Texas Hold'Em: Probability of better hand after two additional cards dealt

soccergirl13

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A hand of Texas Hold’em (a type of poker game) is down to two players, as three players have folded (quit the hand). Here is what has happened so far (two cards remain to be dealt).

Player One’s cards: J of hearts, Q of spades
Player Two’s cards: 9 of hearts, 9 of spades
Community cards: A of hearts, A of spades, 10 of clubs
Folded cards (cards that are no longer in play – the players don’t know that these are out of play, but that doesn’t matter for what I am asking): 3H, 5D, 2S, JD, 4C, 4D


For those of you who are familiar with poker, ignore all of the stuff about gambling. This is completely about the cards. There are two community cards left to be dealt. After they are dealt, each player will make their best five-card hand from the five cards in the community and their own two cards.

If you need information about the rankings of different hands, you can go here: https://www.cardplayer.com/rules-of-poker/hand-rankings

a. Find the probabilities of each player having the better hand when the two remaining cards have been dealt.

b. The next card is dealt. It is the 10 of diamonds. Find the probabilities of each player having the better hand when the remaining card has been dealt. (Note: This question is easier/shorter than the question in part a, so you are probably better off doing this first. In both cases, you have to show your work.)
 
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A hand of Texas Hold’em (a type of poker game) is down to two players, as three players have
folded (quit the hand). Here is what has happened so far (two cards remain to be dealt).


Player One’s cards: J of hearts, Q of spades
Player Two’s cards: 9 of hearts, 9 of spades
Community cards: A of hearts, A of spades, 10 of clubs
Folded cards (cards that are no longer in play – the players don’t know that these are out of
play, but that doesn’t matter for what I am asking): 3H, 5D, 2S, JD, 4C, 4D


For those of you who are familiar with poker, ignore all of the stuff about gambling. This is
completely about the cards. There are two community cards left to be dealt. After they are
dealt, each player will make their best five-card hand from the five cards in the community and
their own two cards. If you need information about the rankings of different hands, you can go
here: https://www.cardplayer.com/rules-of-poker/hand-rankings

a. Find the probabilities of each player having the better hand when the two remaining cards
have been dealt.


b. The next card is dealt. It is the 10 of diamonds. Find the probabilities of each player having
the better hand when the remaining card has been dealt. (note: this question is
easier/shorter than the question in part a, so you are probably better off doing this first. In
both cases, you have to show your work.
What are your thoughts regarding the assignment?

Please share your work with us ...even if you know it is wrong.

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/for
 
This was a question our professor assigned us for extra credit. So since you posted it online and our instructor found it, now my work (that I actually did) won’t count.

This stinks.

I’m assuming you’re an education major and if so, you are the reason our children hate math. Go get a job doing something else, and save teaching children to someone who actually likes the topics. Again, you majorly stink, and you will be a horrible teacher.
 
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This was a question our professor assigned us for extra credit. So since you posted it online and our instructor found it, now my work (that I actually did) won’t count.

This stinks.

I’m assuming you’re an education major and if so, you are the reason our children hate math. Go get a job doing something else, and save teaching children to someone who actually likes the topics. Again, you majorly stink, and you will be a horrible teacher.
Many, many years ago I took a course in abstract algebra, which, for some unknown reason, was required for education majors who wanted to teach math. As the year went on, I realized more and more that public education was a scam designed to give the incompetent a snout in the public trough.
 
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