Poker Hand Question

Sure! There's a game in every hand and a slam in every third hand.

--anonymous optimist

I don't know enough about poker to know the meaning of pat.

In chess pat means a draw by default.

So I suppose it would mean 2 matching face cards and 3 matching number cards.

2 jacks and 3 5's maybe have the same value as 2 Queens and 3 4's.

or maybe a pat is a series of 8,9,10,J,Q *4 vs 4 K's

Sure!

The answer was "sure", 'cause you can make 5 pat hands out of all 52 playing cards, can you not?

Now, the way you phrased the question, "Is it possible to make five pat poker hands from any randomly deal [sic] twenty-five cards from a deck of playing cards?" is the key to success if the twenty-five cards happen to be randomly dealt so that it can be done.

Why not make the problem harder by asking what the probability is to make five pat poker hands from any twenty-five, randomly dealt cards?

That is, in fact, what was asked. Paraphrased, would the probability be zero that any sample of 25 cards would contain five poker hands, each with no throwaway cards...no kickers. Said another way: of all possible samples of twenty-five cards, would the probability that at least one will contain five pat hands with no kickers be greater than zero?

Actually, the question came from an old TV series Maveric - J. Garner was a poker player and he made the statement that any random 25 cards could make 5 Pat hands - i.e. 4 of a kind, full house, flush or straight.

At last the punch line.

That old trickster—ol' Bret never let on how many trips up and down the river before he drew that foursome at a table with eight players (and with all that bosomry pushing out over his shoulder ); he musta started even before Pappy's sayings started making sense. And, as impressive as it was to the lady folk, he failed to mention that the 25 cards would be dealt to one slick player...

But joking aside, it does appear, reasoning heuristically, that we've been given the the "true" odds against five independent pat hands being dealt, without replacement: 1-to-nothing. Would Maverick lie with his hat off?

Very good, my 80 plus year old uncle plays this as one of his solitaire games and makes 5-PAT hands most of the time. However, when I visited him last month, he presented a hand which he had not been able to solve so I told him - no problem - I would figure it out on the plane ride home. So, after studing the cards for awhile, I thought one of my Technical Friends on CR4 could easily solve it with a simple program. Of course, I would take the credit in sending him the solution. The twenty five cards are: Spades: K-8-6-4-2; Hearts: 9-8-3-A; Diamonds: Q-J-8-7-5-4-3-A; Clubs: K-J-9-7-5-4-3-2.

Now, you know the rest of the story.

Anybody other than me play five card stud? They're all potentially pat hands (unless you fold).

As a poker player you really should know better. Of course you could stand on any hand you are dealt...maybe the definition we should consider for pat should be "a hand that a reasonable player, not intent on bluffing, would determine less than even odds of improving with a draw."

I'm guessing the odds of four flushes would be pretty good.

Pardner,

If you ever get caught trying to improve your hand in a game of five card stud, well...the missus is gonna take your life insurance money and run off to Aruba with the pool boy.

A pat hand always anticipates the final showdown, stud or not. The fold idea is basically a logical red herring.

Most unlikely but in a game of chance anything is possible.

As previously said anything is possible...............never been one to work out probabilities but, at a guess................about as much chance as winning a lottery..........maybe the odds are a bit shorter................my chances..............If I bought 99 tickets in a 100 ticket lottery, I would not win..............probably wouldn't win a second prize either!!!!!

Permit me to help with your syntax, please.

Is it possible to make five pat poker hands from any randomly deal twenty five cards [drawn randomly] from a deck of playing cards?

or

Is it possible to draw twenty-five cards containing five pat hands when drawing from a standard deck?

i don't know because I am also very in the poker.

Guys, what do you think - why is poker the most popular with a lot of gambling?

In life, Grasshopper, anything is possible.

Here is a discussion from 2007 that sheds some light:

https://forumserver.twoplustwo.com/25/probability/five-pat-hands-25-cards-sucker-bet-5521/

It suggests that this is possible ~98% of the time. Not a sure bet, but a really good one.