jazayeri's user avatar
0 votes
1 answer
52 views

When calculating probability of a one pair in 5 card poker, why do we use $\binom{12}{3} \cdot \binom{4}{1}^3$ and not $\binom{48}{3}$?

I know that when calculating the probability of getting one pair in 5 card poker, it is done like: $$ P(\text{one pair}) = \frac{\binom{13}{1} \cdot \binom{4}{2} \cdot \binom{12}{3} \cdot \binom{4}{1}^...
altntrance's user avatar
0 votes
0 answers
67 views

Probability of two pair for a poker dice

I understand that the well known way to solve this is Choose the rank for the two pairs from 6 options - $6C2$ Choose the dice for the first pair - $5C2$ Choose the dice for the second pair - $3C2$ ...
rustic.t's user avatar
3 votes
1 answer
360 views

How do I calculate the probability of getting a 5 card straight in 7 card poker?

So here's my progress on this problem. The first straight to examine is $\begin{pmatrix} A & 2 & 3 & 4 & 5 & n & m\end{pmatrix}$. If we start with all one suit, there are $\...
Alfred's user avatar
  • 31
0 votes
1 answer
84 views

How to prevent Nash-EQ solver getting stuck in an infinite loop?

I would like to write a Nash equilibrium solver for a simplified Poker game. I was reading that the way some Nash equilibrium solvers for Poker work is that they iterate until convergence: For a given ...
mercury0114's user avatar
0 votes
1 answer
57 views

What are the odds that 2 players heads-up in poker will both not make a pair or better by the river, assuming they only check?

Here is my current thinking, please let me know if it is correct. The result doesn't seem intuitive and I feel like I'm missing something, hence I am reaching out here. 52 - 4 = 48 cards remaining. (4-...
clef98's user avatar
  • 1
0 votes
2 answers
59 views

Exponentials of stochastic band matrices

Edit: I should probably say the motivation: I was interested in modeling the probability of winning a heads-up poker match if the players will play until one player goes bust. Because the game is zero ...
Davis Yoshida's user avatar
1 vote
1 answer
53 views

Probablity of 5 card holdem hand given 7 cards

The probabilities of getting a straight flush, 4 of a kind, full house, ... , and so on, when dealt 5 cards from a randomly shuffled deck are easily calculated as straight flush .000015, four of a ...
Hober Malloy's user avatar
5 votes
1 answer
163 views

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 ...
kotm16's user avatar
  • 53
1 vote
1 answer
43 views

What are the odds of getting 2 sets in texas holdem?

I'm looking to create a variant of holdem allowing 6 and 7 card hands in special situations. Namely, 3 pair, 2 set, and quads over set (a full mansion). My probability skills are rusty, but I'm still ...
Paul Tudan's user avatar
3 votes
1 answer
266 views

What are the odds of getting 3 pair in texas holdem?

I'm looking to create a variant of holdem allowing 6 and 7 card hands in special situations. Namely, 3 pair, 2 set, and quads over set (a full mansion). My probability skills are rusty, but I'm still ...
Paul Tudan's user avatar
2 votes
0 answers
100 views

Probability of flush given that you observe 4 diamonds out of 5 cards

I came across this probability problem. In a Texas Hold’em game, you are dealt 2 cards in your hands and the 3 flop cards are shown. You observe 4 diamonds out of the 5 cards. What are your chances ...
Emperor Concerto's user avatar
1 vote
1 answer
55 views

Counting problem for finding the probability of two pairs in a five card hand.

I am having trouble understanding what I have wrong in this stats problem for my hw. I am trying to find the probability of getting two pairs in a 5 card hand from a deck of cards. So first we know ...
El_Tuercs's user avatar
2 votes
1 answer
161 views

How to rank a new type of Hold 'Em Poker hand (hard)

I am trying to figure out how to rank a new type of poker hand, henceforth called a 'Block'. A Block consists of 6 cards, and so is not possible in regular Poker - only Hold'em. Each Block consists of ...
Arcra's user avatar
  • 23
1 vote
0 answers
24 views

Probability of a straight ending on specific number in 7-Card Poker

I am trying to calculate the probability of a straight that ends on a specific number, e.g. 6:{2, 3, 4, 5, 6} or Q:{8, 9, 10, J, Q}. Calculate Total number of straights: Assume $x$ in [5,13(K)]. ...
Dylan Finlayson's user avatar
2 votes
1 answer
92 views

