Two Plus Two Older Archives  

Go Back   Two Plus Two Older Archives > General Gambling > Probability

Reply
 
Thread Tools Display Modes
  #1  
Old 10-16-2002, 02:49 PM
JTG51 JTG51 is offline
Senior Member
 
Join Date: Sep 2002
Location: CT
Posts: 3,746
Default A 7 Card Stud probability question

I'm just starting to play a little 7CS, and don't really know how to go about figuring this one.

What are the chances that someone with a single pair showing on their board has a full house or better by 7th street?

Thanks.
Reply With Quote
  #2  
Old 10-16-2002, 07:56 PM
Dynasty Dynasty is offline
Senior Member
 
Join Date: Sep 2002
Location: Las Vegas
Posts: 4,044
Default Re: A 7 Card Stud probability question

I don't know how to figure this out. However, I can tell you this: If somebody gives you the answer, it will not help you make better decisions at the table.

Reply With Quote
  #3  
Old 10-16-2002, 11:21 PM
JTG51 JTG51 is offline
Senior Member
 
Join Date: Sep 2002
Location: CT
Posts: 3,746
Default How did I know you\'d say that?

I've heard you say that several times now. Isn't it OK to just ask questions out of curiosity sometimes?

I think that 1% at best of what's said on this particular forum will help any of us at the table. I'm sure that figuring out which light switch controls which bulb won't help me at the table at all. [img]/forums/images/icons/smile.gif[/img]
Reply With Quote
  #4  
Old 10-17-2002, 12:09 AM
Guest
 
Posts: n/a
Default You must forgive Dynasty............

about half of his responses are dubious at best. He has some large ego that seems to be fed by criticizing others but I do believe he is generally harmless.

Reply With Quote
  #5  
Old 10-17-2002, 12:27 AM
JTG51 JTG51 is offline
Senior Member
 
Join Date: Sep 2002
Location: CT
Posts: 3,746
Default I don\'t think so

I think that 99% of Dynasty's posts are helpful. A much higher percentage than most others.
Reply With Quote
  #6  
Old 10-17-2002, 02:27 AM
Dynasty Dynasty is offline
Senior Member
 
Join Date: Sep 2002
Location: Las Vegas
Posts: 4,044
Default Re: How did I know you\'d say that?

Of course, you can ask just for the sake of knowledge. But, it's also important to know that certain information shouldn't be used to make your decisions at the table.

I'd hate to see you fold Jacks-up on the river because your opponent has a pair of 7's on his board and somebody calculated that there is a 23.8% chance that he has a full house.

BTW, if you want an Excel spreadsheet which calculates the probability of making a flush taking into account the exposed 3rd street cards, e-mail me and I'll send it to you.

Reply With Quote
  #7  
Old 10-17-2002, 03:13 AM
Bozeman Bozeman is offline
Senior Member
 
Join Date: Sep 2002
Location: On the road again
Posts: 1,213
Default Re: How did I know you\'d say that?

You'll probably have trouble at the tables if you can't turn the lights on [img]/forums/images/icons/smile.gif[/img]
Reply With Quote
  #8  
Old 10-17-2002, 08:18 AM
irchans irchans is offline
Senior Member
 
Join Date: Sep 2002
Posts: 157
Default Re: A 7 Card Stud probability question

I will take a shot at this one. I will assume that the 3 face down cards are random. In a real game, this assumption is very wrong so the final probability is merely a guide. We will also have to ignore the possibility of straightflushes. Computations like this one often have many cases so they are frequently wrong. Don't believe the result until someone has confirmed it.

Suppose the opponents up cards are p p x1 x2. There are 3 down cards. There are C(52-4, 3) = 17296 possible sets of downcards. If he has a full house or four of a kind, then the downcards would have to be px-, xx-, pp-, ppx, pxx, or xxx. The size of each of these sets is

px- 2*6*40 = 480 ways
xx- 2*3*40 = 240 ways
pp- 1*40 = 40 ways
ppx 1*6 = 6 ways
pxx 2*2*3 = 12 ways
px1x2 2*3*3 = 18 ways
xxx 2 ways.
x1x1x2 3*3 = 9 ways
x1x2x2 3*3 = 9 ways

The resulting probability is (480+240+40+6+12+18+2+9+9)/17296 ~= 4.7 %.

Another way to derive the probability is p1 + p2 - p3 where

p1 is the probability that exactly 2 of the down cards have values of p, x1, or x2,
p2 is the probability that all of the down cards have values of p, x1, or x2, and
p3 is the probability that the opponent has 3 pair.

p1 = 3*(40/48*8/47*7/46)
p2 = 8*7*6/(48*47*46)
p3 = 6* (40/48*3/47*3/46.)

p1+p2-p3 ~= 4.7 %.

Dynasty might point out that in a real poker game, the opponent is more likely to have a pocket pair or paired door card. Also, the betting and cards exposed by the other players add a lot of information.

Hope that helps.
Reply With Quote
  #9  
Old 10-17-2002, 12:24 PM
SittingBull SittingBull is offline
Senior Member
 
Join Date: Sep 2002
Location: Louisiana
Posts: 826
Default Hello,JTG! If he is a conservative player...

and pairs his doorcard on 4th,it's reasonable to assume he has a set.
Hence, the odds of his filling up by 7th Str. is about 2 1/2 to 1 against.
Of course,if the player plays many 3rd str. hands,this assumption is usually incorrect.
If U are locking horns with a typical player,U need to determine whether or not he has paired his doorcard on the latter Strs. If the single pair is not a doorcard match,then he probably has two pairs.
The odds against filling on 5th S [img]/forums/images/icons/laugh.gif[/img] tr. is about 5 to 1 against,assuming two pair on 5th and 10 to 1 against filling by 7th.

Happy pokering, JTG!
Sitting Bull

Reply With Quote
  #10  
Old 10-17-2002, 01:31 PM
JTG51 JTG51 is offline
Senior Member
 
Join Date: Sep 2002
Location: CT
Posts: 3,746
Default Hello Sitting Bull, That\'s good stuff

Those are some good points, all of which would have to be considered in a real game. Thanks.
Reply With Quote
Reply

Thread Tools
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off

Forum Jump


All times are GMT -4. The time now is 06:24 AM.


Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2021, vBulletin Solutions Inc.