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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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Calculate the probability of poker winning hand type (combination)

There are a lot of libraries that calculate the winning probability of texas holdem poker player and the probability of each player having some combinations(pair, straight...). Does anyone know where ...
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probability for full house and other combinations in bet on poker game

We are trying to calculate probabilities(and odds) for "bet on poker" game on which we are working now. To calculate probabilities and odds for each hand we used https://github.com/cookpete/poker-odds ...
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poker probability question not sure

i am confused with what does the question mean drawing two cards showing same number from one suite? i figured it would be: 13C2 * 4C1 * 4C1 * 31C4 / 53C5?
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What is the probability of drawing two identical poker hands in a row from 1 52-card deck?

Same ranks, not same suit. Without replacement, 5 card hands, standard 52 card deck (no jokers). Example: draw A23QK draw A23QK (different suits)
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Combinatorics of a straight hand (poker)

Quoting the book I'm reading: A poker hand consists of 5 cards. If the cards have distinct consecutive values and are not all of the same suits, we say that the hand is a straight. For instance, ...
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46 views

Calculating combinations of a straight in Texas Hold 'Em

Similarly to a previous question that I've asked, I have now attempted to calculate the amount of all possible seven card combinations that would result in a straight (and nothing better). The ...
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1answer
31 views

Calculating combinations of three of a kind in Texas Hold 'Em

The question sounds quite simple - in a game of Texas Hold'Em (or simply out of ${52 \choose 7}$), how many combinations of cards are there, that would result in three of a kind being the highest hand?...
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45 views

What is the probability of 3 heart and 2 distinct pairs in a hand of five cards?

Given that the hand is drawn from a standard deck of 52 cards, what is the probability that it contains three hearts and two distinct pairs? I know that there are ${52 \choose 5}$ distinct hands of ...
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1answer
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Please vet analysis for wrong way of computing choices for three-of-a-kind.

It is given on page #21 of U.G. book : Combinatorics - A guided Tour, by David Mazur, here an example detailing chances of getting three-of-a-kind in 5 card hands. The problem statement is : From a ...
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1answer
58 views

Poker Probability Problem

I can't even begin to grasp how to approach such a statistics problem. Given 9 different cards: two cards for 2 players, and 5 community cards. Find n, where n is the number of same suited cards out ...
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In a shuffled deck, are the probabilities of finding one pair of cards and a second pair of cards independent events?

This question caused a massive fight in a number theory class I was in a few years ago. Class was split, and no one changed their opinion. Curious if it is obvious to outsiders, or if anyone can offer ...
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271 views

Optimal Double Up for Poker Game Reward in DanMachi Memoria Freese

I am trying to figure out the optimal times to double up my poker game reward in the casino in Danmachi Memoria Freese. Here is the details to figure it out. This poker version uses joker as wild ...
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1answer
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5 card poker hand contains 3 aces, conditional probability question

Really struggling with this question and could use some guidance. If a poker hand (five cards) is known to contain at least three aces, what is the probability that it contains all four aces? I ...
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Poker combinatorics - chance to make two pairs by the river

I'm sorry. I'm really bad with combinatorics, so I'm asking you. Lets say I'm holding $2$ cards $5\spadesuit 6\spadesuit$ preflop. My opponent holds $A\clubsuit5\clubsuit$. That makes it only two $5$...
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1answer
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Poker combinatorics: chances opponent has a full house given that you have 2 pairs

I've read the answers to some very similar problems to this, but I can't manage to apply the knowledge to this specific one, sorry for this redundance. Here's the question: What is the probability ...
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3answers
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Probability of drawing a card from suit giving n cards already drawn and some of them unknown [closed]

Say you have 15 cards already drawn, of which you know five and four of these five are of the same suit, what is the probability of drawing a card of the same suit as of the four from the remaining ...
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Combinatorics: the amount of poker hands with a certain amount of unique cards

The particular problem is: how many poker hands (out of ${52 \choose 5}$) result in one pair and three unique cards? My reasoning goes like this: ${13 \choose 1}$${4 \choose 2}$ gives the amount of ...
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133 views

How many poker hands have two pairs?

I'm trying to calculate how many poker hands called Two Pair, there are. Such a hand consists of one pair of one rank, another pair of another rank and one card of a third rank. A poker hand consists ...
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2answers
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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 ...
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2answers
51 views

5 card draw - discard 2 or 3

In 5 card draw you can discard up to 4. Say you have a pair of kings and an ace. I would like the math behind keep the ace or draw 3. If you draw 3 you have a better chance of trips. But two ...
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3answers
115 views

Probability of 4 of a kind in 7 cards, if first dealt 2 different cards?

Question: In Texas Hold 'Em, you choose your hand from among seven cards: two that are dealt to you, plus five more that are available to all players. Suppose the two cards dealt to you are of ...
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Reference request: Bohr's non-card bluffing game

Can anyone provide a reference where Niels Bohr's proposed game is described? From George Gamow, One Two Three... Infinity (Bantam, New York), p. 212: Although this bluffing [at poker] actually is ...
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82 views

What good algorithms are there for shuffling (scrambling) 1 to n objects?

I have seen many algorithms for generating random numbers, so I wondered what common algorithms exist for scrambling a set of given numbers (or objects). The numbers or objects need not be in any ...
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1answer
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7 cards in sequence (suit does not matter)

Problem: Pick 7 cards from the regular 52 English cards deck, were they must be in order and suits don't matter (aces can loop). As stated here for this similar problem, I suppose the answer would be ...
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1answer
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What's the expected value and variance on repeated poker games, given expected value of a hand?

