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 ...

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Counting the frequency of a flush hand in $7$-card poker

I'm trying to count the frequency of a flush hand in $7$-card poker. Since a flush hand could be thought of as having $5$ cards with the same suit while the other $2$ doesn't matter, I wrote down as ...
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2answers
31 views

How to efficiently calculate probabilities of not getting two pair?

Suppose two guys are playing 2 card draw poker. I am trying to find the probability of neither players drawing a pair. Let $C_1,C_2,C_3,C_4$ denote the cards drawn. We know that any card will do ...
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1answer
94 views

An optimal sequence of length 13

I'm looking for an optimal (or much better than I have now) increasing sequence $t_1, t_2, .., t_{13}: t_i \in N, 0 \le t_i<t_{i+1}$ where $3t_{12} + 4t_{13}$ is minimized, subject to the ...
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0answers
35 views

ways to change a function locally for my poker texas holdem bot

I apologize for the lack of math format and possible ambiguity. If I had more maths knowledge, this could be a two-sentence question, but I don't have that. I want to find a local optimum for my ...
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1answer
38 views

Where am I going wrong on this poker math problem?

Someone gives you two dice. They offer to pay you \$37 if you roll two 6s. However, it will cost you \$1 a roll. What is the EV of this wager? My work: 1/36 = 35:1 = 0.0277 for \$37 = 1.027 ...
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34 views

Expected payout of an optimal hand in Poker

Expected payout of a hand I created a video poker hand evaluator and I am not getting the optimal hand and I know my mistake is because of the way I am calculating the expected payout. Above is a ...
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1answer
26 views

Calculating probability that you are dealt a full house

What is the probability that you are dealt a "full house"? (Three cards of one rank and two cards of another rank.) why can't I calculate the probability in the following way? The number of ways I ...
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1answer
32 views

5 card poker hand double counting cards

This equation calculates the number of ways to get a pair in a 5 card poke hand. How come this equation doesn't need to be divided by two? My rational for dividing by 2 is as follows: The first two ...
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35 views

Ways to get a pair in poker

When drawing a pair the number of ways to get it is: $${13 \choose 1}{4 \choose 2}{12 \choose 3}(4)^3$$ But I don't understand why the following doesn't work: $${13 \choose 1}{4 \choose 2}{12 ...
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1answer
12 views

Probability of dealer having a same-value card as me in Black Jack

In a game of Black Jack, before any additional cards are given out (so everyone has exactly two cards), what are the chances that the dealer has, say, a King, given that one of my cards is a King ? ...
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18 views

Chance of being in a range with observed population tendencies

Actually its a poker related question, but hopefully turning it into a real life example I can get an answer. Let assume we have 2 bag of different colored candies, we have 1326 candies in the two bag ...
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37 views

One jack and one club

How many ways a player can be dealt exactly one jack and exactly one club ? Of course, A player can be dealt 5 cards in a normal poker game So we have 4 different jacks and 13 different club cards. ...
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87 views

Poker hands combination

In a poker game where we have a standard deck ($52$ cards) and each player is dealt $5$ cards, how many hands of each of the following types are possible ? (Type 1, "Low face") one face card ...
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3answers
75 views

5 cards are drawn one at a time without replacement from a deck of 52.

Calculate the probability of landing a straight flush. A royal flush is considered a straight flush. I can't be sure, but I think the answer changes depending on the first card you choose. Like if ...
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0answers
64 views

Probability of an Indisputable winner at Texas Holdem

What are the fraction of hands that can be classified as "indisputable winners" 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 ...
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2answers
89 views

5-Card Poker Two-Pair Probability Calculation

Question: What is the probability that 5 cards dealt from a deck of 52 (without replacement) contain exactly two distinct pairs (meaning no full house)? Solution: ...
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41 views

How many poker hands until statistically significant winner

How many poker hands do I have to play to determine a statistically significant winner? What is the best approach to get a 95% confidence interval? To give some more context: I have been building a ...
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77 views

