# Tagged Questions

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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### Median poker hand (Texas Hold’em)

I try to find the median poker hand (Texas Hold’em). The following is given: 1) There are 52 cards 2) Assuming seven of them are chosen randomly 3) Create the best possibility with 5 of these 7 ...
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### 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 $52$ ...
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### Why is a Pair of Tens better than a Pair of Aces in Texas Hold 'Em?

A couple years ago I developed a program to calculate the optimum betting amount for a round of Texas Hold 'em by using the Kelly criterion. In the process of computing the probability of winning for ...
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### Poker Pot Odds EV Problem

My issue is with how EV is calculated. I think it's wrong in the approach how it treats the Pot. What's put in the Pot belongs to the Pot. Sure! But that's kinda stupid because the Pot will partially ...
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### 5 cards in sequence, don't understand answer

Find the probability that a 5 card poker hand will be 5 cards in sequence regardless of suit, consider ace high, not low. given answer: \begin{align} \frac{{9 \choose 1} {4 \choose 1} ^ 5}{52 \...
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### Interpretation of Pot Odds (mainly in poker)

In the middle is 10 dollars, someone bets 5. I have to call 5 dollars in order to win 10 dollars. My Pot Odds - 5:10 = 1:2 I can interpret it as that i can lose 2 games and win 1 and I ll be break-...
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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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 ...