On the website Wizard of Odds I entered the pay table for a video poker game and it gave me the expected return and variance, which were 1.07 and 13.8 respectively. As it's been a while since I took ...
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230 views

Poker Probabilities of a random variable $J$ which gives the number of hearts in the hand [closed]

A poker hand made of five cards chosen from a standard deck of cards Suppose a random variable $J$ gives the number of hearts in the hand. Find the following: a. $\Pr(J=0)$ b. $\Pr(J=1)$ c. $\Pr(J=2)$...
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Probability of Poker Hands in a 54 card deck? [closed]

Just wondering this out of curiosity as I plan on playing poker with buddies by including the jokers to form a 54 card deck. Assume that the Jokers are each unique cards. What is the probability of ...
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1answer
46 views

Probability of monochromatic poker hands

I play poker occasionally and have been thinking about the probability to make an all-red (diamond, heart) or all-black (club, spade) hand – a monochromatic hand. What I have come up with seems like ...
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1answer
172 views

Probability of hitting trips [Texas hold'em]

Let's say we have [K][9] in hand, what is the probability we hit at least (or better) trips on the flop, turn and river? Trips meaning that [9][9] will come on the board. We have 3 outs left [9][9][9]...
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1answer
51 views

Probability at least one card is hit [Texas hold'em]

The cards in hand = [9][9]. The question is as follows: What is the probability we hit at least one 9 on the flop, turn or river (so, on the next 5 cards)? There are (50, 5) = 2.118,760 board ...
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1answer
75 views

What is the probability of 4 players all getting a straight in a game of 5 card poker

Was playing a silly game of Texas Holdem when every player that was still in got a straight: One player was out, the others all got straight And I was wondering what would be the chance of this ...
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2answers
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How to count the number of 5 card hands possible from a double deck?

I'm an undergraduate taking my first-ever upper division math class. It's Combinatorics, which is pretty There are $\binom{52}{5}$ different hands possible in a single poker deck. In a double deck, ...
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Combinatorics question: Suppose you play a game of cards in which only 5 cards are dealt from a standard 52 deck… [closed]

Suppose you play a game of cards in which only 5 cards are dealt from a standard 52 deck. How many ways are there to obtain at least 3 cards of the same suit?
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Probability of full house with x cards

I am trying to calculate the probability of getting a full house but instead of drawing only $5$ cards, I am drawing $x$ number of cards from the $52$ card deck. I know for a $5$ card hand, I would ...
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1answer
70 views

Poker hand - difference from any full house vs a specific full house

I'm having trouble understanding the solution for the first part of the question below: Problem: In a poker hand consisting of 5 cards, find the probability P(A) of holding 2 aces and 3 jacks. My ...
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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. ...
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4answers
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How many possibilities are there for two full houses to be dealt to two players in one game?

Imagine dealing cards from a classic 52 card deck to two poker players. How many possibilities are there for both of them to be dealt a full house(three cards in same rank and two cards of another ...
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Game theory problem: Three man poker game

Mine question is from Three-Man Poker Game discussed in Nash's paper. This is a greatly simplified version of poker. The cards are of only two kinds, high and low. The three players A, B, and C ante ...
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Dice Poker Solver

Hi everyone I'm trying to program a solver for a game similar to poker dice in Python. The only difference lays in the fact that you are given 5 numbers at the start and choose to change two, the ...
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2answers
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Choose 13 cards from a standard deck of cards. How many 4-of-a-kinds are there?

I believe the answer is 13 * $13\choose4$ * $48\choose9$. There are $13\choose4$ to draw 4 of the same cards, and multiply by 13 for each possible rank (A, 2, 3, ..., K). Then there are $48\choose9$ ...
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Number of flushes in a deck of cards

I am having trouble finding the number of flushes in a deck of 52 cards. My logic is that you have 52 choices for the first card, 12 choices for the second, 11 for the third, etc. The number of ...
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1answer
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combinatorics - poker

I have an assignment in school about combinatorics. Information given: three ppl are playing poker. There are three open cards on the table and two cards in each persons hand. On the table we'll ...
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3answers
314 views

Poker probability question 5

Help would be much appreciated! In a poker game five cards are dealt at random from an ordinary deck of 52 playing cards. Find the probability of: “Two pairs”, where the number of face value of the ...
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3answers
255 views

Number of 5 high lowball hands in a 7 card hand

I am looking at a probability breakdown of lowball hands (lowest $5$ distinct cards, $12345$ being the best) here: http://www.durangobill.com/LowballPoker/Lowball_Poker_7_cards.html The website lists ...
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1answer
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Poker Rank Probabilities in three cards poker game — single deck vs. multiple decks.

Poker is a game that plays with a single deck of cards. However, for the purpose of learning, I want to know the probability of poker hands in multiple decks. To simplify the problem, let's take a ...
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Solve Nash equilibrium for poker

Heads up poker two bots with fixed betting. They can only bet 10, call 10, or fold pre flop. Alternate who is first (in position) each hand. In position has a 2 chip blind and out of position has a 1 ...
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number of ways to obtain a pair

Here is my attempt to find number of hands in a 5 cards poker game that gives one pair: $ \binom{4}{2}\binom{48}{3} \cdot 13$ - 2pairs - full house =1349088-123552-3744=1221792 But it is wrong. What ...
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2answers
72 views

Probability of beating an unknown hand

After watching poker online for a while now, I noticed that there were percentages of each player winning the hand - assuming the hand fully plays out - however they only display the percentages when ...
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267 views

Probabilities of Hands in a Poker-like game with a 48 card deck with 6 suits of 8 cards each

I'm working on designing a new card game. Instead of the traditional 52 cards of four suits consisting of 13 cards each, this deck will have 48 cards with six suits and 8 cards per suit. I'm ...
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Risk of Ruin for normally-distributed games

Classic ruin theory assumes that the income is constant and that only the losses are random with an underlying distribution. Suppose we want to determine the risk of ruin for a game (for example ...