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  Poker - Probabilty calculation of having 3 of a kind by river holding poker pairs?
 
  #1  
09-11-2008, 8:04 PM
TTarkan
Junior Member
 
Plays at: Pokerstars
Posts: 31
Probabilty calculation of having 3 of a kind by river holding poker pairs?

Hi Everyone,
I need some help about calculating the probability of basic things in poker.
I have Poker Propheiser which is a free program to calculate certain probabilities with given hands and I also have and old version of Texas Calculatem which also works the same way.
In this program I gave pocket pairs (like QQ) and no flop. They calculate the probability of having a three of a kind by river as 11.75%. But when I want to calculate it by hand I find much higher value like %20.
My calculation is [2*C(4,49)]/C(5,50). Without multipling by two, 10% is also not the correct answer. Why do I do mistake? Why my approach is wrong? Can someone explain me how to calculate it the correct way?
Thanks in advance
 

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  #2  
10-11-2008, 9:52 PM
Jack Daniels
Gizmo (L) & Jack (R)
 
Location: Soldier Field
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Posts: 11,159
Quote:
Originally Posted by TTarkan View Post
In this program I gave pocket pairs (like QQ) and no flop. They calculate the probability of having a three of a kind by river as 11.75%. But when I want to calculate it by hand I find much higher value like %20.
Both are right because they are giving you answers to two different questions. The programs saying 11.75% is not a set by the river, it is the probability of flopping a set (8.5 to 1). The odds of having a set by the river when you start with a pocket pair is about 4 to 1. Actually it's just under 20% but that's close enough.

Do the math and see:
Flop Set = 1 - (48/50)*(47/49)*(46/48) = 11.76%
Set by river = 1 - (48/50)*(47/49)*(46/48)*(45/47)*(44*46) = 19.22%

Last edited by Jack Daniels : 10-11-2008 at 9:57 PM.
  #3  
16-11-2008, 4:20 PM
DrumDemon
Amateur Member
 
Location: Ny
Plays at: PokerStars
Likes: Holdem
Posts: 72
I don't know the math but I just read this in Harrinton volume one. Suppose you have a pocket pair that misses the flop. With two more cards to come, your odds of hitting the set are 8.4%.
  #4  
16-11-2008, 4:54 PM
Jack Daniels
Gizmo (L) & Jack (R)
 
Location: Soldier Field
Plays at: home.
Likes: Da Bears
Posts: 11,159
Quote:
Originally Posted by DrumDemon View Post
I don't know the math but I just read this in Harrinton volume one. Suppose you have a pocket pair that misses the flop. With two more cards to come, your odds of hitting the set are 8.4%.
True. I didn't illustrate it above, but it works the same just that we're now saying what if we did see a flop, missed, and want a set by the river.

1 - (45/47)*(44*46) = 8.4%
 



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