Video Poker - RTP

This site shows that using a 'simple' strategy or an 'optimal' strategy in Jacks Or Better 'fullpay' pay table(see below) video poker results in $99\%$ return-to-player (RTP). RTP is defined as the ...
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32 views

Poker Combinations Probabilities

I've been asked to write a C# program that computes specific poker probabilities. And I am struggling with how to do it. The game is a Texas hold em. It's a 32 cards deck. You have two cards. You ...
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5answers
56 views

Poker game probability [closed]

From a deck of 52 cards, pick 3 cards randomly, what is the probability that there is a pair among the three cards? (A pair means that two of the cards are the same number) I guess it allows to have ...
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1answer
52 views

How many $3$-of-a-kinds are possible if one ace is missing?

So I know how to do the simpler 'How many $3$-of-a-kinds are possible' question - it has been asked on here multiple times too. But what if say an Ace is missing. How would you go about starting the ...
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2answers
41 views

Explanation for solution of a combinatorial problem

The given problem is: An ordinary deck of cards is dealt to four people: Joe, Bob, Jim, and Larry. If Larry has exactly one ace, what is the probability that Jim has all the remaining aces? My ...
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2answers
104 views

Probability of Poker Hands with Joker

Need help with a homework question: If a five card hand from a standard deck of 52 with an added joker (wildcard) is drawn: What is the probability that a hand contains at least one pair? ...
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1answer
37 views

Simulated probability doesn't match closed-form answer

I am trying to calculate the probability of a hand of 13 cards containing at least five pairs. Three of a kind counts as one pair; four of a kind counts as two pair. I simulated millions of hands and ...
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2answers
583 views

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 ...
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290 views

How many poker hands have exactly two pairs?

I found an interesting solution to the combinatorial question of "How many poker hands have exactly two pairs?" and I cannot figure out (or find) the reasoning of the solution. The answer I found in ...
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1answer
70 views

What's more likely with 7 dice - Straight, Full House, or 3-of-a-Kind

Here's a problem I'm having. I have 7 dice. I want to rank the difficulty of achieving a particular 5 dice combination after all 7 dice have been rolled. A straight is when at least 5 of the seven ...
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1answer
116 views

Expected value of the call option in Caribbean Stud Poker: examples

For the game Caribbean Stud Poker, compute the expected value of the call option for the following cases. I try to solve part (a). There are $\mathsf{A}\mathsf{K}\mathsf{J}$ there. If $\mathsf{Q}$ ...
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46 views

On Casino Holdem game

For the game Casino Holdem, I am told to compute the expected value of the call option for the following hole cards and flop. (8♠,9♣) and (10♣,J♣,2♠) Can anyone help me on this problem. The rule ...
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1answer
34 views

Find the probability that at least one of poker opponents hits a card

In Texas hold'em, when you see the flop there is about 33% chance that one of your 2 cards hits something on the flop, maybe not exactly but let's say it's 33% that your opponent did hit something on ...
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3answers
191 views

Probability of get 3 cards out of 4

How to calculate a probability of choose 3 off-suited and off-ranked cards out of 4 given cards from a standard 52-cards deck (the situation when all the cards off-suited/off-ranked should be avoid). ...
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41 views

How can I find the probability of drawing cards in these cases?

