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 ...
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 ...
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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....
1 vote
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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. ...
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 ...
1 vote
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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 ...
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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 ...
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1 vote
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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 ...
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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 ...
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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,...
1 vote
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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 ...
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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-...
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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 ...
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1 vote
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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 ...
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 ...
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1 vote
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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 ...
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 ...
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 ...
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1 vote
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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 ...
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 ...
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1 vote
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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)]. ...
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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 ...
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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 ...
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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 ...
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....
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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 ...
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 ...
1 vote
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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 $s_i$ $E_i(s_1, ..., s_i', ..., s_N)$ ...
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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 ...
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1 vote
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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 ...
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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 ...
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 ...
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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 ...
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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 "...