Math Help: 7 card flush
(1) What is the probability of getting a 7-card flush when dealt 7 cards, with 52 standard cards? What if we use 52 cards plus one joker to play, but joker can not be used to make a 7-card flush? I think, the total 7-card flush hands should be the same for these two cases, but the probabilities would be different, right?
(2) What is the probability of getting a 7-card flush when dealt 7 cards, playing with 53 cards (52 plus a joker) and that joker can be used to make a 7-card flush?
Best advice: use the resources of the Internet or a TI-30.
Here's a poker math site that would bring you mostly all the way there, and is useful.
Durango Bill's poker pages
Quote: UCivanI wonder if someone could help with the math here?
(1) What is the probability of getting a 7-card flush when dealt 7 cards, with 52 standard cards? What if we use 52 cards plus one joker to play, but joker can not be used to make a 7-card flush? I think, the total 7-card flush hands should be the same for these two cases, but the probabilities would be different, right?
(2) What is the probability of getting a 7-card flush when dealt 7 cards, playing with 53 cards (52 plus a joker) and that joker can be used to make a 7-card flush?
In the following, I am counting straight flushes in with other flushes.
For a 7-card flush with 7 cards from a 52 card deck, the probability would be 4*combin(13,7)/combin(52,7), or about 1 in 19,491. Using 53 cards and not allowing the joker to help make a flush, the probability would be 4*combin(13,7)/combin(53,7), or about 1 in 22,457. And if the joker may help make a flush, the probabilty would be 4*(combin(13,7)+1*combin(13,6))/combin(53,7), or about 1 in 11,228.
Quote: RoyalBJYeah, paraphrase Paigowdan, "I don't really know. But, why don't you go to the library yourself, or get a college degree, or pay someone to do it for you".
Actually, I do indeed know the math, as part of my game development work in Pai Gow Poker. I was also a high school math teacher in Clark County, and know that most students would rather be given the answers instead of doing the math.
I have all the tables, the simulation runs, the statistics - all the work and the poop on poker probabilities.
But I don't share it outside of DEQ and Lubin-Jones, LLC. Why should I? I do it myself, and if I need extra help on a simulation, I pay Charles, and am happy to do so. There are enough people at this board who will do it on such a request. Opinions, yes; math requests: use Excel or a TI-30 and give it a go yourself. Someone will post it back, fine.
Why would Mike or Charles or Stacy or Cindy or Eliot or any game designer or mathematician work for free? We have a lot invested in out IP, we really do.
If you took algebra and statistics as part of your education, then why not take out a TI-30 or fire up Excel and give it a go?
I was being generous with the link.
Quote: Paigowdan
Why would Mike or Charles or Stacy or Cindy or Eliot or any game designer or mathematician work for free? We have a lot invested in out IP, we really do.
Maybe, they just like helping people?
I sure hope, they don't really consider answering a trivial high-school level math question "work", or a straightforward combinatorial formula an "IP".
Thanks, ChesterDog, You're definitely more ethical and more generous than some other member.Quote: ChesterDog
For a 7-card flush with 7 cards from a 52 card deck, the probability would be 4*combin(13,7)/combin(52,7), or about 1 in 19,491. Using 53 cards and not allowing the joker to help make a flush, the probability would be 4*combin(13,7)/combin(53,7), or about 1 in 22,457. And if the joker may help make a flush, the probabilty would be 4*(combin(13,7)+1*combin(13,6))/combin(53,7), or about 1 in 11,228.
Quote: weaselmanMaybe, they just like helping people?
I sure hope, they don't really consider answering a trivial high-school level math question "work", or a straightforward combinatorial formula an "IP".
I agree with that fine spirit, totally - but:
1. A there is a lot of "free math" requests that are better handled by googling gaming math sites for this kind of quotidien grunt work, and
2. There is a lot of requests that people can actually do themselves with the High School diploma or GED or Univeristy degree. If you're online, you probably have access to Excel or a TI calculator, and a little self-sufficiency should be encouraged.
Use The Link....
I think I side with inventors here. That was a unique request, much like asking "What are the chances of having a 5-card Poker hand with a 3-card Flush?"
Landmines everywhere for the inventors.
JMH2c
98Clubs