Combinations Straight Flush in Texas Hold'em Poker

On the Wikipedia page about Poker probabilities for 7-card poker hands (Link) it says the following for the Royal Flush: \begin{equation*} \binom{4}{1} \binom{47}{2} \end{equation*} First we choose 1 ...
Gecko's user avatar
  • 123
0 votes
1 answer
474 views

Probability of a poker hand of winning

Just by curiosity I was looking for the probabilities of poker hands as a simple array of 5 cards, and what I found in many websites are the frequencies asociated to each combination of shown in a ...
Joako's user avatar
  • 1,586
3 votes
1 answer
195 views

Has the game of texas hold em poker been beaten?

I am no mathematician, I guess this is obvious. I hope this question is appropriate. So, I know that in poker the opponents psychology matter, but imagine that you are playing against a perfectly ...
Nikolai Frolov's user avatar
4 votes
2 answers
139 views

Why does calculating probability of 2 pairs seem so different from for a full house?

For 5 card poker without discards/draws, the probability of being dealt a 2 pair hand is about 0.047539, and for a full house is about 0.001441. 1 I first learned about calculating for a 2 pair hand....
user1902689's user avatar
3 votes
2 answers
1k views

What is the probability of getting a full house in a 7 card poker hand

I'm trying to calculate the probability of getting a full house in a 7 card poker hand. This is obviously the number of 7 card full house hands divided by $\binom{52}7$. To try and calculate the ...
diego caples's user avatar
4 votes
3 answers
397 views

Three-of-a-kind Poker Hand Problem

Problem: Three-of-a-kind poker hand: Three cards have one rank and the remaining two cards have two other ranks. e.g. {2♥, 2♠, 2♣, 5♣, K♦} Calculate the probability of drawing this kind of poker ...
80808learn's user avatar
1 vote
1 answer
204 views

Can Nash Equilibrium strategy be exploited, if another player deviates?

Consider a 3 player game (e.g. poker for 3 people). Nash equilibrium is a set of strategies $s_1, s_2, s_3$, such that the expected profit value for each player $s_i$ $E_i(s_1, ..., s_i', ..., s_N)$ ...
mercury0114's user avatar
0 votes
1 answer
35 views

Deriving the Semi-Bluffing Formula in Poker

I am recently taking this MIT Open course, and trying to derive the Semi-Bluffing formula on my own. The formula can be found on Page 52 of the slide. I am a bit confused about why there is a $2$ in ...
JOHN's user avatar
  • 1,176
1 vote
0 answers
36 views

What $n$-tuple am I applying the multiplication principle to when counting Texas Hold'em pocket cards with a pair?

Textbook problem (quoted): In Texas Hold'em poker a player receives 2 cards first. These are called the player's pocket cards. Find the number of pocket card configurations (that is, the number of ...
Ungar Linski's user avatar
0 votes
1 answer
97 views

What's the number of possible five-card poker hands drawn without replacement?

So we know a standard deck has 52 cards and it's asking the number of possible 5 card hands we could get from it without replacement which means without putting them back in the deck. I thought about ...
Michael Vie's user avatar
0 votes
1 answer
153 views

Conditional Probability in poker, Bayes Theorem

In a four person pokergame you are dealt a "king of heart" and "8 of spades". Three cards lay on the table none being a king or 8, meaning there is 41 cards left. Q: What is the ...
Lola's user avatar
  • 3
0 votes
2 answers
69 views

Can this Sum be reduced? It is calculating the expected value of a poker hand when you "Run it multiple times" for the last card.

There is a scenario in poker (Texas Hold'em) where if two players go "all in", they have the option to deal the remaining cards multiple times and it results in multiple pots that they could ...
JackAce's user avatar
  • 103
2 votes
1 answer
121 views

To show that there are two people in the tournament with the same starting hand and position in a Texas Hold'em poker tournament.

A Texas Hold'em poker tournament has $1557$ players, in $9$ distinct positions at $173$ tables. Each table has a standard $52$ card deck, and each player is dealt $2$ cards. Hands are considered "...
User8976's user avatar
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