Given 2 players A and B. We will draw 5 cards for A and then 5 cards for B. Find the probability of this event: A receives Two Pair (contains two cards of the same rank, plus two cards of another ...
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1answer
50 views

Poker probabilities 3 of a kind, 2 pair, 1 pair

I'm finding it hard to understand why the answers are what they are. correct # ways to get 3 of a kind: $13C1·4C3·12C2·4C1·4C1$ my thinking: $13C1 * 4C3 * 12C1 * 4C1 * 11C1 * 4C1$ the logic is ...
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1answer
33 views

Probability Poker Question

You are dealt $20$ cards. What is the probability you have all kings given that you hold at least one king? So I set it up like $$ P(4\textrm{ Kings | at least one king}) =\frac{{4 \choose 4}{48 ...
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1answer
77 views

Another way to calculate probability of full house

I am struggling to understand why my calculation is off by a factor of ten. P(AAABB)= $4/52 * 3/51 * 2/50 * 13 * 4/49 * 3/48 * 12$ My thinking is like this: P(full house) = P(3 of same card) * (# of ...
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1answer
79 views

Probability of five card stud flush

I'm not really good dealing with poker problems... I am doing a practice problem for a midterm coming up, and help would be appreciated. Consider the probability that, in a game of five-card stud, ...
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2answers
72 views

What is the logic behind the probability of getting 'four of a kind' in poker?

This hand ($5$ cards of $52$) has the pattern $AAAAB$ where $A$ and $B$ are from distinct kinds. The number of such hands is $\binom{13}{1} \binom{4}{4} \binom{12}{1} \binom{4}{1}$. The probability ...
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63 views

Odds of two specific Hold'Em hands and an exact board?

The goal is to solve the probability of a Texas Holdem hand occurring where at the river one player has quad $9$s and the other player has exactly a $9$-high straight flush. (For non poker players ...
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2answers
80 views

Poker odds: Chances of a straight flush, given H4,H5

I'm trying to learn Bayes's formula, and am coming up with some poker problems to learn this. My problem is as following: given a $H4,H5$ ($4$ of hearts, $5$ of hearts) hand, what are the odds that ...
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0answers
131 views

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 ...
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1answer
371 views

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 ...
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2answers
53 views

Conditional Probability in Poker

I'm thinking of a ten person Texas hold'em game. Each person is dealt 2 cards at the start of the game. The question is: GIVEN that you have been dealt 2 hearts (Event B), what is the probability ...
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1answer
48 views

Applying Bayes Rule to Cards

I was playing poker with a friend last night when a question occured to us. I had a two Jacks and the flop came out: King Queen and 4. So, suddenly my pocket Jacks are not so great, unless another ...
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0answers
48 views

What are the best $3$ pocket cards in Omaha poker?

In Texas Hold'em poker, the best $3$ pocket cards are AA, KK and QQ respectively. I've been trying to find the best $3$ pocket cards in Omaha poker, where you have to use exactly $2$ pocket cards out ...
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3answers
186 views

What's the probability of a straight in $5$ card poker given $5$ and $7$ of hearts?

Using a standard $52$ card deck, if you are given the $5$ and $7$ of hearts from it, what is the probability that you end up with a straight if $3$ additional cards from that same deck are given to ...
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4answers
134 views

In Texas Hold'em poker, is the ranking according to chance of beating 1 opponent's hand the same as according to beating multiple opponents?

In Texas Hold'em poker, you can rank hands according to the probability of beating one randomly generated opponent's hand. However, no one can compute the exact probabilities of beating $8$ random ...
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103 views

Poker Hand Probabilities in Doomtown Reloaded

The short version of my question is as follows: What is the best way to compute the probability of different hand ranks after redraw in poker? Can this easily generalise to a non-standard deck? ...
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1answer
159 views

Counting number of two pair hands in poker (not standard)

I was doing number counting problem and wanted to check if my result was correct. Problem description: From a standard deck of cards(52 cards, 4 suits, 13 numbers in each suit) there are 5 cards ...
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3answers
147 views

Poker game full house

I'm dealing with an exercise which deals with the poker game. I need to calculate the probability of getting a full house. Full house is getting 3 cards of the same type and 2 cards of the same ...
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1answer
67 views

poker probability texas holdem

I get a few percent off from simulation results when I verify these probability calculations, so I am hoping someone spots it. When there is a suited pair on the flop in texas holdem and nine seats ...